<figure><img src="image_69.png" /></figure>

**Fig. 60** Left: asymmetry $A_s$ of the photon energy spectrum, in $e^+e^- \to \nu_e\bar{\nu}_e\gamma$ events, at the WW threshold and without detector effects, after subtracting the SM asymmetry predicted for $g_Z^{\nu e} = 1$, as a function of the coupling. The yellow band represents the statistical uncertainty expected with an integrated luminosity of 10 ab$^{-1}$. Illustrative measurement points along the prediction, with error bars that span the

uncertainty band, are also shown. Right: statistical uncertainty on the coupling $g_Z^{\nu e}$ expected at the WW threshold, for two example values of the stochastic term of the electromagnetic energy resolution (with a constant term of 0.2% added in quadrature). The uncertainty that would be obtained with a perfect detector is also shown

### 4.6.1 Energy resolution and monophoton final states

For final states that consist of a single photon and nothing else in the detector, the main handle to suppress the backgrounds is the electromagnetic energy resolution. Two physics cases have been considered for such final states: the determination of the $Z\nu_e\bar{\nu}_e$ coupling and the search for long-lived axion-like particles.

#### Measurement of the Z coupling to the $\nu_e$

As described in Ref. [647], the $e^+e^- \to \nu_e\bar{\nu}_e\gamma$ process at FCC-ee can be used to improve the precision measurement of the poorly known coupling of the Z to the $\nu_e$, currently known as $g_Z^{\nu e} = 1.06 \pm 0.18$ [35]. This is possible because of the presence of the t-channel W exchange in the $e^+e^- \to \nu_e\bar{\nu}_e\gamma$ process, interfering with $e^+e^- \to Z(\nu_e\bar{\nu}_e)\gamma$. This interference slightly deforms the distribution of the missing mass $M_{\nu\bar{\nu}}$ (or, equivalently, of the photon energy) in the vicinity of the resonant peak, $M_{\nu\bar{\nu}} = M_Z$, increasing (decreasing) the cross section above (below) the mass peak.

The measurement is based on the asymmetry $A_s$ of the photon energy spectrum obtained from the KKMC matrix element MC generator [605,648]. The asymmetry is defined as $A_s = (N_+ - N_-)/(N_+ + N_-)$, where $N_+(−)$ is the number of entries with a photon energy above (below) the peak energy (approximately equal to $\sqrt{s}/2 \times (1 - M_Z^2/s)$, i.e. 54 GeV at $\sqrt{s} = 161$ GeV).

At the WW threshold, with an integrated luminosity of 10 ab$^{-1}$ and without considering any detector effects, this asymmetry would be measured with a statistical uncertainty of $2 \times 10^{-4}$, which translates into a 1% statistical uncertainty on $g_Z^{\nu e}$, as shown on the left panel of Fig. 60.

To evaluate the impact of a more realistic detector, the study was redone including the resolution from a homogeneous calorimeter with an energy resolution of $\sigma(E_\gamma)/E_\gamma = 0.05/\sqrt{E_\gamma} \oplus 0.002$, resulting in a 50% degradation of the sensitivity to 1.4%, which remains an excellent performance. Should the stochastic term be two times larger (i.e., $0.1/\sqrt{E}$, a value typical for a sampling calorimeter) the sensitivity would degrade to 2.4%. The right panel of Fig. 60 summarises the expected uncertainties. This study brings a clear constraint on the need for a very good calorimeter energy resolution and knowledge of photon energy calibration, to keep the uncertainty due to the calorimeter resolution at the per-cent level, as expected with a perfect detector.

#### Search for long-lived ALPs that decay outside the detector

Very long-lived axion-like particles (ALPs) could be copiously produced at Tera-Z in Z decays ($e^+e^- \to Z/\gamma^* \to a+\gamma$). When the ALP $a$ decays outside the detector, the final state consists in a (monochromatic) single photon, with nothing else in the detector. The relevant mass range for such long-lived ALPs being below $\mathcal{O}(1)$ GeV, the photon energy is about 45 GeV. The sensitivity of FCC-ee to such particles has been studied in Ref. [169]. Simple kinematic cuts allow the reducible background
<figure><img src="image_70.png" /><figcaption>**Fig. 61** Expected sensitivity, at the 2σ level, of an FCC-ee experiment with a relative EM energy resolution of 3%/$\sqrt{E}$ (blue curve) or 14%/$\sqrt{E}$ (orange curve), in the parameter space spanned by the mass of the ALP **a** and its coupling to two photons, from a search for a long-lived axion in the monophoton final state ($e^{+}e^{-} \to Z/\gamma^{*} \to \mathbf{a} + \gamma$) [169]</figcaption></figure>

(dominated by the associated production of a photon with two fermions that escape detection) to be fully eliminated. Since the irreducible background due to $e^{+}e^{-} \to \nu\bar{\nu}\gamma$ production rises very steeply when the photon energy decreases, the ECAL energy resolution is a key driver of the experimental sensitivity. Figure 61 shows the 2σ sensitivities expected for a crystal-based ECAL and for a dual-readout calorimeter, the former allowing significantly lower values of the ALP coupling to be probed. As was shown in Fig. 30, this analysis would uniquely cover the range between $\lesssim 0.1$ and $\sim 1$ GeV, which is beyond the reach of beam dump experiments.

### 4.6.2 Energy resolution and decays of heavy flavoured hadrons into photons or $\pi^0$

The FCC-ee flavour programme at the Z pole significantly expands beyond that of Belle II and LHCb, as described in Ref. [194]. In particular, for all decay modes common to the $B_s$ and the $B_d$ mesons, and that involve neutral particles, the $B_d$ decays constitute an irreducible background to the $B_s$ signal. In that case, the mass resolution, driven by the electromagnetic calorimeter resolution, is the only handle to separate them. Two examples have been looked into: the radiative decay of $B_{(s)}$ into $K^*\gamma$ and the $B_s \to D_s K$ decay where the $D_s$ decays into $\phi\rho$.

#### The radiative decay of the $B_{(s)}$ meson to $K^*\gamma$

Radiative decays, such as $B_d \to K^*\gamma$ ($b \to s\gamma$) and $B_s \to K^*\gamma$ ($b \to d\gamma$), are a sensitive probe for physics beyond the SM and can be used to place complementary constraints on the unitarity triangle. The yet unobserved $B_s \to K^*\gamma$ decay is an example of $b \to d$ transitions that an experiment at a high-luminosity Z factory can probably uniquely study, provided that it can benefit from a precise photon-energy measurement complementing an excellent reconstruction of displaced vertices. A first study of the FCC potential to observe this decay has been reported in Ref. [649]. It assumes perfect charged hadron particle and photon identifications and ignores background contributions. The reconstructed charged kaon and pion corresponding to the $K^* \to K\pi$ decay are combined with the generated photon (the energy of which is smeared to account for the detector resolution). The $B_s$ signal yield is estimated from the CKM matrix elements and the corresponding hadronisation fractions $f_d$ and $f_s$, leading to the ratio $N_{B_d}/N_{B_s} \sim 92$. The distribution of the resulting $K^*\gamma$ invariant mass is shown in Fig. 62 for two values of the stochastic term of the electromagnetic energy resolution.

A sufficiently-high photon-energy resolution is mandatory for the peak of the $B_s$ signal to become visible and distinguishable from the overwhelming $B_d^0$ counterpart spectrum. With a stochastic term of 2%, the ratio of the two branching fractions could be extracted with a relative statistical uncertainty better than 0.1%. Provided that the ratio of the form factors of the two decays is well known, this opens the way to a very precise direct measurement of the $|V_{td}/V_{ts}|$ ratio, as shown in the bottom plot of Fig. 62. A measurement may still be possible with a resolution of 12%/$\sqrt{E}$, but that would require an excellent control of the shapes of the mass distributions, in particular of the tails (assumed here to be perfectly known), and the precision would anyway degrade by at least an order of magnitude.

#### The $B_s \to D_s K$ decay

The copious $B_s$ decay modes to neutral particles are inaccessible at Belle II and challenging at LHCb, and can be uniquely studied at FCC-ee. A few benchmark studies have been performed to extract the necessary detector requirements for PID.
<figure><img src="image_71.png" /><figcaption>**Fig. 62** Top: mass distribution of B mesons decaying into $K^+\gamma$ with an electromagnetic energy resolution of 12%/$\sqrt{E}$ (left) or 2%/$\sqrt{E}$ (right). Bottom: relative uncertainty on $|V_{ts}/V_{td}|$ expected from the measurement of the ratio of the two branching fractions, as a function of the stochastic term of the EM energy resolution. The current uncertainty is shown by the horizontal line</figcaption></figure>

(Sect. 4.5) and calorimetry. One of them is the study of the $B_s \to D_s K$ decay [50], where the $D_s$ decays via $D_s^+ \to \phi\rho \to K^+K^-\pi^+\pi^0$, which could increase the size of the $B_s$ sample by a factor of 3 with respect to that obtained with the single mode studied in Sect. 4.5. Figure 63 shows the impact on the mass resolution of the $B_s$ system when a crystal-like calorimeter is employed, improving the relative resolution of the calorimeter, $\sigma_E/E$, from $0.15/\sqrt{E} \oplus 0.005$ to $0.03/\sqrt{E} \oplus 0.005$. This would correspond to an improvement in mass resolution from 51 to 14 MeV.

### 4.6.3 Requirements on the geometrical acceptance for $e^+e^- \to \gamma\gamma$ and $\ell^+\ell^-$ events at Z-pole energies

The determination of the Z lineshape parameters requires the measurement of the hadron and lepton cross sections at and around the Z pole. With $1.5 \times 10^{12}$ Z bosons produced at each FCC-ee interaction point, statistical precisions of $O(10^{-6})$ are within reach. Critical limiting uncertainties come from the counting of lepton pairs ($e^+e^- \to \ell^+\ell^-$, with $\ell = \mu, \tau$) and from the integrated luminosity measurement. At FCC-ee, the wide-angle diphoton process $e^+e^- \to \gamma\gamma$ becomes statistically relevant and offers prospects for a safer determination (in terms of systematic uncertainties) of the integrated luminosity than the traditional low-angle Bhabha scattering, $e^+e^- \to e^+e^-$.

The definition of the geometrical acceptance (defined, e.g., by a given polar angle lower cut in the centre-of-mass frame of the collision) for both $e^+e^- \to \gamma\gamma$ and $e^+e^- \to \ell^+\ell^-$ is an obvious source of a potentially large systematic bias, which was dominant at LEP. Indeed, any global or local detector misalignment can generate a systematic bias on the acceptance. The tolerance on this bias can be calculated, e.g., either to match the resulting systematic uncertainty on the cross section to
<figure><img src="image_72.png" /><figcaption>**Fig. 63** Distribution of the mass of the reconstructed $B_s$ system (in GeV) for the process $B_s \to D_s K \to \phi \rho K \to K K \pi \pi^0 K$, on top of the main backgrounds, for a calorimeter with an energy resolution of</figcaption></figure>

<figure><img src="image_73.png" /><figcaption>$15\% / \sqrt{E}$ (left) or $3\% / \sqrt{E}$ (right). PID is included. The resolution on the photon angles has a negligible effect on the resolution of the mass of the $B_s$ candidates</figcaption></figure>

<figure><img src="image_74.png" /><figcaption>**Fig. 64** Tolerance on the accuracy of the polar angle cut as a function of the polar angle cut in degrees, expressed as a radial accuracy for a detector situated at 2.5 m from the IP in the centre-of-mass of the collision. Left: for dilepton events, to ensure a systematic precision of $2.2 \times 10^{-6}$. Right: for diphoton events, to ensure a systematic precision</figcaption></figure>

<figure><img src="image_75.png" /><figcaption>of $1.5 \times 10^{-5}$ (lower blue curve). Also indicated is the tolerance corresponding to having a systematic uncertainty equal to the statistical one, assuming either fully correlated (middle green curve) or uncorrelated (upper red curve) displacements in the two endcaps</figcaption></figure>

its statistical precision or to obtain a specific precision, as done in Ref. [650] and displayed in Fig. 64 for a polar angle cut between 1 and 25 degrees.

The tolerance, expressed as the accuracy of the definition of the polar angle cut for a detector situated at 2.5 m from the IP, is similar for dileptons and diphotons, and is in the 10–20 µm range for a cut between 10 and 20 degrees, corresponding to a required polar angle accuracy of 4 to 8 µrad.

Inspired by the work done for integrated luminosity measurements with low-angle Bhabha scattering at LEP, such a tight requirement calls for the design and the construction of the calorimeter (for diphotons) and the tracker (for dileptons) endcaps with a mechanical precision ensuring the specified tolerance of 10–20 µm, complemented by dedicated test-beam measurements and a survey/monitoring of the distance between the two endcaps with a precision of 50–100 µm. While the task is challenging, it should be kept in mind that for the luminosity monitor (LumiCal), situated at lower angles, the transverse
<figure><img src="image_76.png" /><figcaption>**Fig. 65** Analytically-predicted precision of the diphoton acceptance determination (in µrad) as a function of a polar angle cut applied in the event-by-event centre-of-mass frame, assuming a 100 µm tolerance in the azimuthal direction, and exploiting the energy-momentum conservation and the constraints that the beam crossing angle and the longitudinal boost are the same (on average) for all events and constant in time. This result is obtained with a readout cell of 1° × 1° and position resolution of $\sigma_{x,y} = 0.5$ mm in the endcap calorimeter (commensurate with the various proposed options). The arrows indicate two examples of the angular cut that would be typically used in the measurement</figcaption></figure>

(longitudinal) tolerance is of 1 µm (50 µm) at 1 m of the luminous region, for a precision of $10^{-4}$ on the integrated luminosity measurement [44].

With respect to the LEP case, FCC-ee offers an additional totally new and possibly synergistic approach to a precise definition of the acceptance. Indeed, the large and constant beam crossing angle of 30 mrad provides an absolute angular scale to dilepton and diphoton events at all angles. Total energy and momentum conservation allows for the event-by-event determination of this crossing angle (together with the constant longitudinal boost resulting from the specific positioning of the accelerating RF cavities in the FCC tunnel) with excellent accuracy from the final state particle kinematic observables. A global fit of all events, constraining the crossing angle and the longitudinal boost to be constant, would then provide an in-situ local 'calibration' of final state particle angles and, in particular, of the acceptance cut. The required statistical precision was demonstrated analytically [651] to be within reach with the FCC-ee dilepton and diphoton samples, but the actual fit procedure remains to be consolidated.<fnref n="21" /> The sensitivity of this approach is proportional to the magnitude of the crossing angle, and could not be used with the LEP head-on collisions. At FCC-ee, it was already shown [651] that a (mechanical or otherwise) tolerance of 100 µm in the $r-\phi$ direction would allow an acceptance definition of 3–12 µrad, irrespective of the (global or local) endcap radial or longitudinal displacements, consistent with the tolerances mentioned above, as displayed in Fig. 65. More recent developments seem to indicate that the required $\phi$ tolerance can also be reached in situ.

Further work is needed to verify the feasibility of the second method beyond analytical computations, as well as to evaluate the effect of the beam crossing angle on the acceptance determination with the classical method. The large forward cross section of $e^{+}e^{-} \rightarrow e^{+}e^{-}$ events will open the possibility of mutual in-situ alignment of the tracker and the calorimeter, offering a cross-check of the acceptance cut. It will be important to check whether the second approach would also be suitable for the integrated luminosity measurement with low-angle Bhabha scattering in the luminosity monitors. The two approaches are expected to help each other, either by reducing the mechanical constraints of the former or by improving the convergence of the latter, and most likely both. Their combination is expected to provide an excellent understanding of the acceptance, a cross-check of their accuracy, and an explicit requirement on the position and angular resolutions of the tracker and of the calorimeter.

<footnote n="21">²¹ It was already shown in Ref. [22] that this finite crossing angle and longitudinal boost could be used to find and monitor the directions of the x, y, and z axes within a few µrad precision every hour at the Z pole with dimuon events.</footnote>
<figure><img src="image_77.png" /><figcaption>**Fig. 66** Left: reconstructed energy vs. mass for all μγ combinations in simulated $Z \to \tau\tau\gamma$ background events with one $\tau \to \mu\bar{\nu}\nu$ decay. The signal region corresponding to $2\sigma$ resolution is indicated by the red ellipse. Right: present and expected upper limits for $\mathcal{B}(\tau \to \mu\gamma)$ [199].</figcaption></figure>

The dates of the future measurements are mainly chosen for plotting purposes. The expected limits for Belle II and the Super Charm-Tau factories are conservative estimates, assuming that those searches will be mostly background-constrained

### 4.6.4 Sensitivity to charged lepton flavour violation: $Z \to \mu e$ and $\tau \to \mu \gamma$

With its $6 \times 10^{12}$ Z bosons, FCC-ee enables precise tests of charged lepton flavour violation (cLFV) processes. The $Z \to \mu e$ process has an extremely clean signature – a beam-energy electron recoiling back-to-back against a beam-energy muon – with fully reducible background from the $2 \times 10^{11} Z \to \tau^+\tau^-$ events. It is estimated [51] that FCC-ee will improve by 2 to 3 orders of magnitude the current limits of about $10^{-7}$ from the LHC [652]. The most dangerous background comes from the ‘extreme bremsstrahlung’ emission by a muon in a $Z \to \mu\mu$ event that creates a large deposit in the electromagnetic calorimeter, faking an electron. This effect could be limited by improving the ECAL energy resolution and having the possibility of longitudinal segmentation to veto showers starting later in the calorimeter.

The sensitivity of FCC-ee to the LFV $\tau \to \mu\gamma$ decay was established in Refs. [51,198] and the major detector effects on the measurement were evaluated. The analysis strategy requires the identification of a clear SM $\tau$ decay on one side (‘tag’) so that the search for the LFV decay is performed in the other hemisphere. The discriminant variables are the total energy and the invariant mass of the final state. As shown in Fig. 66 (left), the signal region is background dominated and the background density rises linearly away from the $E_{\mu\gamma} - E_{\text{beam}} = 0$ line. This implies that the sensitivity (upper limit) scales linearly with the $E_{\mu\gamma}$ resolution, which is dominated by the ECAL energy resolution. With the full event sample of $4 \times 10^{11} \tau$ decays, an expected 90% CL upper limit of $1.2 \times 10^{-9}$ can be reached [199], as shown in Fig. 66 (right).

This benchmark is particularly interesting because it also shows a requirement for the photon position resolution, which contributes to the invariant mass calculation. In this example, where the calorimeter has a resolution of about $16.5\%/\sqrt{E}$ (as in CLD) and a position resolution of 2 mm, the two contributions in the invariant mass calculation are similar. Therefore, for this measurement, while the sensitivity is found to scale linearly (or slightly more strongly) with the photon energy resolution, a fine-grained crystal calorimeter with a $3\%/\sqrt{E}$ energy resolution would be particularly valuable. This is especially true since it would also provide a significantly better spatial resolution, of around 1 mm, leading to a fivefold improvement in sensitivity compared to the previous example.

### 4.6.5 Bremsstrahlung recovery

Even with an excellent EM calorimeter resolution, for 50 GeV central electrons the resolution of a calorimetric measurement is worse than the resolution of the tracker determination of the momentum. Furthermore, the latter is not as good as that of muons since electrons emit bremsstrahlung radiation: even with the light tracker of IDEA, corresponding to ~10% of a radiation length in the central region, the effective momentum resolution of electron tracks is at least a factor of two worse than that of muons [653]. Several measurements call for a better electron momentum resolution. For example, the determination of the Higgs boson mass from $Z(\mu\mu)H$ events (Sect. 4.3.1) can gain from exploiting the $Z \to e^+e^-$ channel. A resolution
<figure><img src="image_78.png" /><figcaption>**Fig. 67** Likelihood scan of the Higgs boson mass with the recoil method, combining the muon and electron channels. The uncertainties correspond to the quadratic sum of the statistical and systematic terms</figcaption></figure>

improvement can be brought by the recovery of the bremsstrahlung photons in the calorimeter, if their energy can be added to the momentum of the track. An effective recovery requires that the showers of the electron and of the radiated photon(s) be disentangled by the reconstruction algorithm. For 50 GeV central electrons, in a 2 T magnetic field, photons radiated at small radii (where, in the IDEA tracker, most of the bremsstrahlung emissions happen) are separated by typically 2–3 cm from the electron at the calorimeter entrance. The ability to separate showers that are so close to each other calls for a transverse granularity of $1 \times 1 \text{ cm}^2$ or better and may place some demands on the longitudinal segmentation, which helps to disentangle showers that partially overlap. Detailed GEANT simulations and reconstruction algorithms are needed for a precise assessment of these constraints. Meanwhile, it is estimated that, with the recovery of bremsstrahlung photons, the effective resolution of electrons would be 25% worse than the muon resolution for a calorimeter EM energy resolution of $3\%/\sqrt{E}$.

More details can be found in Ref. [653]. The DELPHES simulations used for the studies reported in this document rely on this estimation. With this bremsstrahlung recovery, the $Z \to e^+e^-$ channel significantly contributes to the determination of the Higgs boson mass from ZH events, as shown in Fig. 67, improving the uncertainty by 22% compared to what is obtained from the muon channel alone [65].

### 4.6.6 Prompt decays of ALPs $a \to \gamma\gamma$

A search for ALPs produced in $Z \to a\gamma$ decays, complementary to the one previously mentioned, consists in looking for ALPs that decay promptly into two photons, leading to a three-photons final state. The analysis presented in Ref. [169] compares the sensitivities that are expected with the dual-readout fibre calorimeter of IDEA and with the variant where crystals are placed in front of it.

