<figure><img src="image_126.png" /><figcaption>Fig. 116 Field maps of the CLD (left) and IDEA (right) detector magnets in the (r, z) view, featuring 2 T in the free bore</figcaption></figure>

<table><caption>Table 16 Overview of typical design parameters of the different solenoid variants</caption><thead><tr><td>Variant</td><td>Stored magnetic energy (MJ)</td><td>Cold mass weight (t)</td><td>Energy density (kJ/kg)</td></tr></thead><tbody><tr><td>CLD</td><td>590</td><td>52</td><td>11.4</td></tr><tr><td>IDEA</td><td>130</td><td>10.6</td><td>12.3</td></tr><tr><td>Allegro</td><td>250</td><td>22</td><td>11.4</td></tr></tbody></table>

particle transparency of the cold mass, thermal shields, and vacuum vessel. The design of thin, low-mass magnet systems is discussed in Ref. [11]. Representative field maps are shown in Fig. 116 and typical design parameters are shown in Table 16.

For each variant, a relatively high energy density, of about 12 kJ/kg, is targeted, a value comparable to what was previously shown in the CMS solenoid and the Bess-Polar solenoid [744]. This energy density poses challenges for quench protection and cold-mass mechanics but, relying on technological solutions previously demonstrated for the ATLAS, CMS, and Bess-Polar solenoids, no setbacks were identified. The baseline is to build the solenoids with reinforced aluminium-stabilised low-temperature superconductors. These conductors have been successfully applied in many detector magnet projects worldwide over the past decades and they meet the technical requirements of the FCC detector magnets, regarding the field ranges, the free bores, the transparency to particles, and the mechanics and stability. The preferred technology is co-extrusion of Nb-Ti/Cu Rutherford cable in a high purity aluminium stabiliser. This technology offers the best characteristics for coil quench protection and coil stability, with an indirect cooling. Strong mechanical properties can be reached using either Ni-doped high-purity aluminium stabiliser, or aluminium alloy profiles electron-beam-welded to the coextruded aluminium-stabilised superconductor. It should be noted that this assumes the commercial availability of reinforced aluminium-stabilised Nb-Ti conductor. At the time of the conclusion of the conceptual cold-mass studies, it became clear that companies that had historically made this conductor type commercially available had discontinued production.

As an alternative to aluminium-stabilised Nb-Ti conductor technology, preliminary studies were made concerning the implications of aluminium-stabilised high-temperature-superconducting (HTS) conductors. The use of HTS brings interesting benefits, such as potentially allowing a higher operating temperature and, thus, reduced cryogenic operating costs. The implications for capital costs, cold mass mechanics, quench detection and protection are, however, not yet fully understood and characterised. This technology requires further R&D before it can be concluded that it is a reliable alternative to the Nb-Ti conductor. Two manufacturing methods are considered for the aluminium-stabilised HTS: co-extrusion in high-purity aluminium profiles and soft soldering in copper-plated aluminium profiles. As the HTS are produced in thin tapes, several HTS conductor technologies are envisaged: stacks of tapes, Roebel cables, and conductor on round core (CORC®) conductors.

An Experimental Magnets Committee was established by CERN in 2023 to address the R&D needs of detector magnet projects and to resolve identified issues regarding the availability of technologies and facilities needed to manufacture superconductors for detector magnets. An ongoing programme is targeting to establish access to a co-extrusion line that would allow R&D and prototyping, both with low- and high-temperature aluminium-stabilised superconductors. In addition to the CERN effort, specific R&D for an HTS solenoid for IDEA/ALLEGRO is currently in progress at INFN-LASA.
<figure><img src="image_127.png" /><figcaption>**Fig. 117** Full liner-less tank demonstrator, 1 m length, 0.3 m diameter, and 5 mm wall thickness. Manufacturing process: filament wet-winding, non-crossing, out-of-autoclave curing</figcaption></figure>

## 6.11 Cryostat

The use of carbon composite technologies for cryostat construction is being studied in an R&D programme in the CERN EP Department. In collaboration with industry, a 1 m carbon composite cryostat prototype has recently been developed, as shown in Fig. 117. The manufacturing procedure, based on a wet filament winding process, ensures helium leak-tightness at cryogenic temperatures without the need for a metallic liner.

Recent developments to support large-scale production (larger than 5 m in diameter and length), include the refinement of the winding process and the development of a toughened epoxy resin to enhance resistance to microcracking. Additionally, a novel technique has been developed to wind each ply of material without fibre crossings, minimising porosity and further improving microcrack resistance. Promising helium leak tests at low temperatures indicate that strict cryogenic standards can be met for detector operations.

The ability of cryostat vessels to resist structural instability (buckling) under compressive loads poses an additional challenge. The use of a full carbon honeycomb as a replacement for aluminium honeycomb is being explored. Initial prototypes have undergone extensive testing, including thermal expansion and dimensional stability assessments, underscoring the suitability of carbon honeycomb for large, buckling-sensitive cryostat walls.

The combination of a leak-tight carbon wall with the full carbon honeycomb core represents a promising design direction for next-generation HEP cryostats. A preliminary study, using the ALLEGRO detector concept as an example, revealed a 64% reduction in the material budget and a 30% reduction in wall thickness for buckling-sensitive cryostat walls compared to an aluminium sandwich design, with a thermal expansion coefficient one order of magnitude lower while maintaining comparable mechanical properties.

## 6.12 Muon system

Several technologies are under consideration for use in detector muon systems at FCC-ee, including μ-RWELL [745], resistive plate chambers [746], resistive Micromegas [747], scintillators, drift tubes, and combinations thereof. Apart from muon identification, these systems can offer capabilities for tail catching of calorimeter showers, identification of long-lived particles by providing tracking with good position resolution, or independent triggers.

Three μ-RWELL layers are currently implemented in the IDEA design, in both the barrel and end-cap regions, housed within the iron yoke