The experimental sensitivity is driven by the ability to precisely reconstruct the invariant mass of the two photons coming from the ALP decay. For low masses, up to a few hundreds of MeV, the resolution on this diphoton mass is dominated by the resolution on the photon angles, hence by the precision with which the impact point of the photons at the calorimeter entrance is determined. This contribution decreases with increasing ALP mass and, above 10 GeV, the resolution depends only on the energy resolution of the calorimeter. In addition, at low masses, below ~5 GeV, the two photons from the ALP decay may not be resolved in the detector but be 'merged' into a single reconstructed object. Detailed GEANT simulations and reconstruction algorithms, still under development, are needed for a precise understanding of these effects. A simplified approach is adopted for the current sensitivity study, whereby the angular distance $\Delta\alpha$ between the two photons is used to determine whether the photons are resolved. Taking into account the transverse granularity and the Molière radius of the detectors, it is assumed that photons with $\Delta\alpha > 20$ mrad can be reconstructed in the crystal calorimeter, which corresponds to a separation of 4 cm (four
<figure><img src="image_79.png" /><figcaption>**Fig. 68** Expected sensitivity at the $2\sigma$ level of a FCC-ee experiment, in the parameter space spanned by the mass of the ALP and its coupling to two photons, from a search for ALPs produced in association with a photon, $e^+e^- \to a\gamma$, followed by the ALP prompt decay into two photons. In the legends, $\Delta\alpha$ denotes (in rad units) the angular separation down to which the calorimeter is assumed to be able to resolve two photons</figcaption></figure>

calorimeter cells) of the two photons at the calorimeter entrance. For the dual-readout calorimeter, photons are required to be separated by $\Delta\alpha > 10$ mrad to be resolved, which corresponds to the distance between 10 fibres of the detector.

Taking into account the irreducible $e^+e^- \to \gamma\gamma\gamma$ background, the experimental reach expected for the two calorimeter options is shown in Fig. 68. The crystal calorimeter has a better sensitivity for high masses, where the sensitivity is driven by the energy resolution. The impact point resolution is very similar for the two calorimeters, but the better granularity of the fibre calorimeter is expected to provide a better separation for collimated photons that emerge from the decay of ALPs at very low masses, resulting in a gain in sensitivity compared to that provided by the crystal detector.

As shown by Fig. 68, the parameter space covered by this analysis, that focuses on prompt decays of ALPs, nicely complements the one explored by a search or quasi-stable ALPs in the monophoton final state (Fig. 61). The sensitivity to ALPs with intermediate lifetimes, which are long-lived but decay inside the detector, is more difficult to assess. For ALPs that decay before reaching the calorimeter, it depends on the ability to reconstruct the displaced decay vertex of the ALP into two photons. For ALPs that decay inside the calorimeter, the sensitivity depends on the ability to identify late-starting showers. The requirements that these analyses will place on the longitudinal segmentation of the calorimeter, on the measurement of the timing of calorimeter signals, and on a potential preshower, remain to be studied.

### 4.6.7 Requirements from $\pi^0 \to \gamma\gamma$ reconstruction in $\tau$ decays

The reconstruction of $\pi^0 \to \gamma\gamma$ decays is a crucial component for several measurements of the FCC-ee physics programme, such as the tau branching ratios or the tau polarisation. The kinematic of a $\tau \to \rho\nu$ decay produced at the Z pole provides initial detector requirements [654]. For instance, the momentum of the $\pi^0$ produced in the $\rho$ decay is quite soft and its decay photons are even softer. The capability of identifying these low-energy photons requires a low noise and high energy resolution calorimeter. The energy resolution is important also because it affects the $\pi^0$ identification itself, which relies on a cut on the diphoton invariant mass. The granularity is another important aspect that plays a role in the separation of the two photons. The angular separation between the two photons, $\approx 2m_{\pi^0}/E$, is typically 10 mrad, which leads to a separation of 2 cm at the calorimeter entrance; however, for the highest possible energy ($E_{\pi^0} = 45.6$ GeV) the opening angle is reduced to 6 mrad, corresponding to 1.2 cm separation at the calorimeter entrance.<fnref n="22" /> The granularity is also needed for the correct separation of the photons from charged pions in the decays. A study has been done comparing the performance of different noble liquid calorimeters (LAr and LKr) in $\pi^0$ events. Cases have been considered where the photons from the $\pi^0$ decays can be reconstructed separately (resolved) or are reconstructed as a single EM object (unresolved). As seen in Fig. 69, the $\pi^0$ reconstruction efficiency and the $\pi^0$ mass resolution are better in the LAr option with the finer granularity and improve further in the LKr option, given its smaller Molière radius.

Figure 70 shows the $\pi^0$ reconstruction efficiency, as a function of its energy, all the way to 45 GeV. For higher energies (not shown in the figure), the transverse shape of an unresolved $\pi^0$ electromagnetic shower resembles more and more that of a single photon and the identification efficiency progressively vanishes.

<footnote n="22">²² A large tracking volume, optimised for track momentum resolution, is also beneficial for the identification of collimated objects such as $\pi^0$ decays.</footnote>
<figure><img src="image_80.png" /><figcaption>Fig. 69 Invariant mass distributions of two-cluster $\pi^0$ mesons for different noble liquid calorimeter configurations</figcaption></figure>

<figure><img src="image_81.png" /><figcaption>Fig. 70 Probability of $\pi^0$ identification as a function of its energy for a W+LKr calorimeter with a granularity of 1 × 1 × 2.6 cm$^3$</figcaption></figure>

### 4.6.8 Work ahead

- The measurement of tau polarisation in Z decays, from which the tau and electron asymmetries, $A_\tau$ and $A_e$, are extracted, is a cornerstone of the Tera-Z physics programme. Experience from LEP shows that the precision of this measurement critically depends, in particular, on the design of the electromagnetic calorimeter. While the sizes of the event samples used by the four LEP experiments were similar, the uncertainties differed by nearly a factor of two from one experiment to the other. As noted above, a high calorimeter transverse granularity is indeed crucial to identify and precisely reconstruct the $\pi^0$ mesons produced in $\tau$ decays. The precision that different detector concepts can achieve on this measurement needs to be studied with a full simulation description, which also includes, besides the spatial and energy detector resolution, the effect of fake photons. Work in this direction has started, as is shown in Sect. 4.10.

- The reconstruction of the events on fully simulated detector concepts will be crucial to extract further requirements on the detector performance. For instance, since photon energy contributes 25% of the total energy of a jet, the ability to reconstruct low-energy photons is very important in order to improve the jet energy resolution, which is crucial for Higgs boson hadronic final states, such as $H \to gg$. Moreover, in a study considering multi-jet topologies [619] it has been shown that the absence of photon and $\pi^0$ identification prior to the jet particle-flow reconstruction would worsen the resolution of the reconstructed hadronic objects in about one third of the cases. Preliminary studies will need to be updated once the reconstruction of full simulation detector concepts become available in the coming months.

- The measurement of long-lived particles decaying to photons relies on a precise standalone ECAL measurement of the direction of the shower. The impact of longitudinal segmentation on the pointing capabilities and on displaced vertex reconstruction performance needs to be studied in full simulation.
### 4.6.9 Preliminary conclusions

- An electromagnetic calorimeter with excellent energy resolution (a few %) is required to optimise the expected precision on the Z to $\nu_e$ coupling via the $e^+e^- \to \nu_e\bar{\nu}_e\gamma$ process, lepton flavour violating decays such as $Z \to \mu e$ and $\tau \to e\gamma$, decays of heavy flavoured hadrons to photons or $\pi^0$, and ALPs searches.

- Excellent transverse granularity and resolution is needed for optimal Bremsstrahlung recovery and $\pi^0$ identification. Longitudinal segmentation and pointing capabilities are required for displaced photon vertex identification, such as long-lived ALP decays.

- A knowledge of the acceptance at the level required to match the statistical precision on the $e^+e^- \to \gamma\gamma$ cross section for the absolute luminosity determination requires that the calorimeter be constructed with a mechanical precision of few tens of microns.

- Reconstructing low energy photons from decays of $\pi^0$ mesons, either produced in B or D decays or in $H \to gg$, requires as little material in front the ECAL as possible, as well as a noise term as small as a few tens of MeV.

## 4.7 Requirements for the hadron calorimeter

To fully exploit the statistical power of FCC-ee, precise measurements of processes in their hadronic final states are crucial because of their typically large branching ratios. A clear advantage of $e^+e^-$ collisions over hadron collisions, such as at the HL-LHC, is the almost negligible pile-up and the absence of underlying event and initial-state QCD radiation, as well as the precise knowledge of the total energy-momentum of the final state, resulting in cleaner data and improved jet energy resolutions. For FCC-ee, the possibility of having a full GEANT simulation of the events in the new software has become available only recently, so that a state-of-the-art event reconstruction based on the particle flow approach is not yet validated for complete physics studies. Since the reconstruction algorithm significantly impacts the final resolution on hadronic objects, it is challenging to determine specific requirements for the hadron calorimeter performance from existing studies, performed with fast simulation DELPHES samples. Nevertheless, valuable information can be derived regarding the overall impact that the performance of the calorimeter has on the accuracy of the measurement, profiting from the particle-flow inspired reconstruction available in DELPHES.

### 4.7.1 Reconstruction of Higgs boson hadronic final states

The identification of $H \to jj$ signal events relies on the resolution of the dijet system mass, which is influenced by the performance of the calorimeter. Additionally, the precise separation of different flavours depends on the effectiveness of the flavour tagging algorithm, which also imposes requirements on the vertex detector and on particle identification, as discussed in Sects. 4.4.1 and 4.5.1. Assuming an ideal particle-flow algorithm, with perfect charged and neutral particle identification, the visible energy (and mass) resolution is dominated by the neutral hadron resolution, which is in turn driven by the HCAL stochastic term. A study has been performed to assess the impact of a degraded hadron calorimeter performance [627], by worsening the HCAL stochastic term (50% and 100%) and then compare the resulting $H \to jj$ sensitivity to that of the IDEA detector baseline (which assumes dual-readout calorimetry with a 30% stochastic term).

The results are summarised in Fig. 71 for several Higgs boson decay channels. When the neutral hadron energy stochastic term is degraded to 50% (100%), the expected precision of the measurement of the $H \to s\bar{s}$ branching ratio degrades by about 20% (55%). The larger is the expected signal-to-background ratio in a given channel (the largest being for $H \to b\bar{b}$), the smaller is the effect of the degradation of the neutral hadron energy resolution on the expected precision. The visible mass resolution is, therefore, particularly important for accurately measuring the $H \to c\bar{c}$ and $H \to s\bar{s}$ branching fractions.

### 4.7.2 Measurement of the Higgs boson invisible width

As discussed in Sect. 4.3.1, FCC-ee offers a unique opportunity to use the 'recoil method' for precise, model-independent measurements of Higgs boson properties. This method becomes particularly valuable when studying the Higgs boson decay into an invisible final state. The Standard Model process $H \to \nu\bar{\nu}\nu\bar{\nu}$ has a very small branching ratio, $1.06 \times 10^{-3}$ [655], so that it is beyond the reach of the LHC programme and might only be observable at the FCC-hh. However, with possible extensions of the Standard Model, such as the inclusion of a Higgs portal, the Higgs boson width to invisible final states could
**Fig. 71** Expected precision degradation of the branching ratio measurements for the $H \to b\bar{b}$, $c\bar{c}$, $s\bar{s}$, and $gg$ decays as a function of the HCAL stochastic term. To guide the interpretation, the value 30% would correspond to a dual-readout calorimeter as in the baseline IDEA simulation, 50% corresponds to an ATLAS-type calorimeter, and 100% to a CMS-type calorimeter

<figure><img src="image_82.png" /></figure>

**Fig. 72** The $M_{\text{miss}}$ distribution for several Z decay channels, corresponding to the Higgs boson signal, in HZ events where the Higgs boson decays into an invisible final state. The distributions are normalised to the same number of events and are shown after the $P_{\text{miss}} > 10$ GeV cut and the $M_{\text{vis}}$ selection around the Z mass

<figure><img src="image_83.png" /></figure>

be increased because of decays to non-SM particles, which could be potential dark matter candidates [656,657], making the study of this channel highly relevant.

In a recent study [67], the DELPHES simulation of the IDEA detector was used, along with the state-of-the-art flavour tagging algorithm PARTICLENETIDEA, described above. To maximise the size of the event sample, the analysis considers not only Z decays to ee and $\mu\mu$ but also to $b\bar{b}$, $c\bar{c}$, and $q\bar{q}$. The visible mass ($M_{\text{vis}}$) serves as the discriminant variable in the final fit (with no systematic uncertainties considered at this stage). The results indicate that, with an integrated luminosity of $10.8 \text{ ab}^{-1}$ at $\sqrt{s} = 240$ GeV and of $3 \text{ ab}^{-1}$ at $\sqrt{s} = 365$ GeV, a measurement of the SM branching ratio with a precision of 25% could be achieved. Furthermore, when accounting for the possibility of exotic decays, the study results in the exclusion, at the 95% CL, of branching fractions lower than 0.05%, or a $5\sigma$ observation if greater than 0.13%. The $Z \to q\bar{q}$ decay channel was found to be the one with the best sensitivity, given its higher statistical power, and the run at $\sqrt{s} = 240$ GeV has much better sensitivity than the highest energy run. A preliminary study performed with CLD full simulation can also be found in Ref. [627].

Figure 72 displays the normalised distribution of the missing mass, representing the Higgs boson, for the various Z decay modes, allowing the comparison of resolutions between the lepton and hadron channels. An investigation was also conducted into the effects of a poorer detector energy resolution on the measurement, applying a simple additional Gaussian smearing to the four-vector of the hadronic final state. As shown in Fig. 73, an additional smearing of 5% led to a 110% (90%) increase in the uncertainty on the $q\bar{q}$ channel (combined result). The blue dashed curve in Fig. 73 represents the resolution of the
<figure><img src="image_84.png" /><figcaption>**Fig. 73** The effect of an additional smearing to the hadronic energy of the events on the expected uncertainty in a measurement of the branching fraction of the Higgs boson decay to invisible particles is shown for three individual channels and for all channels combined (solid lines). The root mean squared of the reconstructed Higgs boson mass is also shown, as a dashed blue line (corresponding to the vertical axis on the right side)</figcaption></figure>

<figure><img src="image_85.png" /><figcaption>**Fig. 74** The $M_{vis}$ distribution for background and HNL signal events, $e^{+}e^{-} \to N\bar{v}_{\mu} \to \mu q \bar{q}' \bar{v}_{\mu}$, after a preliminary selection</figcaption></figure>

reconstructed Higgs boson mass for the case where the Z boson decays into hadronic modes, as a function of the additional smearing. It is important to note that this quantity includes other effects from beam spread and ISR. In the future, it may be beneficial to use a better-defined quantity, such as the Z resolution itself, to further evaluate the dependence on the calorimeter performance.

### 4.7.3 Search for heavy neutral leptons

It has been shown in Refs. [658,659] that an $e^{+}e^{-}$ machine like FCC-ee, with the potential to collect a vast event sample at the Z peak holds significant discovery potential for feebly interacting particles, such as heavy neutral leptons (HNL). Such a large dataset, covering a phase space at low coupling strengths, is unmatched by other proposed future colliders and could potentially reach the lower bounds set by theory. The study reported in Ref. [129] focuses on the production of HNLs with masses between 20 and 80 GeV at $\sqrt{s} = 91$ GeV, with an integrated luminosity of $2.05 \times 10^{8}$ pb$^{-1}$, corresponding to $6 \times 10^{12}$ $e^{+}e^{-} \to Z$ events. In particular, the process $e^{+}e^{-} \to N_{\mu}\bar{v}_{\mu} \to \mu q \bar{q}' \bar{v}_{\mu}$ has been investigated. This process has a substantial branching ratio of about 50% over the entire mass range of interest and complements other studies in the leptonic channel with long lifetimes [138,659,660].

In a search for HNLs that decay promptly in the detector, the analysis applies selections on muons, jets, and missing energy to minimise background contaminations. The discriminant variable used in this analysis is the visible mass, which corresponds to the HNL mass, as shown in Fig. 74.

The final selection involves a sliding cut on the search HNL mass, taking into account the observed resolution ($\sigma = 20\%\sqrt{m_{HNL}}$). A study to evaluate the impact of varying the mass resolution has been performed and the result is shown in Fig. 75, indicating a minimal effect at low masses, where the background from $Z \to q\bar{q}$ events is negligible, but becoming more relevant at higher masses, where the background is higher.
<figure><img src="image_86.png" /><figcaption>**Fig. 75** The 2σ significance of an HNL signal, $e^{+}e^{-} \rightarrow N\bar{v}_{\mu}$, for several visible mass width resolutions, from a search for HNLs that decay promptly into a muon and two jets</figcaption></figure>

### 4.7.4 Work ahead

- The total Higgs boson width measurement at $\sqrt{s} = 240$ GeV is statistically limited by the precision on the $H \rightarrow ZZ^{*}$ partial width, which crucially depends on identifying all the hadronic Z decay modes. The separation of the W and Z mass peaks is driven by hadronic resolution and is required in order to suppress the overwhelming $H \rightarrow WW^{*}$ background. The current detector proposals satisfy this requirement in fast simulation studies, but this result has to be confirmed by constrained kinematic fits in full-simulation studies.

- These preliminary studies have been performed using a fast simulation of the detector with close to ideal particle-flow performance and can, therefore, only provide overall guidelines for the needed hadron calorimeter resolution. Full-simulation performance studies with particle-flow reconstruction using integrated tracking, ECAL, and HCAL information, and kinematic fits constrained by the total energy and momentum conservation, are of paramount importance to consolidate the requirements on hadronic calorimeter technology, transverse and longitudinal granularity, and resolution.

### 4.7.5 Preliminary conclusions

- The precision of the Higgs boson couplings to quarks and gluons, in particular the strange and charm Yukawa couplings, as well as the Higgs to invisible one, drives the hadron calorimeter requirements. Heavy neutral lepton hadronic decay modes also benefit from excellent visible energy resolution.

- In particular, assuming an ideal particle-flow reconstruction setup with highly-efficient tracking and neutral hadron identification capabilities, the neutral hadron resolution drives the sensitivity to the strange Yukawa coupling. An excellent visible mass resolution, obtained through particle-flow reconstruction, is of paramount importance for the observation of this mode.

## 4.8 Requirements for the muon detector

At the FCC-ee energies, the muon momentum reconstruction is entirely driven by the tracking system and the main role of the muon detector is to identify muons with a very high efficiency and purity, as well as to serve as 'tail-catcher' for the hadron showers that may not be fully contained in the calorimeter. An important figure of merit is the probability that a pion be misidentified as a muon. An example benchmark measurement to set a requirement on the control of the pion contamination is that of the ultra-rare $B \rightarrow \mu^{+}\mu^{-}$ decay. As illustrated in Fig. 76, the excellent mass resolution of the IDEA detector offers a very good separation of the B and $B_{s}$ peaks. A significant background coming from $B \rightarrow \pi^{+}\pi^{-}$ decays is, however, present under the B peak. Assuming a double $\pi \rightarrow \mu$ mis-identification probability of $2 \times 10^{-5}$, this background contribution (dashed histogram in Fig. 76) would be as large as the signal [194].
<figure><img src="image_87.png" /><figcaption>**Fig. 76** Mass distribution of $B \to \mu^+\mu^-$ and of $B_s \to \mu^+\mu^-$ as expected from the IDEA detector, with an event sample of $5 \times 10^{12}$ Z decays. The background contribution from misidentified pions in $B \to \pi^+\pi^-$ decays is also shown, as the dashed curve. From Ref. [194]</figcaption></figure>

While the measurement of the track momentum in the muon detector alone does not improve (in the momentum range of interest) the excellent prompt muon momentum resolution already provided by the tracker, a good standalone resolution is useful to reduce the pion contamination and to identify pions that decay before the muon detector. In addition, the standalone performance of the muon detector is important in searches for long-lived particles that decay outside the tracker volume. The requirements on the standalone momentum resolution need to be quantified and they are likely to have a significant impact on the technologies that will be chosen for the muon system of an FCC-ee detector [43].

The FCC-ee could uniquely probe yet another suppressed $b \to s$ transition, via the $B_s \to \nu\bar{\nu}$ decay mode [661]. The main backgrounds for this search are the $b \to \tau\nu X$ decays, where the $\tau$ decays semi-leptonically and the decay lepton escapes detection. This configuration can occur when the muon is forward or too soft to reach the muon detector. In this case, a calorimeter equipped to perform muon identification might help, together with a low detector magnetic field.

## 4.9 Precise timing measurements

The motivations for timing measurements at FCC-ee are outlined in this section. Quantified requirements are still to be assessed for most of the use cases.

### 4.9.1 Time-of-flight measurements

As mentioned in Sect. 4.5, charged hadron particle identification relying on the specific energy loss must be complemented by other measurements in order to fill the gap around 1 GeV, where the Bethe-Bloch energy loss function is close to its minimum. Time-of-flight measurements, for example in a layer of silicon sensors at 2 m from the interaction point, with a non-challenging resolution $\sigma_t \simeq 100$ ps, are adequate for this purpose (with a magnetic field of 2 T or less). With a resolution of 30 ps, such (standalone) TOF measurements would allow charged kaons to be separated from charged pions up to $\mathcal{O}(3)$ GeV in momentum, while an excellent resolution of 10 ps would be needed$^{23}$ to extend this momentum range up to 5 GeV.

Such TOF information could also be obtained in a silicon-tungsten CLD-like ECAL, where measurements could be made in several layers, each with a resolution of, e.g., $\sim 100$ ps. Dedicated timing layers made of inorganic scintillator offer another solution. For example, the calorimeter design proposed in Ref. [619] includes two such thin layers, upstream of the crystal-based ECAL mentioned earlier, which could provide a 20 ps timing resolution.

Another well-known use-case of TOF measurements is the determination of the mass and lifetime of new massive particles. An example is provided by feebly coupled heavy neutral leptons that could be copiously produced in $Z \to \nu N$ decays at Tera-Z. In such decays, the energy of the new lepton $N$ depends only on its mass. In subsequent decays, such as $N \to Z(\ell\ell)\nu$ or $N \to W(q\bar{q}')\ell$, the flight distance of $N$ is obtained from the decay vertex of the Z boson and the TOF of the charged

<footnote>$^{23}$ Such a resolution is smaller than the time it takes, at the Z peak, for the two bunches to cross each other (about 36 ps). Hence, to be able to exploit a 10 ps resolution, the ‘event time’, $t_0$, would need to be reconstructed. Simple algorithms should allow this $t_0$ to be reconstructed, for most SM processes, with a resolution of $\sigma_t/\sqrt{N}$ for events with $N$ primary tracks that reach the timing layer.</footnote>
<figure><img src="image_88.png" /><figcaption>**Fig. 77** Left: relative mass resolution of the HNL as a function of its flight distance, for an HNL mass of 40 GeV, using a reconstruction technique exploiting timing measurements; two hypotheses on the resolution of the timing measurements are considered ($\sigma_t = 10$ and 50 ps).</figcaption></figure>

The process $e^+e^- \to N\bar{\nu}_\mu \to \mu q\bar{q}'\bar{\nu}_\mu$ is used here. Right: relative mass resolution expected at FCC-ee, as a function of the HNL mass and of its (squared) mixing with the $\nu_\mu$, in the parameter space where FCC-ee could make a discovery, for a timing resolution of 30 ps

particles provides the time at which N decayed, from which both the lifetime and the velocity (hence the mass) of N can be extracted [130]. The need for a large tracking volume, as well as a timing resolution in the ballpark of a few tens of picoseconds, has so far placed the practical realisation of this idea out of realistic experimental reach. A first study of the expected performance of this measurement technique has been presented in Ref. [662], in the context of FCC-ee. It uses as a benchmark the process $e^+e^- \to N\bar{\nu}_\mu \to \mu q\bar{q}'\bar{\nu}_\mu$, already considered in Sect. 4.7. A simple algorithm has been developed that allows the reconstruction of the time when N decays, despite the fact that the masses of the charged particles produced in the hadronic W decay are, a priori, unknown. Since there is no way to determine the ‘event time’ ($t_0$) of the collision for such interactions, with no primary tracks, it must be assumed that N was produced at the nominal beam crossing time. This leads to a smearing, of about 36 ps, of the reconstructed time of flight of N, from which its velocity is derived. Figure 77 (left) shows the relative resolution with which the mass of the HNL can be reconstructed with this method, as a function of its flight distance, for an HNL mass of 40 GeV and several assumptions on the resolution of the timing measurements, $\sigma_t$. The resolution is defined as the width of the interval between the 16% and the 84% quantiles of the reconstructed mass distribution. The aforementioned smearing prevents reaching the ideal resolution that would be obtained with $\sigma_t = 10$ ps, if the event $t_0$ was known, represented by the lowest curve in Fig. 77 (left). From the two upper curves it can be seen that, provided $\sigma_t$ is smaller than 50 ps, the degradation due to the detector resolution is limited to 20%. For an HNL of mass 40 GeV that decays at 1.5 m from the interaction point, this technique provides a mass resolution below 1%, which is significantly better than what can be obtained by measuring the visible mass in the detector. The right panel of Fig. 77 shows that, in the parameter space that FCC-ee can probe and that extends beyond the sensitivity of the HL-LHC, timing measurements with $\sigma_t = 30$ ps would allow the HNL mass to be reconstructed at the per-cent level.

It should be noted that, should the magnetic field be increased to 3 T (as could be considered for the runs at $\sqrt{s} = 240$ GeV and beyond), particles with a momentum of 1 GeV may not reach the outer radius of the tracker<fnref n="24" /> of about 2 m. Hence, to provide PID capabilities in the momentum range around 1 GeV, where the measurement of ionisation energy per unit length does not provide any separation, the TOF measurements should be made either at a smaller radius or when the particle eventually reaches the endcaps. In the latter case, in particular at normal incidence, it is essential to investigate the effects of multiple scattering and energy loss resulting from interactions with the beam pipe and the tracker material. While this may pose less of an issue for a gaseous tracker, it remains important to study this aspect in detail. In the former case and for the IDEA detector, the outermost layer of the vertex detector, at a radius of 35 cm from the beams, could be used for that purpose, at the expense of an increased material budget. With a time resolution of 30 ps, such standalone TOF measurements would

<footnote n="24">²⁴ Prompt particles with a curvature radius $\rho$ are confined to radial distances below $2\rho$ and, hence, need to have a transverse momentum $p_T$ (GeV) > 0.3 × R (m) × B (T)/2 to reach a barrel layer situated at a radius R. Particles with a momentum of 1 GeV and a polar angle of 45° only reach R ~ 1.6 m in a 3 T magnetic field.</footnote>
ensure a $K/\pi$ separation larger than $3\sigma$ in the whole momentum range where PID based on $dN/dx$ is ineffective. The impact that the larger material would have on the measurement of the track parameters remains to be studied. In a detector design with a full silicon tracker, the TOF measurements could be made in one of the layers of the outer tracker.

### 4.9.2 Time measurements very close to the IP

At FCC-ee, the distribution of the 'event time' ($t_0$) of the collisions follows a Gaussian distribution to a very good approximation, with a width ranging between 36 ps during the Tera-Z run and 6.5 ps during the $t\bar{t}$ threshold run. The arrival time of a particle in the innermost layer of the vertex detector depends only minimally on its nature ($K, \pi, \mu, e, \text{etc.}$), such that a measurement of this time provides (for primary particles) a measurement of the particle production time and of the event time $t_0$. For a given resolution of each measurement, $\sigma_t$, the event $t_0$ can then be determined with a resolution of $\sigma_t/\sqrt{N}$, with $N$ being the number of charged primary particles crossing this layer. Measuring the event $t_0$ offers several advantages, as listed below.

- It provides a robust reference for some of the TOF measurements outlined above.

- The spread of the $t_0$ distribution being proportional to the beam energy spread, its measurement provides an independent determination of the latter.

- Because of the crossing angle, the $t_0$ of a collision and the longitudinal position of the colliding particles within their respective bunch are correlated. With respect to a time origin, defined as the time when the centres of the two bunches coincide with the IP, collisions that occur early (late) always involve particles that are in the head (tail) of both bunches. Collisions that happen at a time close to the origin involve particles that are in the middle of the bunches. Splitting the events into early, central, and late collisions can provide relevant accelerator-related information. For example, the mass distribution of dimuon events at Tera-Z would provide a check that there is no unexpected difference in the centre-of-mass energy between head and tail collisions. Alternatively, the longitudinal boost distribution of dimuon events at $\sqrt{s} = 125$ GeV would exhibit a correlation [663] between the centre-of-mass energy and the longitudinal position that could improve the effective monochromatisation (Sect. 9). Moreover, further checks of the beam-beam effects could be made, by exploiting the fact that these effects depend strongly on the longitudinal position of the colliding particles [664].

Moreover, the measurement of the production time of the particles complements the spatial reconstruction of primary vertices in view of a direct pile-up measurement (expected to be at the per-mil level at Tera-Z). However, achieving precise timing measurements in the innermost layer of the VXD, without heavily compromising the material budget, will probably be a challenge.

### 4.9.3 Time measurements in the calorimeters

Besides the TOF measurements mentioned earlier, time measurements in the calorimeters provide handles to exploit the shower development in space and time. The hadronic energy reconstruction, in particular in a non-compensating calorimeter, as in the CLD design, can benefit greatly from such measurements, which allow the delayed signal from neutrons to be identified. The possible benefit of timing for pattern recognition in high-granularity imaging calorimeters remains to be studied in detail.

Finally, in the DR calorimeter of IDEA, a Fourier transform of the full signal from the SiPMs reading out the fibres would provide high precision (better than 100 ps) timing for the individual fibres and, in turn, longitudinal segmentation; the potential benefit in a particle-flow reconstruction algorithm adapted to the hybrid segmented crystal and fibre dual-readout calorimeter of Ref. [619] remains to be studied. It could also benefit the identification of low energy neutral hadrons, potentially providing neutron vs. $K_L$ separation, assuming that the initial time $t_0$ is known. However, a concrete implementation has to be studied in detail.

## 4.10 Selected studies with full simulation

Most of the requirements discussed in the previous sections have been obtained using fast parametrised simulations. While a full simulation and event reconstruction with every detector concept is beyond the scope of this feasibility study, a few selected preliminary reconstruction performance and physics results obtained with full simulation are presented in this section. With
the exception of ML-based tracking, all of them use the reconstruction of the CLD detector concept. A high-level machine-
learning-based particle-flow reconstruction algorithm is first discussed. An initial implementation of a full simulation flavour
tagging algorithm in CLD is described next and the achieved performance is compared with the fast simulation results. Finally,
the Higgs mass measurement using the recoil mass method and the τ polarisation measurement at the Z pole are addressed.

4.10.1 Machine-learning event reconstruction

The Higgs boson decays preferentially into hadrons. Therefore, the optimal identification and reconstruction of hadronic jets
is crucial for measuring Higgs boson properties. In particular, resolving the mass peaks from W, $Z \to jj$ hadronic decays at
the $3\sigma$ level requires reconstructing the dijet masses with a resolution $\sigma_m$ at the $\Gamma/m \approx 2.5\%$ level, where $\Gamma$ is the natural W
or Z width. Moreover, the measurement of rare hadronic Higgs decay rates, such as $H \to c\bar{c}$ and $H \to s\bar{s}$, requires excellent
dijet mass resolution, since the relative uncertainty on these modes scales with $\sqrt{\sigma_m}$, as discussed in Sect. 4.7.

The visible energy of hadronic jets is roughly distributed as follows: $f_{\pm} = 65\%$ from charged hadrons ($\pi^{\pm}$, $K^{\pm}$, ...), $f_{\gamma} = 25\%$ from photons originating from $\pi^0$ decays, and $f_n = 10\%$ from neutral hadrons (n, $K_L$, ...). The particle-flow approach relies on the tracking system to measure the momenta of charged particles, benefiting from its superior resolution, compared to the calorimeters, while the energies of photons and neutral hadrons are measured with the calorimeters. In an ideal PF algorithm, the visible mass resolution is dominated by the HCAL resolution, despite the neutral hadron energy content being subdominant. Achieving the best mass resolution requires efficiently identifying neutral hadrons and disentangling them from mismeasured clusters originating from charged hadron showers.

An optimal PF algorithm requires nearly 100% tracking efficiency and purity over the full momentum range for an accurate
measurement of the charged energy component. Fine transverse and longitudinal calorimeter segmentation is necessary for
optimal geometrical matching of extrapolated track trajectories to electromagnetic and hadron showers. Additionally, low-
noise high-resolution calorimetry and efficient clustering algorithms are essential for identifying and reconstructing individual
photon and neutral hadron showers. Excellent electromagnetic and hadron calorimeter resolutions are crucial for comparing
tracking and calorimeter energy measurements after geometrical matching. A low material budget in the tracker and before the
calorimeter (e.g., pre-shower or solenoidal magnet) is desirable to minimise nuclear interactions and conversions that could
compromise track, photon, and neutral hadron reconstruction efficiency. Moreover, the PF reconstruction performance depends
critically on the transverse and longitudinal granularity for optimal track-cluster matching and neutral hadron identification.
Finally, maximising the hermeticity and uniformity of the detector design is crucial for PF reconstruction.

Electron and muon identification and momentum determination, whether isolated or within jets, also benefit from a holistic
treatment of all detector components [665,666]. For example, as shown in Sect. 4.6, photon bremsstrahlung emissions within
the tracker requires combining tracking and ECAL information. Similarly, muons are identified by combining data from
tracking, calorimetry, and muon detectors. A comprehensive PF reconstruction should encompass a wide range of tasks,
aiming at providing an exhaustive list of identified final-state particles produced in the collisions and interacting with the
detector, along with accurate measurements of their momenta and origin vertices.

A novel approach to full event reconstruction based on graph neural network (GNN) methods is described in the following.
The goal is to improve every aspect of the reconstruction process, from efficiency to resolution, and to enable rapid iterations
over various detector concepts and geometries, so as to estimate performance and, hence, optimise detector technologies and
design options. The effectiveness of this approach is shown in Fig. 78. The left panel displays the tracking efficiency achieved
with machine learning (ML) methods using the GGTF algorithm [667] for the CLD and IDEA detectors in $Z \to jj$ events at
the Z pole. The ML approach significantly improves the CLD performance with respect to the standard tracking (a similar
comparison for the IDEA case cannot be made because the baseline reference is missing). It also shows that IDEA, with
its superior number of track measurements, can reconstruct much lower transverse momentum tracks, which are crucial for
optimal PF reconstruction since a significant portion of the visible jet energy is carried by soft charged particles. The right
panel illustrates the visible mass resolution in $ZH \to \nu\bar{\nu}s\bar{s}$ events at $\sqrt{s} = 240$ GeV obtained with ML-based PF (MLPF)
compared to the PANDORA particle-flow reconstruction [668,669], showing similar performance. This result was obtained
using GNN-based PF reconstruction, described in more detail in Ref. [620], taking as input reconstructed classical tracks
and low-level calorimeter hit reconstruction. Although this is work in progress, it indicates that the established PF algorithm
performance can already be reproduced with this approach. Further improvements are foreseeable by optimising the clustering
step, enhancing the neutral hadron identification efficiency, and making use of further optimised tracking algorithms.
<figure><img src="image_89.png" /><figcaption>**Fig. 79** Flavour tagging output in the full (solid) and fast (dashed) CLD simulation for charm (left) and gluon (right) multi-variate discriminants for various jet species</figcaption></figure>

<figure><img src="image_90.png" /></figure>

### 4.10.2 Jet flavour tagging

The first investigation of jet-flavour tagging performance with a full simulation of the CLD detector concept at FCC-ee is briefly presented here, and discussed in more details in Ref. [670]. As discussed in Sects. 4.4.1 and 4.5.1, jet-flavour tagging is essential for precision measurements of the Higgs couplings to quarks and gluons. A modified DELPHES configuration simulates the CLD detector geometry and resolutions in fast simulation, referred to as the CLD fast simulation. The full simulation uses the CLD conformal tracking (the baseline tracking reconstruction in CLD) to reconstruct charged particles. The PANDORA particle flow algorithm [668,669] is used for global event reconstruction, to build a particle-level view of the event.

Jets are clustered with the $k_T$ Durham algorithm [395] using $N = 2$ exclusive clustering on $e^+e^- \to ZH \to \nu\bar{\nu}jj$ events. The inputs to jet clustering are the reconstructed tracks and the neutral particles reconstructed by PANDORA. The jet flavour tagger [491] is then applied to assign each jet a probability of originating from a given flavour among seven possible categories: g, u, d, s, c, b, and τ. The tagger uses the information of all the input particles within a jet, including kinematic displacement, and particle identification properties. Adding direct vertex information (positions and invariant masses of secondary vertices) to the network does not improve performance, indicating that the model effectively learns vertexing from the track displacement, the charged particle content, and the kinematic variables.

The implementation of the algorithm in DELPHES and its performance are described in detail in Ref. [491]. Both fast and full simulation datasets are trained using identical input features. For illustration purposes, Fig. 79 shows the charm and gluon score, defined as the monotonic transformation of the tagging probability $\log(P/(1-P))$. The fast- and full-simulation output scores agree reasonably well. Additional jet tagging scores and performance figures can be found in Ref. [670].

It is observed that fast simulation features better performance across all tagging categories. For instance, in c-tagging, the efficiency of correctly identifying c-jets vs. misidentifying light-quark jets decreases from 80% in fast simulation to 70% in full simulation, for a 1% light quark misidentification rate. This loss in performance is under investigation but can be largely explained by track reconstruction inefficiencies in full simulation and a sub-optimal particle-flow algorithm parameter tuning.
<figure><img src="image_91.png" /><figcaption>**Fig. 80** Higgs boson mass determination using the recoil mass method in the dimuon channel in the full (red curves) and fast (black curves) simulation. Left: the $m_{\text{recoil}}$ distribution. Right: likelihood scan of the Higgs boson mass and corresponding precision</figcaption></figure>

This study shows that initial jet-flavour tagging performance in full simulation in CLD is sub-optimal. Future work should focus on improving CLD reconstruction to mitigate the identified limitations, such as low tracking efficiency at low momentum and large neutral hadron mis-identification probability. In addition, exploring the use of energy loss per unit length (dE/dx) information from the silicon tracker may provide additional particle identification capabilities, which can be useful for strange jet identification and can also provide additional exploitable information for charm, bottom, and tau tagging. Making progress in these areas is crucial to achieve the FCC-ee precision Higgs physics goals.

### 4.10.3 Higgs boson mass determination

Measuring the Higgs boson mass precisely at FCC-ee is important because it constitutes a limiting parametric uncertainty in the calculations of the branching ratios of the Higgs boson decay channels. Achieving a precision of 4 MeV makes this uncertainty negligible and leads to more accurate predictions of the Higgs boson decay properties. Also, knowing $m_H$ with a precision comparable to the Higgs boson natural width is the minimum requirement for potentially measuring the electron Yukawa coupling at $\sqrt{s} = 125$ GeV, the Higgs boson pole (Sect. 9.4).

The Higgs boson mass measurement prospects have been studied in full simulation using the CLD detector [65]. Track reconstruction and muon identification are the main event reconstruction features required for this measurement, which allows a straightforward comparison to fast simulation. The Higgs boson mass recoil method and the resulting sensitivity obtained with fast simulation in the dimuon and dielectron channels are extensively discussed in Sects. 4.3.1 and 4.6, assuming the IDEA detector performance with a gaseous drift chamber or, alternatively, a CLD-like silicon tracker. The driving experimental factor for the sensitivity is the track momentum resolution, ultimately limited by the multiple scattering induced by the beam pipe and tracker material. A gaseous tracking device is, therefore, preferred for this measurement. In this study, the recoil mass method has been applied to the CLD silicon tracking full simulation and compared to the CLD-like fast simulation results, as shown in Fig. 80. The recoil mass distribution obtained in $e^{+}e^{-} \to ZH \to \mu^{+}\mu^{-}H$ events is shown on the left panel; the resolution obtained with the full simulation is 15% worse than with the fast simulation. This small discrepancy is most likely explained by a small difference in the tracker material description and is currently under investigation. The right panel shows the corresponding precision on the Higgs boson mass determination, obtained from a likelihood scan using different mass hypotheses, yielding a precision of 6.4 MeV for full simulation, compared to 5.1 MeV in fast simulation.

This study shows that the full simulation of the CLD detector is available to perform a complete physics benchmark study. Further work is needed to understand the discrepancy in the observed precision between fast and full simulation, which may also point to shortcomings in the full event simulation and reconstruction. Extending the study to the dielectron final state,
which requires the implementation of photon bremsstrahlung recovery to fully reconstruct the final-state electron momentum, will be an important step forward in the understanding of the CLD detector performance in this important measurement.

### 4.10.4 Tau polarisation

The Z-pole running will provide an unprecedented sample of $2 \times 10^{11}$ clean $\tau^+\tau^-$ events and a unique opportunity for the determination of the tau polarisation, which is in turn very sensitive to the electroweak couplings of the Z boson ($\sin^2\theta_W$). The tau polarisation is defined as $P_{\tau} = (\sigma_+ - \sigma_-)/(\sigma_+ + \sigma_-)$, where $\sigma_+$ and $\sigma_-$ are the production cross sections of left-handed and right-handed taus, respectively. It can be expressed as a function of the electron and tau asymmetry parameters, $A_e$ and $A_{\tau}$, and it depends on the angle $\theta$ between the tau momentum and the electron beam in the centre-of-mass frame of the collision:

$$P_{\tau}(\cos\theta) = - \frac{A_{\tau}(1 + \cos^2\theta) + 2A_e \cos\theta}{1 + \cos^2\theta + 2A_e A_{\tau} \cos\theta} \quad (8)$$

The measurement of $P_{\tau}(\cos\theta)$ allows the determination of $A_{\tau}$ and $A_e$, as a test of the universality of the Z boson couplings to electrons and taus. Integrating over $\cos\theta$, one obtains $P_{\tau}^{\text{total}} = -A_{\tau}$. At LEP, the uncertainty in $A_e$ was statistically dominated [671], while for $A_{\tau}$ systematic and statistical uncertainties were at the same level. The large FCC-ee data samples and advanced detector capabilities are expected to significantly reduce these uncertainties. Assuming a factor 10 improvement in the systematic uncertainty with respect to LEP, the systematic uncertainty in $A_{\tau}$ could be as low as 0.02%, with $A_e$ having an even smaller uncertainty.

To confirm our expectations that this precision can be achieved, a full simulation study of the CLD detector is underway, focusing on tau reconstruction and identification. Tau identification relies on reconstructing charged hadrons and photons from $\pi^0 \to \gamma\gamma$ decays. About 65% of tau decays are hadronic, decaying to one or three charged hadrons accompanied by photons from $\pi^0$ decays. An algorithm based on the PANDORA particle-flow candidates has been developed to reconstruct the main decay modes: $\tau \to \pi\nu$, $\tau \to \rho\nu \to \pi\pi^0\nu$, and $\tau \to a_1\nu$. In parallel, a GNN method is being developed to improve the identification performance.

A first analysis limited to $Z \to \tau\tau$ events in which one of the taus decays leptonically in one hemisphere and the other decays hadronically in the other hemisphere has been performed [672].

Figure 81 shows the optimal variables for the three main configurations considered in the analysis. The first mode is designed to select $\tau \to \pi\nu$ decays. In this case the optimal variable is directly the energy fraction $x_{\pi} = E_{\pi} / E_{\text{beam}}$. The other two configurations correspond to the $\tau \to \rho\nu \to \pi\pi^0\nu$ channel with the reconstruction of either one or both of the $\pi^0$ decay photons. Here the optimal observable at LEP was defined to be

$$\omega_{\rho} = \frac{W_{+}(\theta^{*}, \psi) - W_{-}(\theta^{*}, \psi)}{W_{+}(\theta^{*}, \psi) + W_{-}(\theta^{*}, \psi)}, \quad (9)$$

where $W_+$ and $W_-$ represent the angular distributions of the $\rho$ decay products for different helicity states, and $\theta^*$ and $\psi$ are angles describing the decay products in the $\tau$ rest frame [673]. The reweighted $P_{\tau} = \pm 1$ signal templates are shown in comparison to the SM prediction. Additionally, the backgrounds coming from tau misidentification are also shown. No other backgrounds are considered at this stage. Further studies of the full simulation samples and optimisation of the reconstruction algorithm are in progress.

An analysis aiming to extract $A_{\tau}$ was performed using a log-likelihood fit of the optimal variable in the $\rho$ channel with two resolved photons. For an integrated luminosity of $17 \text{ ab}^{-1}$, corresponding to data collected by one FCC-ee experiment in a single year, the statistical uncertainty achieved is $7 \times 10^{-5}$. Future work includes refining the tau reconstruction algorithms, expanding the analysis to cover more decay channels and backgrounds, and performing a comprehensive extraction of the polarisation parameters across multiple $\cos\theta$ bins. In addition, focus will be placed on deriving explicit calorimeter requirements to reduce the dominant systematic uncertainties reflecting the $\pi^0$ and fake photon identification efficiencies as close as possible to (or below) the statistical uncertainties.

### 4.10.5 Summary of detector requirements

The FCC-ee detectors are expected to perform precise measurements across a wide range of physics processes, requiring optimised designs. This summary provides a simplified overview of the key requirements, but it is important to recognise that these specifications often involve trade-offs, which should and will be studied in full simulation. For instance, incorporating a
<figure><img src="image_92.png" /></figure>

<figure><img src="image_93.png" /><figcaption>**Fig. 81** Optimal variables used to extract the τ polarisation in three decay modes: π (top), ρ with one identified photon (bottom left), and ρ with two identified photons (bottom right)</figcaption></figure>

RICH or time-of-flight detector for particle identification may negatively impact the resolution of visible energy measurements. Identifying low-momentum muons effectively requires smaller detectors or a reduced magnetic field, which compromises the ability to accurately track high-momentum particles, impacting the overall physics programme. Finally, it should be noted that over-ambitious requirements could compromise the overall feasibility and the reliable operation of the detector systems. It is therefore of the utmost importance that the continued and creative effort to soften certain detector requirements with in-situ methods be consolidated and amplified.

An incomplete list of requirements is summarised in Table 13. For physics channels involving charm, bottom, and tau production, the beam-pipe is required to have a minimal material budget, particularly critical for processes such as the $B \to K^*\tau\tau$ decay. The vertex detector must achieve a spatial resolution of 3 µm or better and a material thickness below 1% of a radiation length, to improve the precision of certain important measurements, such as the measurement of $R_c$ at the Z pole or that of the branching fraction of the aforementioned $B \to K^*\tau\tau$ decay. The $\tau$ lifetime measurement requires the knowledge of the length scale of the vertex detector to be monitored with optical techniques with a precision of $\delta\tau_\tau < 10$ ppm. The
<table><caption>**Table 13** Summary of detector requirements</caption><thead><tr><th></th><th>Aggressive</th><th>Conservative</th><th>Comments</th></tr></thead><tbody><tr><td>Beampipe</td><td>X/X<sub>0</sub> &lt; 0.5%</td><td>X/X<sub>0</sub> &lt; 1%</td><td>B → K<sup>*</sup>ττ</td></tr><tr><td>Vertex</td><td>σ(d<sub>0</sub>) = 3 ⊕ 15 / (p sin<sup>3/2</sup> θ) µm<br>X/X<sub>0</sub> &lt; 1%<br>δL = 5 ppm</td><td>—</td><td>B → K<sup>*</sup>ττ<br>R<sub>c</sub><br>δτ<sub>τ</sub> &lt; 10 ppm</td></tr><tr><td>Tracking</td><td>σ<sub>p</sub>/p &lt; 0.1%<br>for O(50) GeV tracks</td><td>σ<sub>p</sub>/p &lt; 0.2%<br>for O(50) GeV tracks</td><td>δM<sub>H</sub> = 4 MeV<br>δΓ<sub>Z</sub> = 15 keV<br>Z → τμ</td></tr><tr><td>ECAL</td><td>t.b.d.<br>σ<sub>E</sub>/E = 3% / √E</td><td>σ<sub>θ</sub> &lt; 0.1 mrad<br>σ<sub>E</sub>/E = 10% / √E</td><td>δΓ<sub>Z</sub>(BES) &lt; 10 keV<br>Z → ν<sub>e</sub>ν<sub>e</sub> coupling,<br>B physics, ALPs</td></tr><tr><td>HCAL</td><td>Δx × Δy =<br>2 × 2 mm<sup>2</sup><br>δz = 100 µm,<br>δR<sub>min</sub> = 10 µm (θ = 20°)<br>σ<sub>E</sub>/E = 30% / √E<br>Δx × Δy =<br>2 × 2 mm<sup>2</sup></td><td>Δx × Δy =<br>5 × 5 mm<sup>2</sup><br>In-situ constraint with<br>dilepton/diphoton events<br>σ<sub>E</sub>/E = 50% / √E<br>Δx × Δy =<br>20 × 20 mm<sup>2</sup></td><td>τ polarisation<br>boosted π<sup>0</sup> decays bremsstrahlung recovery<br>Alignment tolerance for<br>δL = 10<sup>-5</sup> with γγ events<br>H → s̄s, c̄c, gg, invisible HNLs<br>H → s̄s, c̄c, gg</td></tr><tr><td>Muons</td><td>Low momentum (p &lt; 1 GeV) ID</td><td>—</td><td>B<sub>s</sub> → ν̄ν</td></tr><tr><td>Particle ID</td><td>3σ K/π<br>p &lt; 40 GeV</td><td>3σ K/π<br>p &lt; 30 GeV</td><td>H → s̄s<br>b → sν̄ν, ...</td></tr><tr><td>LumiCal</td><td>Tolerance δz = 100 µm,<br>δR<sub>min</sub> = 1 µm acceptance 50–100 mrad</td><td>—</td><td>δL = 10<sup>-4</sup> target (Bhabha)</td></tr><tr><td>Endcap acceptance</td><td>100 mrad</td><td>—</td><td>e<sup>+</sup>e<sup>-</sup> → γγ<br>e<sup>+</sup>e<sup>-</sup> → e<sup>+</sup>e<sup>-</sup>τ<sup>+</sup>τ<sup>-</sup> (c̄c)</td></tr></tbody></table>

momentum resolution in the tracking systems, $\sigma_p / p$, needs to be better than 0.2% for O(50) GeV tracks in order to achieve a precision of 4 MeV on the Higgs boson mass. Achieving a precision of O(10) keV on the Z width requires an exceptional track momentum resolution for such tracks, better than 0.1%. It also demands a precise knowledge of the BES, for which an angular tracking resolution $\sigma_\theta$ better than 0.1 mrad is needed. For flavour physics at the Z peak, where low momentum tracks are involved, a low mass gaseous tracker is advantageous since the momentum resolution is minimally affected by multiple scattering. Having a highly-efficient and pure tracking from 100 MeV to tens of GeV is of crucial importance to improve the dijet energy and mass resolution with particle-flow reconstruction.

Electromagnetic calorimetry with excellent energy resolution (few %) is required to improve the precision on the Z → ν<sub>e</sub>ν<sub>e</sub> coupling via the e<sup>+</sup>e<sup>-</sup> → ν<sub>e</sub>ν<sub>e</sub>γ process, on lepton flavour violating decays such as the Z → μe and τ → μγ decays, on decays of heavy flavoured hadrons to photons or to π<sup>0</sup> mesons, and on ALPs searches. The electromagnetic calorimeters must provide an energy resolution of $\sigma_E / E = 3\% / \sqrt{E}$ for aggressive scenarios and 10% / $\sqrt{E}$ for conservative ones, with spatial granularity between 2 × 2 mm<sup>2</sup> and 5 × 5 mm<sup>2</sup>. High granularity is crucial for τ polarisation measurements, boosted π<sup>0</sup> decays, and bremsstrahlung photon recovery. Additionally, alignment tolerances of $\delta z = 100$ µm and $\delta R_{min} = 10$ µm (measured at a 20° polar angle) are essential for a precise calibration of the acceptance for diphoton events or, equivalently, of the luminosity. For dilepton events, the definition of a polar angular cut of 10 degrees should be controlled with a similar accuracy of 8 µrad, in order to not limit the precision of, in particular, the leptonic decay width of the Z. The large dilepton and diphoton samples will be instrumental to ascertain in-situ the acceptance determination.

A good particle identification performance is required to achieve 3σ K/π separation up to 30 GeV and is essential for studying H → s̄s decays, to study rare decays such as b → sν̄ν, and, more generally, to maximise the FCC-ee flavour physics potential.

Hadron calorimeters with sufficient resolution and granularity are crucial for the success of the Higgs boson physics programme. In particular, the expected precision in the Higgs couplings to quarks and gluons is driven by the particle-flow
global event reconstruction capabilities and the visible mass resolution. The hadron calorimeters must feature a stochastic term of less than 30% in the aggressive scenario or less than 50% in the more conservative scenarios. The transverse granularity should range from 2 × 2 mm² to 20 × 20 mm². The luminosity monitors must have a spatial tolerance of, at least, $\delta z = 100$ µm and $\delta R_{min} = 1$ µm, with an acceptance range of 50–100 mrad. The detector must ensure optimal hermeticity. Requiring no gaps (and possibly a small overlap) between the LumiCal and the combined tracker plus calorimeter system sets the requirement for the tracker and calorimeter acceptance at 100 mrad. Forward coverage is necessary for the detection and identification of photons produced in the $e^{+}e^{-} \to \gamma\gamma$ process, which promises to provide an independent measurement of the luminosity. Processes involving the production of forward electrons, for example $e^{+}e^{-} \to e^{+}e^{-}\tau^{+}\tau^{-}(c\bar{c})$ might also benefit from even more forward coverage.

Finally, the muon systems will be used mainly to identify muons, given that their momenta will be optimally measured by the tracking system at FCC-ee. They should provide excellent identification for pion rejection and standalone momentum measurement for long-lived particle searches.

## 4.11 Outlook

Both software and analysis tools have matured during the Feasibility Study, and the common software framework (Sect. 8) was instrumental in developing a number of key physics case studies in view of extracting some of the necessary detector requirements. So far, most of the studies have been performed with a fast simulation of the response of a few detector benchmarks, similar to those presented in the Conceptual Design Report. Variations around these baseline concepts were applied to quantify the generic sensitivity dependence of key observables on the detector performance. In the next phase of the study, more explicit requirements will be obtained with a (full) simulation, reconstruction, and analysis strategy, optimised to the specific capabilities of the considered hardware, when the current R&D efforts start converging in concrete and definite detector proposals.

Matching experimental systematic uncertainties to the FCC-ee statistical precision will remain a critical objective of the entire physics programme. This perspective constitutes a superb opportunity for detector designers. It also continuously generates new and creative ideas from the analysts to control uncertainties from the data themselves: past experience has shown that a careful analysis of systematic effects and corrections almost always boils down to a statistical problem. This strategy will be generalised and will lead to a better precision for most observables, owing to the very large event samples expected at FCC-ee.

With 6 × 10¹² Z and 3 × 10⁸ W pairs, the leading challenge for the detector and analysis designs will continue to be the precision target with which the electroweak observables (Table 2) can be measured. Work on the hadronic, dilepton, and diphoton cross-section measurements has started, but much remains to be done, for example, to consolidate the in-situ acceptance determination method for lepton pairs and for the luminosity measurement with photon pairs and low-angle Bhabha scattering. The field of measurements at FCC-ee is huge, even when limited to the benchmark processes listed in Ref. [53]. An even stronger connection between theorists and experimentalists will help streamlining and refining the list of observables and the parameter space to be explored. Clearly, physics requirements will remain the primary driver in the design of the FCC-ee detector concepts, encouraging the exploration of novel technologies while remaining conscious of the trade-offs between competing performance goals and realism.

## 5 Machine-detector interface

The FCC-ee interaction region (IR) is designed to reach the highest luminosities at all centre-of-mass energies, from the Z pole to the $t\bar{t}$ threshold. This design is based on the crab-waist collision scheme, with nano-beams at the interaction point (IP), large horizontal crossing angle, and crab-waist sextupoles [674]. The Machine Detector Interface (MDI) of FCC-ee has a compact and complex design [18,675] that fulfils constraints imposed by the machine [18] and detector requirements (Sect. 4).

The main beam parameters are recalled in Table 14, for the four main operational centre-of-mass energies. In FCC-ee, the two beams circulate in different vacuum chambers, which merge at 1.3 m from the IP. The distance between the face of the superconducting final focus quadrupole (FFQ) and the IP (ℓ*) is 2.2 m, well inside the detector volume (Sect. 6). In addition to the optics constraints on the IR layout, physics considerations strongly advocate for hermetic detectors and for constraining
<table><caption>**Table 14** Key collider parameters for the FCC-ee IRs with 4 IPs. The bunch sizes at the IP in the (horizontal and vertical) transverse directions are denoted $\sigma_x^*$ and $\sigma_y^*$, respectively. The bunch length, $\sigma_z$, and the relative beam energy spread, $\sigma_\delta$, are different for non-colliding</caption><thead><tr><th></th><th>Z</th><th>W<sup>+</sup>W<sup>-</sup></th><th>ZH</th><th>t̄</th></tr></thead><tbody><tr><td>Beam energy (GeV)</td><td>45.6</td><td>80</td><td>120</td><td>182.5</td></tr><tr><td>Luminosity/IP (10<sup>34</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>145</td><td>20</td><td>7.5</td><td>1.41</td></tr><tr><td>Beam current (mA)</td><td>1294</td><td>135</td><td>26.8</td><td>5.1</td></tr><tr><td>Bunch number/beam</td><td>11,200</td><td>1852</td><td>300</td><td>64</td></tr><tr><td>Bunch spacing (ns)</td><td>27</td><td>163</td><td>1008</td><td>4725</td></tr><tr><td>σ<sub>x</sub><sup>*</sup> (μm)</td><td>9.5</td><td>21.8</td><td>12.6</td><td>36.9</td></tr><tr><td>σ<sub>y</sub><sup>*</sup> (nm)</td><td>40.1</td><td>44.7</td><td>31.6</td><td>43.6</td></tr><tr><td>σ<sub>z</sub> (mm) SR/BS</td><td>4.7/14.6</td><td>3.46/5.28</td><td>3.26/5.59</td><td>1.91/2.33</td></tr><tr><td>σ<sub>δ</sub> (%) SR/BS</td><td>0.039/0.121</td><td>0.069/0.105</td><td>0.102/0.176</td><td>0.151/0.184</td></tr></tbody></table>

bunches (determined by 'synchrotron radiation', SR) and colliding bunches (determined by 'beamstrahlung', BS). Non-colliding bunches are used for centre-of-mass energy calibration by resonant depolarisation, as explained in Sect. 9

the accelerator components within a cone of 100 mrad from the IP, along the z axis.<fnref n="25" /> These requirements demand a compact MDI design with tight space constraints.

The crab-waist scheme requires a large horizontal crossing angle of 30 mrad. The incoming beams point straight to the IP, while the outgoing beam trajectories are strongly bent from the IP, so that the beams can successfully merge back close to the opposite ring [676]. This scheme ensures that most of the synchrotron radiation (SR) generated at the IR magnetic elements does not strike the IR central beam pipe. The intense radiation emitted during the collision in the electromagnetic field of the opposite beam, known as beamstrahlung (BS), is mostly collinear with the outgoing beams, similarly to the SR [677]. Both the BS and SR photons are stopped at about 500 m downstream of the IP, in dedicated dumps [678]. To minimise the level of SR photons that reach the detectors, the closest bending magnet is located at more than 100 m from the IP and those located up to 500 m have a SR critical energy below 100 keV.

To counteract the beam rotation and deflection that would be caused by the simultaneous effects of the detector magnetic field of 2 T and the crossing angle, a compensating solenoid delivering a magnetic field of −5 T is placed at 1.23 m from the IP, cancelling out the longitudinal magnetic field integral along the z axis from the last focusing quadrupole to the IP. Consequently, the front face of the luminosity calorimeter (LumiCal), placed in front of the compensating solenoid, is only 1 m from the IP. The LumiCal is centred around the outgoing beam direction and measures the integrated luminosity from the rate of low-angle Bhabha events, $e^+e^- \rightarrow e^+e^-$. The first layer of the vertex detector must be placed as close as possible to the IP to optimise the precision of the primary and secondary vertex position determination, with direct impact on the efficiency and purity of flavour tagging algorithms. The smallest affordable distance is set by the central beam pipe radius of 1 cm. The total length of the vertex detector (1.86 m) is chosen to cover the angular region $|\cos\theta| < 0.99$. A lightweight mechanical structure is designed for its support. To avoid any material in front of the LumiCal, all other detector elements must be placed above 110 mrad with respect to the z axis.

An overall design of the interaction region is shown in Fig. 82. The next sections describe the main features of the MDI. A more detailed discussion can be found in Ref. [679].

## 5.1 Interaction region layout

The mechanical layout of the IR (Fig. 82) comprises an 18 cm long central beam pipe with a 10 mm internal radius, a pair of ellipto-conical beam pipes about 1064 mm long on either side, a silicon vertex detector covering the radial range from 13.7 to 315 mm, and the LumiCal at 1074 mm from the IP, 190 mm thick, covering the angular range between 50 and 134 mrad. All these elements are held in place by a lightweight carbon fibre and honeycomb rigid structure support tube, which allows the

<footnote n="25">²⁵ The coordinate system of the detector has the origin centred at the nominal collision point. The z axis is defined as the bisector of the axes of the incoming and outgoing beams, ideally in the direction of the axis of the experiment solenoid. The x axis is in the plane subtended by the two beams and pointing away from the centre of FCC. In this way, the positron beam is travelling towards positive values of z (mainly) and x (subordinately). Perpendicular to the (x, z)-plane, the y axis points upwards. The polar angle, $\theta$, is then measured with respect to the z axis and the azimuthal angle, $\phi$, with respect to the x axis in the (x, y) plane. The radial coordinate, $r = \sqrt{x^2 + y^2}$, is the distance from the z axis.</footnote>
**Fig. 82** Layout of the interaction region. The support tube allows the integration of the luminosity calorimeter (LumiCal) and the vertex detector. The three segments of the final focus quadrupoles (QC1) are shown with the screening and compensating solenoids

<figure><img src="image_94.png" /></figure>

<figure><img src="image_95.png" /></figure>

**Fig. 83** Left: the central chamber in AlBeMet162 with its cooling inlets and outlets, and its internal gold coating layer. Right: chamber cross section and zoom on the cooling channel for the paraffin flow

<figure><img src="image_96.png" /></figure>

**Fig. 84** Ellipto-conical vacuum chamber

overall integration before the insertion in the experiment [680]. The vacuum chambers are made of AlBeMet162, an alloy of Aluminium (38%) and Beryllium (62%), chosen for its high elastic modulus and low density.

The central beam pipe has a double layer structure, cooled by liquid paraffin flowing between the two layers, as displayed in Fig. 83. A cross-sectional view of the central beam pipe and of the cooling manifolds, also made of AlBeMet162, is shown in Fig. 83 as well. The double-layer structure is made of two concentric cylinders, each one 0.35 mm thick and assembled with 1 mm gap for the paraffin flow, thus bringing the effective diameter of the central beam pipe and its cooling layer to 23.4 mm. An internal 5 µm coating layer of gold ensures a good electrical conductivity to minimise the beam heat load to nearly 60 W [681] and to shield the vertex detector from residual high energy SR photons.

The ellipto-conical vacuum chamber, shown in Fig. 84, extends between 90 and 1154.5 mm from the IP. Following a short transition from the central chamber, its thickness remains at a constant value of 2 mm. Water flows in the cooling channels to extract an expected heat load of about 130 W; an asymmetric design is needed to match the angular acceptance of the luminosity calorimeter.
<figure><img src="image_97.png" /><figcaption>**Fig. 85** Left: material budget of the beam pipe, in per cent of a radiation length, as a function of the cos θ polar angular. Right: distribution of the material budget of the beam pipe in the transverse plane, in the</figcaption></figure>

0 < θ < 0.2 rad angular range, at the entrance of the LumiCal. The red lines represent the LumiCal angular coverage

<figure><img src="image_98.png" /><figcaption>**Fig. 86** Layout of the vertex detector cooling cones assembly, together with the main elements to be integrated around it</figcaption></figure>

A thermo-structural analysis has been performed to calculate the temperature distribution, stress, strain and displacement of the beam pipes. The maximum temperature of the central chamber reaches 29°C, cooled with paraffin entering at 18°C, while it amounts to 50°C for the conical chamber cooled with water entering at 16°C. The maximum stress has been calculated considering the constraint configurations of a cantilevered support, resulting in a maximum displacement of 0.5 mm and a maximum stress ten times lower than the AlBeMet162 yield strength (193 MPa). The resulting material budget distribution for the vacuum chamber is shown in Fig. 85 as a function of the polar angle. The material encountered by a particle produced at normal incidence corresponds to 0.68% of a radiation length ($X_0$).

Several vertex detector designs are described in Sect. 6. The integration study performed here is based on the engineered version currently adopted by the IDEA concept (Sect. 6.5). This version features two main subsystems, of active elements based on 50 µm thick ‘Monolithic Active Pixel Sensors’: an inner vertex detector, composed of three barrel layers at a radial distance between 13.7 and 35.6 mm, covering an angular acceptance of about $|\cos\theta| < 0.99$; and an outer vertex detector, composed of two barrel layers at 13 and 31.5 cm, and three disks on either side of the IP.

The inner vertex detector is cooled by flowing gas (air or helium) through a system of carbon fibre cones, shown in Fig. 86, that forces gas convection inside the detector volume. The same carbon fibre structure supports the power and readout
<figure><img src="image_99.png" /><figcaption>**Fig. 87** Longitudinal section of the beam pipe and inner vertex layers. The dark gray object is the conical support of the vertex detector, which is supported by the conical beam pipe. The inlet/outlet paraffin of the</figcaption></figure>

central chamber cooling manifolds are visible at the edge of the support cone. The orange structures represent the cooling cones

circuits. The inner vertex detector is mounted on top of the conical vacuum chamber by means of two thin peek-based rings, anchored on either side at about 170 mm from the IP and soldered on a conical carbon fibre structure supporting three layers of silicon vertex ladders, also integrating the central beam pipe cooling circuits (Fig. 87). The outer vertex detector and disks are mounted on the inner surface of the support cylinder, by means of insert rings, and cooled by water pipes.

The luminosity monitor is described in Sect. 6.13.1. It consists of two cylindrical devices, placed at about 1 m away from the IP, on either side of the IP. Each device covers radii between 54 and 115 mm around the outgoing beam, for the sensitive part, plus a service region from 115 to 145 mm, which houses the electronics readout, cables, and cooling. In order to achieve the desired accuracy of $10^{-4}$ in the measurement of the luminosity, the calorimeter has a stringent requirement on the knowledge of its boundaries. In particular, the relative positioning of the two sides along the z axis needs to be known with a precision of $\pm 100$ µm and, once assembled, the calorimeter must be a rigid hollow cylinder. This is guaranteed by dimensioning the bellows of the beam pipe such that their external dimensions are smaller than the internal calorimeter bore and such that it could possibly slide inside. The beam pipe has been carefully designed to minimise the material effects on particles reaching the luminosity calorimeter. In fact, the material budget ranges from approximately 0.07 $X_0$ to 0.5 $X_0$ (Fig. 85). The maximum values, driven by the AlBeMet cooling manifolds, are at a safe distance from the 50 mrad LumiCal acceptance cone. The design of the cooling manifolds has been optimised to limit the effects of showers originating from electrons scattering in the beam pipe. Ongoing studies show that the impact on the luminosity measurement is limited.

The IR magnet system [18] includes the final focus quadrupoles, the compensating solenoid, the screening solenoid, and magnetic correctors for IR tuning. The limited space available constitutes a challenge to the design of the IR magnet system, currently envisaged to fit in an envelope of 100 mrad around the z axis. The system design includes a cryostat partially located inside the detector, surrounding the compensating solenoid and the first final focus quadrupole (QC1), which is itself embedded in the screening solenoid (for the part inside the detector). It also includes the second final focus quadrupole (QC2), starting 0.30 m upstream of QC1.

## 5.2 Integration and alignment

The accelerator and detector components that are placed within $\pm 1.5$ m from the IP are mounted in a single rigid structure, which provides a cantilevered support for the pipe and avoids loads on the thin-walled central chamber during assembly. This rigid structure also supports the LumiCal and the vertex detector (Fig. 88). The support tube is an empty cylindrical structure made of a 4 mm honeycomb structure interleaved within two 1 mm thick carbon fibre walls. It is longitudinally split in two halves and is complemented by two aluminium flanges and two endcaps that support the LumiCal and the beam pipe. Six aluminium ribs are fixed inside the tube in order to support the outer vertex layers.

A structural analysis, performed to calculate the stress and displacement of each part of the support tube taking into account the estimated weights of detector elements, including services material, shows that the structural resistance is safely respected.
<figure><img src="image_100.png" /><figcaption>**Fig. 88** Support tube showing the beam pipes and bellows, the vertex detector with air-cooling cones, the luminosity detector, and, in brown, the vacuum chambers internal to the cryostat (not shown)</figcaption></figure>

The insertion of the support tube in the detector is foreseen either with a few sleds or with longitudinal rails fixed to its external surface. A possible option could then be to slide these sleds (rails) inside hollow carbon fibre rails, permanently fixed on the inside wall of the tracker to guarantee the structural rigidity while inserting the support tube. The corresponding calculations and simulations are beyond the scope of this feasibility study.

The alignment and monitoring device [682] is composed of three main subsystems:

- The deformation monitoring system is capable of monitoring the shape of the screening solenoid support, which is then used as a reference [683]. It exploits in-line multiplexed and distributed frequency scanning interferometry (IMD-FSI) [684] to monitor sections of optical fibres firmly installed on the inner surface of the screening solenoid support. This system occupies no more than $5 \text{ cm}^3$ within the assemblage and requires an interface with the endcap of the first final focus quadrupole.

- At the end of each fibre used in the deformation monitoring system, a mirror is installed to redirect the laser beam towards the centre of the assemblage, targeting the final focusing quadrupoles, the beam position monitors (BPMs), the LumiCal, and any other component that requires position monitoring. This subsystem is very similar to the FSI heads installed on the low-$\beta$ quadrupoles in the HL-LHC MDI [685]. The corresponding distance measurements monitor the position of the inner components relative to the cryostat.

- Finally, to ensure the alignment of both sides of the MDI with respect to each other, a long-range alignment system is foreseen, also based on FSI but with a different optical setup to enable longer-distance measurements.

A dense network of such measurements around the detector provides a continuous link between the endcaps of the QC1 on each side of the MDI, which serve as the reference surface for the cylinder monitored by the deformation system. Reference points are placed on the supporting feet of the detector, easy to access for a technician or a robot, and used to link to the cavern survey network and the rest of the accelerator.

A network of Frequency Scanning Interferometry is proposed for the alignment of the inner tracker. This network will be implemented similarly to what has been done for the ATLAS SemiConductor Tracker [686], but with the latest version of the technology, more compact and precise. This system also allows the measurement of the positions of the LumiCal and of the beam pipe relative to the FFQs.

### 5.3 Maintenance and detector opening

Periodic (or exceptional) detector maintenance requires, in general, access to the internal subsystems, known as 'opening the detector'. The design of the MDI region must carefully anticipate the intertwined requirements from the civil engineering, the machine, and the detector. Three opening scenarios, with their own advantages and drawbacks, have been examined.

1. In a first scenario, the two endcap calorimeters are moved along the z axis to disengage them from the barrel, as displayed in the left panel of Fig. 89, by a couple metres if only access to the central tracker is needed and by up to 7 m if the tube supporting the LumiCal, the vertex detector, and the central vacuum chamber requires extraction (and re-insertion). The mechanical stability of the final focus quadrupoles requires rigid supports, as close as possible to the detector boundaries. These supports, if fixed, would make the longitudinal opening of the detector endcaps impossible. Removable supports would then need to be designed to allow safe removal of the FFQs, and a quick re-installation and alignment following the
<figure><img src="image_101.png" /><figcaption>**Fig. 89** Longitudinal (left) and short longitudinal plus transversal endcap (right) detector opening</figcaption></figure>

access to the inner detectors. In this scenario, in addition to the re-alignment issue, the beam-pipe vacuum is broken. As the removal of the FFQs from inside the detector would first require the removal of other machine elements just behind them, this scenario can be envisaged only for medium or long machine shutdowns (several weeks or months), as done with the BELLE II detector at SuperKEKB.

2. A second option involves vertically splitting the detector endcaps, allowing opening without removing the FFQs. In this scenario, the two split endcaps are first moved longitudinally for about 2 m and then moved from the beamline in the transverse direction, as shown in the right panel of Fig. 89. The FFQs could stay cold, with the beam pipe under vacuum. This scenario could be very effective in the case of a quick access. The only constraint from the machine side is to keep all the services needed by the FFQs (supports, vacuum, cryogenics, powering) in the shadow of the FFQs, i.e., inside the detector forward acceptance cone. The main drawback of such a vertical splitting is that it implies a complete (and less precise because based on a smaller number of events) recalibration of the calorimeter angular acceptance after each opening.

3. A third, currently preferred, possibility consists of moving the complete detector along the *x* axis, away from the beamline. As in the first scenario, this requires a disconnection of the internal FFQs from the rest of the machine, but allows them to be kept inside the detector. The FFQs can then be easily removed without touching any other machine element, before proceeding to a longitudinal opening of the endcaps without any obstacle. The detector integrity is preserved and, although the beam vacuum is broken and a re-alignment of the FFQs is needed, relatively short access periods (few weeks) can be envisioned. As the FCC-ee detectors have a diameter of typically 12 m, this scenario requires enough transverse free space on one side of the detector, which is currently not available in the two small experiment caverns (Sect. 7). Another location for the balconies (in green on Fig. 122, Sect. 7) may have to be found in these caverns, e.g., by placing all of them on the other side of the detector, and a small additional alcove (typically 25 m long and a few metres deep) might also be needed, depending on the exact transverse size of the detector. Designing the small caverns so that their axis can be transversely displaced from the beamline by a few metres, if compatible with the size of the specialised FCC-hh detectors (Sect. 7), would alleviate the need for such an alcove.

Technical mitigation solutions for the drawbacks of these three scenarios will be investigated in detail during the next phase of the study.

## 5.4 Beam-induced backgrounds in the detectors

The beam-induced backgrounds in the detectors arise from two categories of sources: those generated by processes involving only a single beam, and those generated by the interactions between the two beams at each IP, usually called luminosity backgrounds.

Although the collimation system and absorbers remove the bulk of the particles produced by single beams (electrons/positrons and photons) before they can hit the detectors, some background may remain because the particles can scatter off them. Elastic and inelastic interactions of the beam with the molecules of the residual gas produce scattered particles, deviating from the original orbits, as well as photons from inverse-Compton scattering. Showers may also be produced for a very small fraction of events.

Intra-beam particle interactions, also known as Touschek scattering, are negligible at FCC-ee, given that they are suppressed by a large energy factor in comparison to lower energy colliders, such as SuperKEKB and DAΦNE. Synchrotron radiation [687]
<figure><img src="image_102.png" /><figcaption>**Fig. 90** Number of IPC particles produced for each FCC-ee bunch crossing, as a function of their transverse momentum and polar angle, for the Z (left) and t̄ (right) working points. The area limited by the red lines represents the acceptance of the vertex detector</figcaption></figure>

has been simulated with BDSIM [688] and the GEANT4 [689] toolkit. The bulk of SR is emitted almost collinearly with the beam, and the IR optics keeps it away from the detector sensitive layers. Magnet misalignments, imperfections, and beam tails, however, may cause SR to reach the detector. Studies are ongoing to optimise the design and the position of dedicated masks (a few metres upstream of the detector) in order to minimise the effects of SR in the detector.

A variety of processes such as space-charge effects, beam instabilities, interaction with residual gas, intra-beam scattering, magnet misalignments, and magnetic field errors can lead to the population of a beam halo, potentially leading to beam particle losses. These particles are mostly intercepted by the collimators located in the dedicated section of the collider [18], following the approach used for LHC [690]. The relevant studies have been performed with the XSUITE-BDSIM simulation tool [691,692]. The vast majority of the beam halo losses in the MDI are intercepted by the SR collimators, so that no losses are observed beyond the last SR collimators before the IPs, in all cases. The background contribution from beam halo particles that leak from the beam halo collimation system is, therefore, not expected to be an issue. Tertiary collimators have been included upstream of the SR collimators, strongly further reducing the effects of residual losses.

Beam-gas interactions depend on the residual gas pressure profile in the rings and on the outgassing materials inside the vacuum chambers. Simulations of the beam-gas interactions have been performed with MOLFLOW+ [693], with a residual gas pressure profile resulting from 1 h beam conditioning at a full nominal current of 1.27 A at the Z pole. Within ±500 m from the IP, the gas composition is 85% hydrogen, 10% carbon monoxide, and 5% carbon dioxide, at an average pressure of 10⁻¹¹ mbar and spikes of 10⁻⁸ mbar in the vicinity of the SR absorbers. This vacuum level, conservatively estimated at the beginning of the machine commissioning, is expected to progressively improve over time. Preliminary results obtained with FLUKA indicate that the dose and fluence due to beam-gas interactions within ±500 m from the IP in the Z pole run are not the leading contributors: for a pressure profile resulting from only one hour of beam conditioning, the estimated dose and fluence in the innermost vertex detector layers are as low as 3 kGy/year and ~ 7 × 10¹¹ cm⁻²/year, further decreasing with increasing conditioning.

The most relevant luminosity background arises from incoherent pairs creation (IPC) [694], a class of interactions between two photons emitted by a single electron and a single positron at the IP, $e^+e^- \rightarrow (e^+e^-)e^+e^-$. The simulation of these backgrounds has been performed with GUINEAPIG [695] and interfaced to KEY4HEP (Sect. 8). The resulting $e^+e^-$ pairs are predominantly produced in the forward direction, with small transverse momenta. Although the production cross section is large, only a small fraction of these particles are in the detector acceptance, as shown in Fig. 90 for the Z-pole and t̄ runs; a few others hit the region where the two beam pipes bifurcate (crotch) and scatter off the detector.

The largest effect occurs in the Z-pole run, given its instantaneous luminosity, the highest of the FCC-ee programme. In the innermost layer of the IDEA vertex detector, the hit rate reaches about 70 MHz/cm², for an average of 5 pixels per cluster,
<figure><img src="image_103.png" /><figcaption>Fig. 91 Total ionisation dose (top) and 1 MeV $n_{\text{eq}}$ fluence (bottom) in the interaction region of the IDEA detector</figcaption></figure>

which imposes a rather stringent requirement on the readout electronics of the order of 200 MHz/cm² with, conservatively, a safety factor of 3. In the IDEA drift chamber, where the pairs created by several successive bunch crossings need to be integrated during the drift time (400 ns), the occupancy is about 7%. Incoherent pairs may also reach larger radii and their effects have been studied for the ALLEGRO liquid Argon electromagnetic calorimeter. The first layers of the calorimeter are the most affected, but the effect can be largely mitigated by setting a minimum readout energy threshold of 20% of the energy released by a minimum ionising particle, resulting in an occupancy of 0.03% in the barrel and 0.2% in the endcaps.

Radiative Bhabha (RB) scattering, $e^{+}e^{-} \rightarrow e^{+}e^{-}\gamma$, is another important luminosity background that may severely affect the superconducting FFQs. Radiative Bhabha events were generated with BBBREM [696] and GUINEAPIG, and processed by FLUKA [697–699]. Their study shows that a substantial annual dose of power is deposited in QC1, which necessitates a tungsten shielding of approximately 2 mm around the beam pipe to protect the superconducting magnets. This shielding decreases the annual dose power deposition peak value to about 3 MGy (a reduction by an order of magnitude) and the deposited power density to about 1.5 mW/cm³. These values are compatible with the design dose limit of 30 MGy for the full magnet lifetime and the quench limit of 10–20 mW/cm³ adopted at the LHC. Other radiation sources contributing to the energy deposition in QC1, like beam-gas scattering, incoherent pair creation or synchrotron radiation, still need to be carefully evaluated at the FFQs. They are expected, however, to be much more benign than radiative Bhabha events. The integration of this shielding with the design of QC1 will be performed in the next phase of the study.

The total ionisation dose (TID) and the 1 MeV neutron-equivalent ($n_{\text{eq}}$) fluence from the main radiation sources in the Z-pole operational mode (i.e., RB and IPC) have been estimated in the IDEA interaction region with FLUKA, and are displayed in Fig. 91. The peak annual dose and fluence in the inner vertex detector are at the level of a few tens of kGy and a few $10^{13} \text{ cm}^{-2}$, respectively, for the innermost layers. These numbers are compatible with most of the technologies currently under consideration for the monolithic active pixel sensors. At higher centre-of-mass energies, the TID and fluence are expected to be smaller, given the reduced instantaneous luminosity.

## 5.5 Implementation tests and prototyping

Design and simulation studies must be complemented by actual prototyping and implementation tests, to develop dedicated setups and evaluate technical solutions to the integration challenges. The following activities are proposed or planned; some are already ongoing.
- The realisation of a full scale mock-up of the beam pipes of the IR is being carried out at INFN (LNF and Pisa). This study includes the integration of the vertex and LumiCal detectors in the support tube, with particular emphasis on the paraffin and water cooling of the pipes and on the air cooling of the inner vertex detector. This activity is fully integrated with the R&D carried out in the ECFA DRD8 Working Group [700].

- The experimental validation of the alignment system of the FFQ is ongoing with the FSI system at CERN, using a 1:2 mock-up of the beam pipes and cryostat.

- The design of the compensating solenoid and the production of QC1 corrector prototypes are proposed at the Brookhaven National Laboratory (BNL), leveraging their 'direct winding technology' [701].

- The fabrication of a High Temperature Superconducting (HTS) magnet is proposed by LAPP Annecy for the final quadrupole QC1, together with its integration with the water-cooled beam-pipe.

In summary, a lot of progress has been made in the past years. The layout has been significantly improved by reducing the material budget in front of the LumiCal and also through a careful design of the cooling manifolds, re-engineered in AlBeMet162 material. The feasibility of the inner vertex detector cooling has been validated and the routings of its services have been designed and integrated with those of the beam pipe. More studies are on the way to optimise the design and confirm its validity experimentally. A careful analysis of the detector maintenance and FFQ integration has been performed, leading to the identification of the main optimisation issues to be tackled during the next phase of the study. An alignment strategy has been outlined, based on the technology planned for HL-LHC. Finally, the study of the beam-induced backgrounds and the evaluation of the main radiation doses and fluences in the IR region led to the development of mitigation measures, like the design of the collimation system and SR shielding.

## 5.6 Outlook

Studies carried out during the Conceptual Design Study and the Feasibility Study have converged to a baseline MDI design with satisfactory overall performance. Further investigations to consolidate this design and to improve its performance will be performed. Refinements will also be needed when actual detector proposals are finalised.

Several options are currently considered for the QC1 cryostat design. Most importantly, a choice will be made for the operating temperature of the cooling scheme, among three options: 1.9-2.1 K in pressurised He II; 4.5 K for supercritical He; or 10-20 K for He gas forced flow. Another important design decision concerns the dimensions of the cryostat, which currently covers a cone of 100 mrad around the z axis. While the forward acceptance of the detector calorimetry would benefit from a smaller cryostat, the operability of the collider, and the integrated luminosity, would advocate for more relaxed dimensions, calling for a complete optimisation study.

In the baseline MDI design, the detector solenoid field of 2 T is 'locally' compensated with -5 T solenoids placed within $\pm e^*$ around the IP. The performance of an alternative 'non-local' scheme, with -2 T solenoids positioned outside the detector at about ±20 m from the IP [702], will be studied and compared to that of the baseline. First observations show that the non-local scheme might achieve a better residual vertical emittance, opening the possibility to increase the strength of the detector solenoid field to 3 T. An adverse consequence of the non-local scheme seems to be a higher spin depolarisation, so that further investigations are needed to preserve the possibility of beam-energy calibration with resonant depolarisation (Sect. 9).

The main beam-induced background sources have been studied during the Feasibility Study, with the exception of the injection backgrounds and thermal photons, which will have to be included. The studies of the impact of all backgrounds in the data taking and in the physics performance will be finalised, and proposed mitigation solutions will be consolidated. To this aim, the FLUKA software interface between the simulation of the machine backgrounds and the simulation of the detector will be refined. A deeper understanding will be sought of the synchrotron radiation background mitigation, in particular the positioning of the SR masks or the tolerances of the machine elements that might impact the detectors, such as the alignment of the FFQs, the collimators, and the vacuum system. More generally, the effectiveness of the shielding elements to protect the detector and the superconducting FFQ magnets will be thoroughly evaluated.

As the design of the sub-detectors (e.g., vertex detectors, luminometers, superconducting pipes, supporting structures) and of the accelerator components (e.g., beam position monitors, vacuum pumps, remote vacuum connections, cryostat supporting structures) get finalised, their integration, as well as the impact on the maintenance and assembly of the interaction region, will be established in more detail. Finally, methods for the alignment, the opening, and the maintenance of the detector and accelerator elements will be developed, and possible consequences on the cavern dimensions will be evaluated.
# 6 Detector concepts and systems

A thorough discussion of a possible experimental apparatus that would operate at FCC-hh can be found in Ref. [703] and is very briefly summarised in the next section. Here, only detectors and subsystems currently being studied or envisioned for FCC-ee are addressed.

The development of detectors for FCC-ee represents a challenge that drives technological developments beyond the present state of the art. The main challenge arises from the richness of the physics programme and the large number of events, especially at the Z pole run. Matching the experimental accuracy to the statistical precision and the detector configuration to the variety of channels and discovery cases, lead to performance requirements (Sect. 4) that exceed those studied for TeV-class linear colliders over the past decades. To preserve the low emittance of the FCC-ee beams during the Z-pole run, the strength of the detector magnetic field crossed by the beams under an angle of 15 mrad is limited to 2 T (Sect. 5). This constraint calls for larger tracking volumes that can, in part, be compensated by shallower calorimeter systems, given the FCC-ee emphasis on the lower energies. In addition, with continuous bunch crossings at rates of up to 50 MHz, the front-end electronics needs to be permanently powered and, given the much higher bandwidth of data to be recorded, the instantaneous power (and cooling) demand is also higher than in cases where power pulsing can be applied. Meeting these demands while preserving the material budget of the tracking detectors, the compactness of the calorimeters, and therefore their performance, requires further developments. In order to fully exploit the excellent precision potential, in particular at the Z resonance, events must be recorded at rates of about 100–200 kHz, comparable to first-level trigger rates in the upgraded HL-LHC detectors.

These challenges motivate the development of new detector technologies, followed up in the framework of newly created CERN-anchored detector R&D Collaborations (DRDs). This framework aims at maximising synergies with parallel or consecutive developments ('stepping stones'), such as the development of an ultra-lightweight Si-based tracking system for the ALICE experiment. Such innovative R&D efforts towards FCC-ee will be intensified in the coming years, as the major detector upgrades of the ATLAS and CMS multi-purpose experiments come to an end.

This section presents an overview of the currently proposed technologies for detector systems, and the status and plans for R&D. Detector concepts that, in this context, denote consistent and preliminary arrangements of detector systems in a full experiment, informed by engineering considerations and realised in a simulation software suite, are also introduced. These detector concepts may or may not become proposals for future FCC-ee detectors, as the outcome of the ongoing and future innovative R&D efforts might well motivate new concepts and change the overall landscape very significantly. Detector concepts are, however, indispensable to guide R&D efforts, to reveal typical system integration constraints, to optimise the design and technology choices of detector systems, and to study their impact on the overall physics performance in the interplay of all components, e.g., for flavour tagging or particle-flow reconstruction.

Some performance studies require a detailed implementation of the detector characteristics in full GEANT4 simulations. The related software developments have, therefore, been a strong focus of the detector concept work in the feasibility study, and will have to intensify during the next phase of the study. In order to optimise the use of still sparse human and financial resources, and to maximise interchangeability, the software framework KEY4HEP (Sect. 8) is used throughout the FCC detector studies. For example, the studies for the integration of the vertex detector and beam pipe into the interaction region (Sect. 5) are to be considered a generic proof-of-principle for the machine-detector interface of all four experiments. In general, the combination of technologies for tracking, calorimetry, and particle identification is still very much open. For example, the ALLEGRO concept considers both gaseous and silicon-based tracking. The KEY4HEP framework [704] allows for different combinations in a 'plug-and-play' approach, without duplicating the sub-detector developments and simulation implementations for each concept.

The presently considered detector concepts (CLD/ILD, IDEA, and ALLEGRO) are briefly described, before a discussion of the sub-system developments, within or beyond these concepts. The integrated luminosity determination is discussed at the end of the section.

## 6.1 Detector concepts

A fundamental difference among the current concepts derives from their different approaches to calorimetry, as this choice profoundly impacts the overall detector architecture. All concepts aim for a calorimeter segmentation that allows for particle separation within jets, and consequently for particle-flow reconstruction, but with different balances between spatial and energy resolutions. Hadron-shower tracking demands the full calorimeter to be inside the coil, whilst such an arrangement is at variance with the larger depth required by fibre-based dual read-out techniques, or with the cryogenic infrastructure requirements of liquid noble gases.
<figure><img src="image_104.png" /><figcaption>**Fig. 92** The CLD concept detector: end-view cut through (left) and longitudinal cross section of the top right quadrant (right). The detector has an overall diameter of 12.0 m and an overall length of 10.6 m</figcaption></figure>

The coordinate system used for the description of detector concepts is as follows. The *z* axis is defined as the bisector of the axes of the incoming and outgoing beams. The *x* axis is in the plane subtended by the two beams and pointing away from the centre of the FCC-ee ring. In this way, the positron beam travels towards positive values of *z* (mainly) and *x* (subordinately). Perpendicular to the (*x*, *z*) plane, the *y* axis points upwards. The polar angle, *θ*, is measured with respect to the *z* axis and the azimuthal angle, *φ*, with respect to the *x* axis in the (*x*, *y*) plane. The radial coordinate, $r = \sqrt{x^2 + y^2}$, is the distance from the *z* axis.

## 6.2 The CLD and ILD detector concepts

The CLIC-like detector CLD [618], illustrated in Fig. 92, is an adaption to the experimental conditions at FCC-ee of the CLIC detector model [625,705], itself developed from the ILD [624] and SiD [624] concepts, originally designed for linear colliders. Both ILD and SiD, and consequently CLD, have a design driven by very-high-granularity calorimeters. They feature electromagnetic and hadron calorimeters (ECAL and HCAL), both located inside a solenoidal coil, to ensure continuous topological reconstruction of shower evolution. To achieve a fine 3D-imaging segmentation, their front-end read-out electronics is embedded in the active volumes of the sandwich structures. The CLD ECAL has tungsten as the absorber and is read out with silicon sensors, while the steel HCAL has scintillator tiles directly coupled to silicon photo-multipliers (SiPMs) as the active medium. These technologies were originally developed by the CALICE Collaboration [706] and are presently being applied at large scale in the CMS high-granularity calorimeter (HGCAL) upgrade [707].

With respect to the original CLIC detector, CLD has an interaction region adapted to the larger crossing angle and the more invasive machine-detector interface (Sect. 5), a bigger tracking volume to compensate for the magnetic field limitation of 2 T, and the calorimeter depth adapted to the FCC-ee energy range. The tracking system of CLD features a silicon pixel vertex detector (VXD) and a silicon tracker.

A full simulation suite, including full-event reconstruction, already exists and provides realistic estimates of full-detector performance figures of merit, such as jet resolutions, flavour-tagging efficiencies and purities, background levels, etc. Recently, to provide additional handles on particle identification, a novel ring-imaging Cherenkov system, ARC [640–642], has been suggested as an extra barrel layer between the tracker and the ECAL; the tracking system has been correspondingly re-optimised, on the basis of full simulations.

The ILD detector concept is also being studied for a tentative adaptation to FCC-ee. It is similarly based on highly granular calorimeter technologies with embedded electronics, including silicon pads, monolithic active pixel sensors (MAPS), scintillator strips for the ECAL, and scintillator tiles and various gaseous technologies (RPCs, MPGDs) for the HCAL. Like in the CLD concept, both sections are placed inside the magnet coil. The major distinction with CLD is that ILD focuses on a radically different tracking choice, a gaseous time projection chamber (TPC), favoured for its transparency and particle identification capabilities, complemented by a surrounding silicon layer to maximise momentum and timing precision.

The long signal collection times of a TPC, together with the beam-induced background, which scales with the high bunch crossing rate, raises the question of how reliably a TPC can be operated at FCC-ee, in particular during the Tera-Z run. This issue is currently being investigated with full-simulation studies using a plug-and-play combination of CLD and ILD,
**Fig. 93** Longitudinal cross section of the top right quadrant of the IDEA concept detector. The LumiCal, the compensating solenoid, and the final-focus quadrupole are displayed along the z axis, below the 100 mrad acceptance line

<figure><img src="image_105.png" /></figure>

which merges the interaction region and inner tracking system of CLD with the ILD TPC and calorimeters. First results [708] indicate that there are distortions due to space-charge effects in the centimetre range. Work is ongoing to mitigate these effects and possibly demonstrate the feasibility of reaching the performance goals in the Z-pole run conditions.

## 6.3 The IDEA detector concept

The Innovative Detector for $e^{+}e^{-}$ Accelerator (IDEA) [709–711], illustrated in Fig. 93, is a detector concept specifically designed for FCC-ee, introduced during the Conceptual Design Study [11]. It is based on a silicon pixel vertex detector, a gaseous central tracker, and a crystal-based electromagnetic calorimeter placed inside a superconducting solenoidal magnet, surrounded by a dual-readout fibre calorimeter and completed by a muon detection system placed in the iron yoke that closes the magnetic field.

The tracker is composed of a silicon pixel vertex detector, a large-volume extremely-light short-drift wire chamber for central tracking and particle identification, and a surrounding wrapper made from silicon micro-strip sensors for improved momentum resolution. The wire chamber provides up to 112 space-point measurements along a charged particle trajectory with particle-identification capabilities provided by the cluster-counting technique. Energy resolution for electrons and photons is provided by a finely-segmented crystal electromagnetic calorimeter. The particle identification capabilities of the drift chamber are complemented by a time-of-flight measurement, provided either by LGAD technologies in the Si wrapper or by a first layer of LYSO crystals in the ECAL. Outside a thin (about 30 cm thick) low-mass (corresponding to less than 0.8% of a radiation length) superconducting solenoid, the calorimeter system is completed by a dual readout fibre calorimeter, providing enhanced energy precision for isolated hadrons and hadron showers, and a return path for the magnetic field. The muon detection system is based on the μ-Rwell detectors, a recent micro-pattern gas detector that provides a space resolution of a few hundred microns, giving the possibility of reconstructing secondary vertices at a large distance from the interaction point.

## 6.4 The ALLEGRO detector concept

The ALLEGRO (A Lepton-Lepton collider Experiment with Granular Read-Out) detector concept is relatively recent and under rapid development. Its design, illustrated in Fig. 94, is articulated around a high-granularity noble liquid electromagnetic calorimeter in a cryostat made from novel lightweight materials, thus taking advantage of the excellent stability of this technology, and it capitalises on recent progress in electronics integration and advanced mechanical structures. The inherent
<figure><img src="image_106.png" /><figcaption>**Fig. 94** Longitudinal cross section of the top right quadrant of the ALLEGRO concept detector. The LumiCal, the compensating solenoid, and the final-focus quadrupole are displayed along the z axis</figcaption></figure>

linearity, stability, and uniformity of noble liquid calorimeters allow exquisite control of systematic uncertainties, a unique asset for high-precision measurements.

The tracking system consists of a silicon vertex detector and a main tracker that remains to be identified. The silicon vertex detector is expected to use MAPS or DMAPS technology, with the possible inclusion of an LGAD layer for precise timing measurements. Both a drift chamber and a straw layer are considered for the gaseous tracker option. If a gaseous tracker is chosen, a silicon wrapper is foreseen at the outer periphery of the tracking volume, to provide precise track measurements at the entrance of the calorimeter and possibly a precise measurement of the time of flight by using LGAD technology. A fully silicon-based tracking system, like in CLD, is also being considered and is used in full-simulation particle-flow studies.

A high-granularity-sampling noble liquid ECAL surrounds the tracker. The options considered consist of lead (or tungsten) and liquid argon, or tungsten and liquid krypton. The use of innovative, low-power, cold front-end electronics, placed inside the cryostat, could provide a noiseless readout, but the option of placing low-noise electronics outside the cryostat is also being studied. The thin, lightweight coil is located around the ECAL, within the same cryostat. The high-granularity HCAL is made of steel absorber plates interleaved with scintillator tiles, corresponding to at least 8 interaction lengths. Two design options are being considered, one with SiPMs directly coupled to the scintillating tiles (as for CLD), and the other with wavelength-shifting (WLS) fibres used to guide the light to SiPMs located outside the detector (as for the ATLAS HCAL). The HCAL also acts as a return yoke for the magnetic field.

The geometry described above, with a barrel and two end-caps, is considered as a 'baseline'. An alternative layout is also being considered, with a somewhat longer barrel and the end-caps replaced by smaller radius end-plugs fitting in the barrel opening. This solution would provide several engineering advantages, including the routing of the cables in and out of the barrel cryostat and the reduction of the gap-widening issue in the end-cap ECAL modules.

For the muon system, several options are under consideration, including drift tubes or chambers, resistive plate chambers (RPCs), and micromegas (MM). Here, the development of eco-friendly but performant gas mixtures is a compelling line of R&D.

## 6.5 Vertex detectors

Vertex detector design is undergoing a strong technological development that can be summarised by the terms lighter, closer, and more precise. The development is driven by upgrade activities in Belle II and in the LHC experiments. The second and
third generation ALICE vertex detectors, ITS2 and ITS3 [712], are of particular relevance for FCC-ee, with many common conditions and requirements, such as moderate radiation environments and the need for high resolution and low multiple scattering. The technology of choice, CMOS MAPS, can be thinned down to a thickness of 50 µm or less, so that the sensors can ultimately be bent into cylindrical layers around the beam pipe with very little support material.

A comprehensive description of the silicon vertex detector, considered for the IDEA and ALLEGRO detector concepts, is presented in this section. This detector element is currently the most advanced from an engineering point of view, being already integrated in the complex Machine Detector Interface layout (Sect. 5). A much briefer description of the vertex detector considered for CLD follows.

The vertex detector considered for IDEA and ALLEGRO features two main subsystems, whose active elements are based on 50 µm thick MAPS:

- an inner detector, located close to the beam pipe, at radii between 13.7 and 35.6 mm, covering an angular acceptance of about $|\cos\theta| < 0.99$;

- an outer detector, located at radii between 130 and 315 mm, composed of a middle barrel, an outer barrel, and three disks on each end-cap.

Two layouts are being explored for the inner vertex detector. The baseline layout uses a traditional approach, with modules mounted on a carbon fibre support structure. An alternative, less advanced, ultra-light layout is based on curved detectors, using a concept similar to the ALICE ITS3 [712]. The baseline layout of the vertex detector is displayed in Fig. 95.

In the baseline layout, the inner vertex detector is composed of three concentric barrel layers mounted on a carbon fibre structure. The elementary unit is a module of $32 \times 8.4 \text{ mm}^2 \ z \times r\phi$ dimensions. Each module has two chips abutted together in z, inspired from the ARCADIA R&D [713]. The chip active area features 640 ($z \times 256$ $r\phi$) pixels of $25 \times 25 \text{ µm}^2$ area. A 2 mm inactive space is envisaged in $r\phi$, corresponding to the periphery of the chip. A conservative power consumption of 50 mW/cm$^2$ is assumed, based on the ~30 mW/cm$^2$ measured for the current ARCADIA prototype, read out at 100 MHz/cm$^2$, and considering the higher expected FCC-ee data rate. In order to allow for a 2 mm radial clearance in view of its insertion, the first layer is located at a radius of 13.7 mm. The length is constrained by the central beam pipe cooling manifolds. The first layer comprises 15 staves with 6 modules each, along z. The staves overlap in $\phi$, as shown in Fig. 96, to allow internal alignment.

A lightweight support on each ladder provides rigidity and facilitates the mounting of the MAPS. The structure is made of thin carbon fibre walls interleaved with Rohacell [714], which holds the sensors (facing the beam pipe) and two 1.8 mm wide buses (one for data, the other for power) at the edges of the structure. The thickness of the bus comprises 200 µm Kapton and 50 µm aluminium, for a total of 0.09% $X_0$. The ladders are arranged in a pin-wheel geometry.

The second layer, with a structure similar to the first, is made of 24 ladders of 10 modules each, at a radius of 23.7 mm, arranged in a pin-wheel geometry opposite in orientation to that of the first layer, to mitigate possible charge-dependent effects on charged-particle track reconstruction. The third layer has 36 ladders, each composed of 16 modules. The ladders are arranged in a $\phi$-symmetric lampshade fashion: half of the ladders are located at a radius of 34 mm, the other half at 35.6 mm. Each layer contributes 0.25% $X_0$ at normal incidence, about one fifth of it coming from the overlap between staves of the same layer. The vertex detector layers are mounted on conical carbon fibre support structures using two rings of peek material for thermal isolation during bakeout. The conical support structures also guide cooling gas inside the detector volume and support the power and readout circuits. The middle barrel and the disks, together with the support cones, are shown in Fig. 86 (Sect. 5). The amount of detector material crossed by a particle originating from the main IP ('material budget') is shown in Fig. 97, for the inner vertex layers and for the complete vertex detector.

The main geometric dimensions of the vertex detector, together with the power dissipated by each layer, are reported in Table 15. The inner vertex detector is planned to be cooled with gas passing through channels embedded in the conical support structure. Both atmospheric air and helium are considered as coolant gases. The gas is contained in a cylindrical, 200 µm thick, carbon fibre envelope surrounding the detector. The cooling performance has been analysed using computational fluid dynamics (CFD) simulation models, and the result is that the largest temperature difference between the modules along a stave is less than 15°C. Although this is considered an acceptable level, further optimisations are ongoing to reduce this temperature difference. A mechanical vibration analysis based on Finite Element Analysis (FEA) in ANSYS showed a maximum displacement amplitude in the radial direction of about 1.5 µm for a nominal air flow of 0.7 g/s, resulting in a negligible effect on the impact-parameter resolution.

A second, ultra-light layout for the inner vertex detector is being explored, albeit with a less advanced system engineering. The layout is based on a concept similar to the ALICE ITS3 curved sensor technology, which facilitates a self-supporting
<figure><img src="image_107.png" /><figcaption>**Fig. 95** Engineered layout and main characteristics of the baseline vertex detector for the IDEA and ALLEGRO detector concepts. Top-left: cross sectional view showing the barrel layers. Top-right: longitudinal view showing the outer barrel and disks. Bottom-right: longitudinal</figcaption></figure>

view with the inner and middle barrels, as well as the disks. All dimensions are in mm. The bottom-left panel lists the main elements for the outer, middle, and inner barrel detectors, together with the dissipated power

structure with essentially no material besides that of the Si sensors. The ITS3 uses a stitching technique to form wafer-scale sensors from multiple repeated sensor units (RSUs). Each layer comprises two half-cylindrical sensors featuring ten RSUs in z and three, four, or five in $\phi$ for the first, second, and third layers, respectively. Unlike ITS3, a vertex detector for FCC-ee must have the largest possible polar-angle coverage. The inner vertex detector has four layers, of which the first three are arranged to have approximately the same angular acceptance while the fourth has the same length as the third. The first layer, at 13.7 mm radius, uses two $\phi$ rows of 10 RSUs in z and is supported by only two carbon foam longerons and rings. The spacing between the two half-shells is 1.25 mm, thus leaving a gap in the $\phi$ acceptance. This gap is recovered by a rotation in $\phi$ of 1.25 mm of the second layer, although with a worse impact parameter resolution. The second layer is composed of three $\phi$ rows of 13 RSUs. The first two layers are read out and powered from both ends. For the third and fourth layers, the use of two sensors in z per half-layer is foreseen to circumvent the limitation of the 12-inch wafer diameter. The third layer uses 8 layers on the $-z$ side and 10 on the $+z$ side, while the fourth layer has a reversed distribution (10 on the $-z$ side and 8 on the $+z$ side); in this way, the acceptance gap in z of one layer, of about 10 mm, is covered by the other. For these layers, the readout occurs only at the far ends in z. This layout design is illustrated in Fig. 98. Integration studies are ongoing to validate its technical feasibility. The material budget is very much reduced with respect to the more classic design, as shown in Fig. 99.

A single layer contributes only about 0.07% $X_0$, a reduction by about a factor three compared to the traditional design. Furthermore, the material is more uniformly distributed in $\phi$, given the absence of overlapping structures in the same layer, as can be seen by comparing the left and right panels of Fig. 100.
<figure><img src="image_108.png" /><figcaption>**Fig. 96** First layer of the baseline inner vertex detector for the IDEA and ALLEGRO detector concepts. Transverse (top-left) and longitudinal (top-right) cross sections of the assembly; 3D view (bottom-left); and detailed view showing the overlaps and the different structures</figcaption></figure>

(bottom-right). All dimensions are in mm. The 50 µm thick MAPS sensors face the centre of the structure. The brown structures are the buses and the golden parts are the electronic hybrid circuits for readout

<figure><img src="image_109.png" /><figcaption>**Fig. 97** Material budget (expressed as a percentage of a radiation length) for the silicon vertex detector considered for ALLEGRO and IDEA for the inner vertex detector (left) and for the complete vertex detector (right), in the baseline design, as a function of the cosine of the polar angle</figcaption></figure>
<table><caption>**Table 15** Main parameters of the baseline vertex detector considered for the IDEA and ALLEGRO detector concepts</caption><thead><tr><th>Subsystem</th><th>Layer ID</th><th>Radius (mm)</th><th>|z| (mm)</th><th>No. staves</th><th>No. modules/stave</th><th>Power (W)</th></tr></thead><tbody><tr><td>Inner barrel</td><td>1</td><td>13.7</td><td>&lt; 96.5</td><td>15</td><td>6</td><td>12</td></tr><tr><td>Inner barrel</td><td>2</td><td>23.7</td><td>&lt; 160.9</td><td>24</td><td>10</td><td>32</td></tr><tr><td>Inner barrel</td><td>3</td><td>34 and 35.6</td><td>&lt; 257.5</td><td>36</td><td>16</td><td>77</td></tr><tr><td>Middle barrel</td><td>1</td><td>130</td><td>&lt; 163.1</td><td>23</td><td>8</td><td>316</td></tr><tr><td>Outer barrel</td><td>2</td><td>315</td><td>&lt; 326.3</td><td>51</td><td>16</td><td>1400</td></tr><tr><td>Disks</td><td>1</td><td>34.5 &lt; r &lt; 275</td><td>304.7</td><td>56</td><td>2–6</td><td>135</td></tr><tr><td>Disks</td><td>2</td><td>70 &lt; r &lt; 315</td><td>620</td><td>48</td><td>3–7</td><td>420</td></tr><tr><td>Disks</td><td>3</td><td>105 &lt; r &lt; 315</td><td>930</td><td>40</td><td>4–7</td><td>370</td></tr></tbody></table>

<figure><img src="image_110.png" /><figcaption>**Fig. 98** Ultra-light inner vertex detector layout for the IDEA and ALLEGRO detector concepts. The four half-layers are shown separately in the top-left and in the bottom. The arrangement of the first two layers is shown in the top-right view</figcaption></figure>

For both alternatives, the outer vertex detector is composed of two barrel layers and three disks on each side. The elementary unit is a module of area $40.6 (z) \times 42.2 (r\phi) \text{ mm}^2$. Each module has four hybrid pixel sensor chips, inspired by the ATLASPIX3 R&D [715]. The 50 µm thick sensor has $372 \times 132$ pixels of $50 \times 150 \text{ µm}^2$ area. The power consumption is assumed to be 100 mW/cm$^2$, half of the level observed at the current stage of development, but still too high (by at least a factor of two) to be handled by air cooling. The modules are placed on a lightweight triangular truss structure. The staves are mechanical structures that hold the modules. A stave is composed of a carbon-fibre multilayered structure, consisting of 120 µm thick carbon fibre KDU13 and two carbon fleeces of 65 µm in total, to support two 90 µm thick polyimide tubes of 2.2 mm diameter, where demineralised cooling water circulates. An electronic bus, providing power distribution and readout and control signals, runs along the entire stave length and is placed on top of the modules. It is terminated, at the end of both sides, by a hybrid circuit.

The middle barrel layer is positioned at a radius of 130 mm and is composed of 22 ladders, each with 8 modules. The outer barrel layer is placed at a radius of 315 mm and is composed of 51 ladders, of 16 modules each. The outer and middle barrels are supported by a flange attached to an external support tube. The flange also supports the two innermost disks. Three disks per side, located at $|z| = 304.7, 620, \text{ and } 930 \text{ mm}$, complete the outer vertex tracker. The inner disk is located inside the barrel. Each disk is composed of eight petals, four facing the IP and four facing the opposite direction, made of modules of the same type as those of the barrels. The support structure of each disk is made of a sandwich of thin carbon fibre walls (each 0.3 mm thick) interleaved with 5.4 mm thick Rohacell [714]. The material budget of the outer vertex detector is about
<figure><img src="image_111.png" /><figcaption>**Fig. 100** Material budget (expressed as a percentage of a radiation length) for the silicon vertex detectors considered for ALLEGRO and IDEA in the baseline (left) and the ultra-light designs (right), for the complete vertex detector, as a function of the azimuthal angle vs. the cosine of the polar angle</figcaption></figure>

1% of a radiation length at normal incidence, increasing to about 3% at the edges of the middle and outer barrel, because of the supports and hybrid circuits.

The vertex detector of the CLD concept [618], composed of a cylindrical barrel and forward disks, is located at radii below 112 mm. The layout is based on double layers of ultralight MAPS fixed on a common support structure that includes cooling circuits. The 125 mm long barrel comprises three double layers (0.63% $X_0$ each) at radii 12.5–13.5, 37–38, and 57–58 mm. Three disks on each side (0.70% $X_0$ each), at distances from the IP of 160, 230, and 300 mm, complete the detector. For simulation studies, a point resolution of 3 × 3 µm² is assumed.

Full simulation studies [716] with the smaller radius beam pipe introduced since the publication of Ref. [618] (the inner radius decreased from 15 to 10 mm) and a corresponding reduction of the radius of the inner barrel layer confirm earlier conclusions from fast simulations [618] of a better impact parameter resolution and a significantly improved flavour-tagging performance. Even with a simultaneous increase of the beam-pipe material budget from 0.45% to 0.61% $X_0$, the studies show, for example, an impact parameter resolution improved by 20% for 10 GeV tracks.
<figure><img src="image_112.png" /><figcaption>**Fig. 101** Stacked material budget (expressed as a percentage of a radiation length) of the different parts of the CLD tracking system (plus the beam pipe), as a function of the polar angle and averaged over the azimuthal angle, including contributions from sensitive layers, cables, supports, and cooling</figcaption></figure>

## 6.6 Main tracking systems

### 6.6.1 Silicon tracker

The CLD concept features an all-silicon tracker, complementing the vertex detector (briefly described at the end of the previous section) with a 'main tracker', itself divided into inner and outer sections by a lightweight (1.25% $X_0$) carbon-fibre support tube, at a radius of 690 mm. The inner tracker comprises three barrel layers and seven forward disks on each end-cap, while the outer tracker has three more barrel layers and four disks on each side. The material budget of the modules (200 µm of silicon sensors, or 0.21% $X_0$, including electronics), plus cooling and connectivity, is estimated to range between 1.1% and 1.3% $X_0$. In addition, carbon-fibre support structures, which differ from layer to layer, contribute between 0.13% and 0.37% $X_0$. For simulation studies, point resolutions of $5 \times 5$ µm$^2$ and $7 \times 90$ µm$^2$ are assumed for the innermost disk of the inner tracker and for all other layers, respectively. The material budget of the complete CLD tracking system, including the vertex detector and the main tracker (plus the beam pipe), is shown in Fig. 101.

Full-simulation studies to assess the performance of the CLD tracker are reported in Ref. [618]. Figure 102 shows some essential performance figures for single muons: the momentum and impact parameter resolutions, as well as the polar and azimuthal angular resolutions. For $p_T > 100$ GeV, the momentum resolution curves start to flatten out, reaching an asymptotic value of $\delta(1/p_T) \simeq 1 \times 10^{-5} \text{ GeV}^{-1}$. For lower momenta, the momentum resolution is dominated by multiple scattering. More studies are needed to further reduce the material budget, in particular for the support structures and services.

A smaller tracker outer radius would, in particular, allow for the insertion of a compact RICH detector, such as the ARC detector (Sect. 6.7.2), which could provide improved particle identification performance at the cost of a worse momentum resolution. A recent full-simulation study [716] confirms fast-simulation indications that a reduction of the tracker outer radius from 2.31 to 1.80 m leads to a degradation of the momentum resolution by about 15%, showing that the momentum resolution scales roughly like $1/R$, where $R$ is the outer tracker radius. This observation is compatible with expectations in cases where multiple scattering is the dominant effect (otherwise, a $1/R^2$ dependence would be expected). The study also confirms that an increase of the magnetic field strength from 2 to 3 T would lead to a ~30% improvement of the $p_T$ resolution.

### 6.6.2 Drift chamber

The IDEA concept features the InTrEPIId (Inner Tracking Equipped with Particle Identification) drift chamber, designed to provide tracking with high-precision momentum measurement and particle identification by cluster counting. A high transparency is obtained by a novel approach for the wiring and assembly procedures [717]. The total amount of material is about 1.6% $X_0$ at normal incidence (dominated by the outer container material), increasing to about 5.0% $X_0$ in the forward direction (the end plates instrumented with front-end electronics contributing 75% of that value). The drift chamber is a single-volume, high-granularity, all-stereo, short-drift, low-mass cylindrical wire chamber, co-axial with the 2 T magnetic field. It extends from an inner radius of 0.35 m to an outer radius of 2 m, has a length of 4 m along the z axis, and consists of 112 co-axial layers, at alternating-sign stereo angles, arranged in 24 identical azimuthal sectors. The angular coverage
<figure><img src="image_113.png" /><figcaption>**Fig. 102** Top-left: transverse momentum resolution for single muons as a function of momentum at five fixed polar angle values. Polar-angle dependence of the impact parameter resolution in the transverse plane (top-right), of the polar angle resolution (bottom-left), and of the azimuthal angle resolutions (bottom-right), for muon momenta of 1, 10, and 100 GeV. From Ref. [618]</figcaption></figure>

extends down to ~13° (227 mrad). The size of the approximately square cells ranges between 12 and 14.5 mm, for a total of 56,448 drift cells. The challenges potentially arising from a large number of wires (about 350,000 in total) are addressed by the design of the wiring procedures, successfully exploited during the recent construction of the MEG2 drift chamber [718].

A very light gas mixture, 90% He and 10% $iC_4H_{10}$, corresponding to a maximum drift time of ~400 ns, is expected to be used in operation. The number of ionisation clusters generated by a minimum ionising particle is about 12.5 cm$^{-1}$, allowing cluster counting/timing techniques to be exploited, to improve both the spatial resolution (better than 100 µm) and the particle identification resolution (~3%). A spatial resolution around 120 µm has been achieved in the 7 mm cell size MEG2 drift chamber with the same gas mixture and very similar electrostatic configuration [719]. An even better spatial resolution is expected in InTrEPId, with the application of cluster timing techniques on the one hand and with the longer drift on the other, which mitigates, on average, the effects of the short-drift stochastic behaviour.

Fast simulation studies have been performed with DELPHES to evaluate the tracking performance, with the vertex detector, the drift chamber, and a surrounding double layer of silicon microstrip detectors. This 'Si wrapper' provides an additional accurate space point with an assumed resolution of $7(r\phi) \times 90(z)$ µm$^2$, and a precise definition of the tracker acceptance. Details of ionisation clustering to exploit the cluster counting/timing technique were not simulated, conservatively limiting the spatial resolution of the drift chamber to 100 µm. The resulting momentum resolution is displayed in Fig. 103. For transverse momenta in excess of ~20 GeV, the resolution is well described by $\delta p_T / p_T^2 = 3 \times 10^{-5} \text{ GeV}^{-1}$. Angular resolutions better than 0.1 mrad are obtained in both the azimuthal and polar angles.

Cluster counting and timing provide a $\pi$/K separation better than three standard deviations up to momenta about 30 GeV, except in a narrow gap between 0.9 and 1.6 GeV, where the Bethe-Bloch energy-loss curves for the two particle types cross. These values were obtained with a fast simulation study that parametrised GARFIELD++ [720] results within DELPHES. As illustrated in Fig. 104, the gap can be adequately covered with a time-of-flight measurement over a distance of 2 m, with a non-challenging resolution of $O(100)$ ps.

### 6.6.3 Straw tracker

A straw tracker with thin Mylar walls may also be a promising option to meet the stringent FCC-ee detector requirements, when combined with a pixel detector near the beam pipe and a silicon wrapper as an outer layer. A straw tracker can provide a spatial resolution of 100–120 µm per straw and a low material budget of 1.2% $X_0$ at $\theta = 90^\circ$ for 100 layers of straws made
<figure><img src="image_114.png" /><figcaption>**Fig. 104** Significance (in standard deviations) of the $\pi$/K separation in the IDEA drift chamber, from a fast DELPHES simulation study, with the cluster counting performance parametrised from GARFIELD++ results (yellow curve). A better than $3\sigma$ separation is obtained up to momenta ~30 GeV. The $p < 1.6$ GeV region is covered by a time-of-flight system, extending over a distance of 2 m and with a timing resolution assumed to be 100 ps (orange curve). The combination of the drift chamber and the time-of-flight system is represented by the dashed red curve</figcaption></figure>

<figure><img src="image_115.png" /></figure>

with 12 µm-thick Mylar walls. With $\mathcal{O}(100)$ hits per track, such a straw tracker is well suited for both pattern recognition and searches for long-lived particles. In addition, it can provide excellent particle identification capabilities, such as $\pi$/K and K/p discrimination, across a wide momentum range and could also be used for triggering purposes, making it valuable for both collider data taking and cosmic ray studies.

Each straw functions as an independent channel, providing significant flexibility for design optimisation. The operational robustness also benefits from the fact that each straw can be easily disconnected if its wire breaks. The electric charges generated within a straw remain confined to that specific unit. The electric field within a straw is radially symmetric, making the resolution independent of the particle incident angle and leading to a good single-hit resolution. Straws with different radii can be used in various detector regions to optimise hit occupancy, material budget, and channel counting. The gas mixture can be optimised to enhance particle identification capabilities and different gas mixtures can be simultaneously used for straws in different layers.

Figure 105 shows an example layout of a straw tracker implemented in a GEANT4 simulation, featuring $\mathcal{O}(60,000)$ straws with a diameter of 1–1.5 cm and a length of 5 m, arranged in ten concentric superlayers. Straws are arranged in both axial
<figure><img src="image_116.png" /><figcaption>**Fig. 105** (Left) An example layout of the straw tracker with ten superlayers, each superlayer containing ten sublayers. (Right) Simulated hits from 5000 muons, revealing the layout of the straw tracker in the GEANT4 simulation</figcaption></figure>

and stereo layers with a stereo angle of a few degrees to determine the hit position with an accuracy of a few mm along the z direction. Initial simulations [721] predict similar momentum resolutions as with the InTrEPId drift chamber.

Significant R&D is required to realise such a detector design. Close collaboration with straw manufacturers is essential to produce $O(12)$ µm-thick-walled aluminium-coated straws with high yields. Optimising the detector layout and developing a robust mechanical design for the end-plates and support structure of these 5 m-long straws are critical tasks. Further investigations into gas mixtures, GARFIELD simulations, and front-end electronics are important for $dE/dx$ and $dN/dx$ measurements. Fast algorithms need to be developed and implemented in the front-end ASIC or FPGA in order to effectively identify individual clusters. In the coming years, prototype chambers will be built and tested with cosmic-ray muons and with beams, in view of validating the simulated performance.

### 6.6.4 Time projection chamber

Time projection chambers (TPCs) provide continuous 3D tracking over a large volume with minimal material interference, while also enabling particle identification via energy deposition in the gas. A TPC is expected to provide, under favourable background conditions, a similar performance as a drift chamber, in terms of momentum resolution and particle identification capabilities, with possible differences depending on details of the engineering solutions. The gas choice is critical to maximise ionisation signal yield and minimise transverse diffusion, which strongly depends on the magnetic field strength and on the drift velocity. Minimising transverse diffusion calls for a ‘hot gas’, commonly achieved so far with a small admixture of $CF_4$. Given that $CF_4$ has a strong greenhouse effect, a replacement gas will have to be identified. For particle identification via cluster counting, $dN/dx$, small, sub-millimetre pad sizes are needed, in which case digital readout is sufficient.

Mechanical alignment must be precise, within a few tens of microns, to avoid systematic errors. Electric and magnetic fields must be parallel, to prevent $E \times B$ distortions, calling for a highly uniform magnetic field. Minimising space-charge build-up is essential, as transverse electric field components distort electron drift paths. Hence, beam backgrounds (such as low-energy X-rays and muons from beam-halo interactions, both generating low-$p_T$ particles that curl and deposit significant ionisation) must be controlled, or corrective strategies must be implemented. First estimates of the effect of beamstrahlung backgrounds were recently presented [708], with the conclusion that distortions expected with the FCC-ee Tera-Z luminosities are at the same level as those observed in ALICE. Ion feedback, where ions from the amplification process drift towards the cathode (over ~0.5 s), must be carefully managed. Operating at low gain with effective passive backflow mitigation, such as double misaligned meshes or graphene filters, would be necessary. If space charge effects are unavoidable, correction techniques (built on the experience of ALICE) should be employed. The operability of a TPC at FCC-ee luminosities is still under discussion in the community and is being actively investigated.
## 6.7 Particle identification

The identification of charged hadrons (π, K, p) significantly enhances the physics potential of experiments at FCC-ee, as discussed in Sect. 4.5. In particular, it improves the flavour-tagging performance in the selection of Higgs boson decays to c̄c or s̄s, and is crucial for the extensive flavour physics programme with the Z-pole data. From simulation studies, the momentum region to be covered is up to a few tens of GeV. For experiments with gaseous trackers, the specific energy loss (dE/dx) provides separation power up to moderate momenta, in conjunction with time-of-flight to cover the overlap region around 1 GeV, where the dE/dx separation is poor. As already mentioned for drift chambers or straw trackers, the performance can be enhanced with cluster counting, dN/dx. For experiments with silicon-based tracking, however, neither dE/dx nor dN/dx would provide the required level of performance. There, ring-imaging Cherenkov (RICH) detectors could deliver particle identification over a very wide momentum range. The following two sections describe the use of precision timing and RICH detectors to enable the required particle identification performance.

### 6.7.1 Precision timing detector

The identification of charged hadrons based on their specific energy loss must be complemented by other measurements to fill the gap around 1 GeV, where the Bethe-Bloch energy-loss curves for the different particle types cross over. Time-of-flight measurements, for example in a layer of silicon sensors at 2 m from the interaction point, with a non-challenging resolution of ~100 ps, are adequate for this purpose. With a resolution of 30 ps, time-of-flight measurements alone would allow kaons to be separated from pions up to $O(3)$ GeV in momentum, while an excellent resolution of 10 ps would be needed to extend this momentum range up to 5 GeV. Such TOF information could also be obtained in a silicon-tungsten ECAL, where measurements, each of a resolution of, e.g., 100 ps, could be made in several layers. Dedicated timing layers made of inorganic scintillator offer another solution. An example is the segmented crystal ECAL design of MAXICC (described in Sect. 6.8), which includes two such thin layers, potentially providing a 20 ps timing resolution.

Because of the finite length of the colliding bunches, the ‘event time’, $t_0$, has a natural spread of about 36 ps at the Z pole, reducing all the way down to 6.5 ps at $\sqrt{s} = 365$ GeV. To exploit timing resolutions better than that value, $t_0$ needs to be determined on an event-by-event basis. In events with a high charged-particle multiplicity, it is possible to reconstruct $t_0$ from the timing measurement of the other tracks. For lower multiplicity events, e.g., $Z \to \tau\tau$, this method is less effective. As an alternative, an additional timing measurement close to the interaction point could be established, possibly in the form of an LGAD silicon sensor layer at low radius. This solution would allow a direct track-by-track time-of-flight measurement independent of $t_0$. Studies are needed in order to quantify the implications of such a layer in terms of additional material for readout electronics and cooling.

### 6.7.2 Compact RICH detector

Studies are underway to develop a compact RICH detector for inclusion in CLD, with the goal of fitting it in a 20 cm radial envelope and contributing less than 10% of a radiation length to the material budget, hence limiting its impact on the other subsystems of the experiment, such as tracking and calorimetry. It is enabled by the new generation of photodetectors, in particular silicon photomultipliers (SiPM), that hold the promise of providing high detection efficiency and spatial granularity in a low thickness. A focusing geometry has been developed, where the surface of the detector is tiled with a large number of similar RICH detector elements, in a cellular approach, a concept named ARC, for ‘Array of RICH Cells’ [640–642].

The components of an ARC cell are shown in the top panel of Fig. 106. The lightweight vessel is made of carbon-fibre composite, with a wall thickness that depends on whether the contained gaseous radiator needs to be pressurised. The RICH uses dual radiators, silica aerogel and gas, with Cherenkov photons from both radiators focused via a spherical mirror onto a common SiPM detector plane. The baseline choice for gaseous radiator is $C_4F_{10}$ at atmospheric pressure, given its attractive optical properties, as used for example in the RICH1 detector of LHCb, aiming for a leak-free closed circulation system. With the high photon-detection efficiency achievable with SiPMs, this option can provide a sufficient number of detected photons, about 16 for a high-momentum particle, despite the limited radiator length of only around 15 cm. On the timescale of FCC, however, such fluorocarbons may be banned, so that R&D is required to find alternative gases, such as xenon with mild pressurisation, to ensure a sufficient yield of detected photons. The aerogel radiator extends the particle identification performance to low momenta, while also serving as an efficient thermal insulator, separating the gas radiator from the SiPM detector plane, which is likely to need cooling to limit the dark-count rate (although the option of suppressing noise with
<figure><img src="image_117.png" /><figcaption>**Fig. 106** Top: schematic cross section through the ARC barrel detector, showing the various components of a single cell. Bottom left: ARC barrel and end-cap as described in the detector geometry of the simulation, with colours used to distinguish the cells. Bottom right: Momentum dependence of ARC's $K/\pi$ separation (in standard deviations), with two radiator options</figcaption></figure>

timing cuts will also be investigated). This insulator would allow the SiPMs to be operated at around -40°C, e.g., with mixed-phase CO₂ circulation, while maintaining the radiator gas at room temperature to prevent condensation.

The performance of such a RICH concept has been evaluated with full simulation studies [722]. The geometry of each cell, in terms of mirror and photodetector position and angle, depends on the position of the cell in the detector. Given symmetry considerations, there are about 40 unique cell geometries across the detector, which have been optimised in an automated procedure. The resulting detector description has been implemented in the KEY4HEP software framework (Sect. 8), with DD4HEP for the geometry and GEANT4 for the simulation, as illustrated in the bottom-left panel of Fig. 106. Taking the integration into CLD as an example, 10% of the original tracker volume has been reassigned to ARC, the tracker dimensions being adapted to fit in the remaining space. Studies are underway to develop pattern recognition and particle identification algorithms, as well as to check the impact on the experiment, e.g., on the performance of the tracking and particle-flow calorimetry. Meanwhile, the performance has been studied using standalone ray-tracing software, as shown in the bottom-right panel of Fig. 106. The overall resolution per detected photon is around 2 mrad, balanced between contributions from the chromatic dispersion, focusing errors, and pixel size, where mm-scale pixelisation of the SiPMs has been assumed. Excellent $K/\pi$ separation is achieved for momenta above 2 GeV. For lower momenta, a TOF system would provide complementary information. The development of ARC is established as a task within the newly formed DRD4 collaboration [723], with the milestone of a full conceptual design within a year and a prototype of a single ARC cell to be delivered within three years. Such a prototype will provide an excellent test-bed for the study of the key developments required for this detector, as well as the possibility of including RICH detectors as integral parts of the FCC-ee tracking detectors.
## 6.8 Electromagnetic calorimeters

### 6.8.1 Silicon pads, MAPS, scintillator strips

Electromagnetic calorimeter technologies with embedded front-end electronics and high 3-dimensional segmentation have been studied extensively [706]. They include silicon pads, MAPS sensors and scintillator strips, and capitalise on the possibility of power-pulsing and overall modest bandwidth requirements. Adapting them to a circular collider such as FCC-ee, with continuous readout and high rates, poses challenges for data concentration, powering, and cooling, requiring a full re-optimisation to maximally preserve their compactness. Silicon diodes are currently implemented in the CMS end-cap calorimeter upgrade, but the FCC-ee goals in terms of compactness (Molière radius), energy resolution, and granularity are considerably more ambitious.

Related R&D has begun, in the framework of the DRD6 Collaboration. As a first step, quantitative requirements are being studied in simulations. Tools have been developed to evaluate hit occupancy, bandwidth and, with model assumptions on the embedded electronics, power consumption as a function of position in the detector [724].

### 6.8.2 Noble liquid

The proposed ALLEGRO noble-liquid electromagnetic calorimeter is a sampling detector using liquid argon as active medium and lead/steel absorbers as passive material. The absorbers and electrodes are straight, and inclined (in the barrel) in the (x, y) plane by 50° with respect to the radial direction. The detector has both transverse and longitudinal segmentation. Alternative design options include liquid krypton as active medium and tungsten for passive material, as well as trapezoidal absorbers to maintain the sampling fraction constant as a function of depth.

The calorimeter is located inside a cryostat, made of 33.8 mm-thick aluminium in the current simulations while novel, lightweight materials are being considered (Sect. 6.11). The 2 mm-thick absorber plates are composed of a sandwich of lead (1.8 mm) with steel sheets glued on either side. Between adjacent absorbers are two equal-size liquid argon gaps, separated from each other by a 1.2 mm-thick electrode, realised as a multilayer PCB. The use of multilayer PCBs as readout electrodes allows for great flexibility in the choice of granularity as a function of depth. In the present geometry, the liquid argon gaps have thicknesses, projected along the direction orthogonal to the electrode, of $2 \times 1.25 \text{ mm}$ at the inner radius and $2 \times 2.43 \text{ mm}$ at the outer radius. The electrodes are segmented longitudinally into 11 layers. The first layer, about half as thick (1.5 cm) as the others (3 to 5 cm), is used as a presampler. To achieve a $\phi$-uniform response of that first layer, the absorber does not contain lead, to form a 'LAr-only' homogeneous presampler. The sampling fraction is about 38% in the presampler layer and increases from 13.5 to 17.3% throughout the other 10 layers. A depth of $22 \times 10^3 \text{ m}$ is achieved in a thickness of 40 cm for the Pb-LAr solution and about two thirds of that for denser solutions based on W and LKr.

The segmentation in $\phi$ is naturally provided by the absorbers. The baseline is to read out two gaps together, forming a single cell spanning $\Delta\phi = 2\pi/768 = 8 \text{ mrad}$. The segmentation along the electrode and in $\theta$ is formed by cells on the readout electrode. It amounts to $\Delta\theta = 0.56^\circ$, except in one of the first layers, where a four-times finer granularity ($\Delta\theta = 0.14^\circ$) is implemented, to discriminate between single showers from prompt photon and collimated pairs of showers from neutral pion decays. The total number of readout channels for the barrel part of the calorimeter is around 2 million. The expected sampling term of the resolution ranges from $\sim 7.5\%/\sqrt{E}$ for a solution based on LAr, down to below $5\%/\sqrt{E}$, for a denser solution based on LKr.

An adapted geometry is needed for the detector end-caps. The inclined absorber and electrode planes of the barrel calorimeter are replaced by 'blades' arranged in a turbine-like structure. In order to avoid having too large variations of gap sizes and sampling fractions between the inner and outer radii, the detector is assembled as three nested wheels, with similar gap sizes at the inner radius of each wheel.

The geometries of both the barrel and the end-cap sections are implemented in the GEANT4 full simulation of the KEY4HEP software framework. Algorithms for digitisation and clustering (fixed-size sliding-window and topological clusters) are also implemented. Example displays of reconstructed clusters from single-photon and single-$\pi^0$ events are shown in Fig. 107.

Examples of performance studies are illustrated in Fig. 108, where the energy resolution and response expected with the (LAr plus tungsten) baseline model are shown, together with the ROC curves for a simple BDT-based photon/$\pi^0$ discrimination algorithm exploiting the shower shapes computed from the cell energies. The latter, which shows the area-under-curve (AUC) of the efficiency vs. rejection curve of the BDT algorithm for various alternative configurations corresponding to different positions of the strip layer, demonstrates how the simulation can help design choices.
<figure><img src="image_118.png" /><figcaption>**Fig. 109** Jet energy resolution vs. jet energy, with or without a dual-readout particle flow algorithm</figcaption></figure>

studies of heavy-flavour physics with low-energy final-state photons [725] and to improve the resolution of the mass recoiling against $Z \to e^+e^-$ in ZH events with a recovery of bremsstrahlung photons. Furthermore, it enables an efficient clustering of photon pairs from $\pi^0$ decays, which can effectively reduce the splitting of the two photons across different jets in multi-jet events [619].

The MAXICC calorimeter design is optimised for integration with a dual-readout hadron calorimeter section to provide an energy resolution for charged and neutral hadrons of about $27\%/\sqrt{E} \oplus 2\%$. The inclusion of longitudinal segmentation and the enhancement of transverse granularity with ~1 cm$^2$ cells (compared to the previous generation of crystal calorimeters) provide a powerful handle for particle identification and association of charged-particle tracks with calorimeter clusters in particle-flow jet reconstruction, with the potential to achieve an energy resolution of 4.5% for 45 GeV jets [726], as shown in Fig. 109. A complete simulation of the detector integrated with other IDEA sub-detectors, within the KEY4HEP framework, is in progress, to allow more detailed physics studies [727].

As shown in Fig. 110, the baseline calorimeter design features two longitudinal layers of high-density crystals (such as PWO or BGO), with 6 $X_0$ in the front layer and 16 $X_0$ in the rear layer, for a total of 22 $X_0$ to ensure full containment of electromagnetic showers. The light from the crystals is read out with silicon photomultipliers (SiPMs) of active area in the range between 4 × 4 and 6 × 6 mm$^2$. One SiPM is glued on the front side of the front layer and two are glued on the rear face of the rear layer. One of the rear SiPMs embeds an optical filter that cuts out the scintillation light based on wavelength discrimination and detects a pure Cherenkov signal for dual-readout corrections. An alternate approach also uses pulse shape analysis to differentiate scintillation and Cherenkov components. The front-end boards, electronics, and cooling services are located in the front and rear parts of the calorimeter to minimise the impact of passive material on energy resolution.

The MAXICC calorimeter can provide a time resolution better than 30 ps for electromagnetic showers with energy of 20 GeV or higher, as obtained from beam tests with similar calorimeter prototypes [728]. In addition, two thin and highly segmented layers of LYSO:Ce crystals, for a total of 1 $X_0$, could be added in front of the PWO crystals for time tagging of minimum ionising particles, using a technology similar to that used by the CMS MTD [729], with a time resolution of 20 ps.

The required technological R&D, prototyping, and simulation are progressing steadily, through a coordinated effort of many international collaborators within the DRD6 WP3 (task 3.1.2). Single calorimetric cells have been tested with beam in 2024 and full containment calorimeter prototypes (one using PWO and the other using BGO) are being built for beam tests in 2025. Each prototype will instrument ~100–200 channels for readout, covering a transverse size of at least five times the Molière radius and a depth of 22 $X_0$.
<figure><img src="image_119.png" /><figcaption>**Fig. 110** Segmented crystal calorimeter prototype cell and module with SiPM dual-readout</figcaption></figure>

### 6.8.4 The GRAiNITA ECAL

The GRAiNITA concept features a novel electromagnetic calorimetry design, with a detection volume filled with millimetric grains of high-Z and high-density inorganic scintillator crystals immersed in a bath of transparent high-density liquid. The multiple refractions of the light on the grains ensure the stochastic confinement of the light, as in the LiquidO detection technique [730]. The scintillation light can be collected towards the photodetectors by means of WLS fibres, regularly distributed in the detection volume as for a conventional Shashlik detector, allowing a potentially-large transverse granularity. This extremely-fine sampling of the electromagnetic shower promises an excellent energy resolution, comparable to what is known from crystal calorimeters.

The main high-Z and high-density inorganic scintillator crystal considered for GRAiNITA is ZnWO₄ [731], providing a light yield of ~10,000 photons per MeV. A considerable advantage is that ZnWO₄ can be successfully grown in the form of transparent granules of the desired size, with the method of spontaneous crystallisation from a flux melt [731], significantly reducing the cost of the calorimeter. Such a high energy-resolution granular calorimeter would then meet the requirements, from physics and otherwise, of an FCC-ee experiment. It would, moreover, be particularly useful to address a comprehensive flavour physics programme with rare decays involving photons or neutral pions in the final state. Given that the Z production rate at FCC-ee is of the order of 100 kHz and since these events should typically hit less than 1% of the calorimeter cells, the 20 µs signal decay time of the ZnWO₄ should not be a concern. Nevertheless, the possible use of other types of crystals will be investigated.

Measurements with a small prototype (2.8 × 2.8 × 5.5 cm³) equipped with a green LED confirm that, as expected, the signal remains confined in the vicinity of its production point [732]. From the analysis of cosmic-ray muons [732] and of data from a muon beam test performed in summer 2024 at CERN with the same small prototype, it is clear that the collection of about 10,000 photo-electrons per GeV is within reach with a GRAiNITA-like calorimeter. This result paves the way for a statistical fluctuation of $1/\sqrt{E}$ on the energy resolution from photo-electrons (Fig. 111). The next steps, following this proof-of-principle, include the system aspects, including a mechanical configuration and an electronics read-out concept.
<figure><img src="image_120.png" /></figure>

**Fig. 111** Number of photo-electrons recorded in a small GRAiNITA prototype, where the ZnWO₄ grains are immersed in a heavy liquid to increase the density of the medium. Left: cosmic-ray muons with

<figure><img src="image_121.png" /></figure>

ZnWO₄ grains immersed in ethylene-glycol (from Ref. [732]). Right: muon tracks from a beam test at CERN with ZnWO₄ grains immersed in LST Fastloat (density = 2.8 g/cm³) [733]

<figure><img src="image_122.png" /></figure>

**Fig. 112** The HCAL tile module concept. Each module consists of 13 radial layers of scintillating tiles with different radial extension (5, 10, and 20 cm), and each radial layer is divided into two tiles in azimuth (hatched red). Scintillation light is brought to SiPMs at the outer radius via WLS fibres. In the z direction, tiles are read out in groups of 3 or 4

## 6.9 Hadron calorimeters

### 6.9.1 Scintillator tiles

One of the considered hadron calorimeter designs is a non-compensating sampling calorimeter based on the ATLAS Tile-Cal [734], with steel as absorber and plastic scintillating tiles as active material. The light from the scintillator is collected and transported to the SiPMs located outside the calorimeter via WLS fibres, as shown in Fig. 112.

The radial orientation of the tiles and the light collection via the WLS fibres along the tile edges allow a hermetic implementation in $\phi$. The location of the photodetectors and their associated electronics in the modules' girder at the outside radius makes them serviceable during collider shutdown periods. It also embeds the calibration system with movable radioactive $^{137}$Cs photon sources that can pass through all calorimeter cells [735].
<figure><img src="image_123.png" /><figcaption>**Fig. 113** The HCAL tile energy resolution for hadron clusters</figcaption></figure>

The proposed design uses 5 mm low-carbon steel absorber plates interleaved with 3 mm plastic scintillating tiles. The barrel is segmented into 128 modules in $\phi$ and 13 radial layers (of different depths: four of 5 cm, six of 10 cm, and three of 20 cm, as shown in Fig. 112). Each layer is divided in $\phi$ in two longitudinal read-out compartments. In each compartment, the tiles are read out in groups of three or four along the z axis, which leads to a cell granularity $\Delta\phi \times \Delta\theta$ of 24.5 $\times$ 22 mrad$^2$ at normal incidence. Steel-scintillator technology is also being considered for the end-cap hadron calorimeter.

The performance of the tile HCAL, evaluated with a sliding window clustering algorithm, is shown in Fig. 113. The optimisation of the calorimeter details, including the choice of the absorber and scintillating materials, as well as their segmentation, is ongoing. These R&D studies are coordinated by the DRD6 WP3 (task 3.3.2), including the characterisation of perspective scintillating materials, like PEN and PET [736], and the light collection from scintillating tiles via WLS fibres with SiPM photodetectors [737].

A complementary approach is also being explored, with the so-called SiPM-on-Tile technology and with front-end electronics embedded into the active layers of a steel sandwich structure. The SiPMs are integrated into the electronics PCBs, which also hold read-out ASICs, power distribution, and a LED-based calibration system. Reflector-wrapped scintillator tiles are glued onto the PCB, with a dimple leaving space for the SiPMs underneath, which read each tile individually.

While the ATLAS-style geometry offers easier access and space for service routing, including cooling for a calorimeter placed outside the coil, the SiPM-on-Tile approach is the natural choice for calorimeter systems entirely inside the solenoid, such as in the CLD concept, where radial compactness (especially in the barrel) is strictly mandated by cost considerations. The technology was originally developed by the CALICE Collaboration; a scalable prototype with 22,000 channels was built and has been successfully tested in beams since 2018 [738]. The main challenge in the adaptation to FCC-ee lies in coping with the continuous readout (i.e., without power-pulsing) and with the much higher rate, bandwidth, power, and cooling requirements, without compromising granularity and compactness.

The R&D has common challenges with other concepts based on embedded electronics and is pursued in the framework of the WP1 of the DRD6 Collaboration. The SiPM-on-Tile technology is currently being applied in a large scale in the CMS HGCAL, a detector with 280,000 tiles. Although the CMS HGCAL has to address radiation hardness and other challenges not present at FCC-ee, it has more relaxed performance and compactness requirements, and remains more than an order of magnitude smaller in terms of channel count than, e.g., the CLD HCAL.
**Fig. 114** From Ref. [742]. Invariant mass distributions of W (blue), Z (red), and H (green) hadronic decays, from e$^+e^-$ to W$^+W^-$ and ZH events fully simulated and reconstructed at $\sqrt{s} = 240$ GeV in a dual-readout fibre-sampling calorimeter. To highlight the detector performance, semileptonic b decays are excluded

<figure><img src="image_124.png" /></figure>

### 6.9.2 Gaseous detectors

Gaseous detector technologies with two-dimensional transverse segmentation are also pursued as read-out options for hadron calorimeters. Proof-of-principle elements have been tested using GEM and micromegas detectors, and larger prototypes with glass RPCs have been built and successfully tested, with up to 500,000 channels [739,740]. Granularities finer than with tiles are easily achievable, but to maintain the designs cost-effective and to limit read-out power consumption, trade-offs must be found between energy and space information. The channel amplitude is encoded in one or two bits only, hence the name digital or semi-digital HCAL.

The related R&D is pursued both in the DRD6 ('calorimeters') and in the DRD1 ('gas detectors') projects. The challenges of data concentration, powering, and cooling are shared with other ECAL and HCAL technologies with embedded readout. The quest for improving the detection technologies themselves, in terms of rate capability and stability, is common with R&D for muon detectors, and both face the imperative of replacing the currently used gas mixtures with high global warming factors by more eco-friendly solutions.

### 6.9.3 Dual readout

A fibre-sampling Dual-Readout (DR) calorimeter [741] can, in principle, be used as a single system for electromagnetic and hadron showers. This option is considered in the IDEA concept, with a calorimetric section made of a dual-readout, longitudinally unsegmented and fully projective, fibre-sampling calorimeter, providing both electromagnetic and hadron shower measurements. Another option is to use this technology as a hadron calorimeter behind an electromagnetic section based on crystals, as discussed in Sect. 6.8.3.

Alternate rows of scintillating and Cherenkov (clear) fibres are inserted in capillary tubes made of brass or iron. Each fibre is individually read out with a SiPM. In order to significantly reduce the number of readout channels, the analogue grouping of 4–8 SiPM signals is foreseen. The optimal granularity is different if the detector has to provide both electromagnetic and hadronic shower measurements or just the latter. The present choice (1 mm fibres in 2 mm capillary tubes) is designed to address both.

The hadron energy resolution is estimated to be about 30%/$\sqrt{E}$, with a negligible constant term. The expected separation reachable for the W, Z and H hadronic decays is shown in Fig. 114, obtained with a stand-alone simulation and subsequent reconstruction of the DR calorimeter, and excluding semi-leptonic decays [742]. Similar studies show that this detector can provide excellent stand-alone electron-pion separation. Moreover, the RD52 lead prototype obtained an efficiency of about 99% in identifying electron showers, for a rejection ratio of charged-pion showers higher than 500 [743].

Advances in solid-state light sensors, such as SiPMs, have opened the way for high transverse granularity, which gives the detector the capability to determine shower angular positions at the mrad level, or better. In the present design, without a crystal-based electromagnetic calorimeter in front, the 1 mm diameter fibres are placed in an iron absorber matrix, at a distance (apex to apex) of 1.5–2 mm. The lateral segmentation could be pushed down to the mm level, largely enhancing the
<figure><img src="image_125.png" /><figcaption>**Fig. 115** Lateral shower profile of positrons with an energy of 20 GeV. The black circles (triangles) refer to the scintillation (Cherenkov) options. The red and blue bands correspond to the simulation predictions for the scintillation and Cherenkov signal, respectively</figcaption></figure>

resolving power for close-by showers, with a significant impact expected, for example, on the isolation and reconstruction of $\tau \to \rho\nu$ final states. For the setup with crystals in front, the segmentation of the DR sections remains to be optimised.

The high photo-detection efficiency of SiPMs should lead to light yields of $\mathcal{O}(100)$ photo-electrons per GeV, for both the scintillation and Cherenkov signals, which guarantees a stand-alone EM resolution close to $10\%/\sqrt{E}$. Readout ASICs providing time information with about 100ps resolution may allow the reconstruction of the longitudinal shower position with a resolution of about 5 cm.

On the other hand, the large number and density of channels require an innovative readout architecture for efficient information extraction. Both charge integration and waveform sampling ASICs are available on the market and candidates for early testing have been identified. A first implementation of a scalable readout system is well-advanced. Looking further ahead, digital SiPMs (dSiPMs) should allow a significant simplification of the readout architecture, but the technology is not yet sufficiently mature. A specific R&D programme has been approved for the 2025–2026 period.

The mechanical assembly and integration of a system with $\mathcal{O}(10^8)$ sensitive elements require the development of a robust and engineered procedure. A scalable mechanical solution has been conceived for both non-projective and projective modules. A small ($\sim 10 \times 10 \times 100 \text{cm}^3$) EM prototype has been built, based on the gluing of capillary tubes. This procedure is being used for the construction of a hadron calorimeter prototype (of size $\sim 60 \times 60 \times 250 \text{cm}^3$) that should be completed by mid 2025. Alternative approaches, for both mechanical assembly and readout architecture, are being investigated within DRD6.

The EM prototype was tested with beam at the CERN SPS and the results (Fig. 115) show that simulations model the instrumental effects well. The performance in the reconstruction of the properties of both hadron and EM showers is sufficient to retain the possibility of an integrated dual-readout solution based on fibre-sampling only, for the calorimetric system of an FCC-ee experiment. The huge amount of information made available by the fibre SiPM readout is well suited to take advantage of deep-learning algorithms.

## 6.10 Coil

Conceptual studies of 2T superconducting solenoid variants have been concluded for the CLD, IDEA, and ALLEGRO FCC-ee detector concepts. From a conceptual perspective, the CLD solenoid is similar to that of CMS, with the calorimeters located inside the solenoid bore. A relatively high energy density is targeted, for the purpose of limiting the weight of the cold mass, with various benefits, in particular regarding the overall cost and easier transport from the manufacturer to CERN. For the IDEA and ALLEGRO concepts, the solenoid is located inside the hadron calorimeter and the free-bore diameter is substantially smaller. The advantage of this variant is that the cold-mass weight is reduced, albeit at the cost of requiring high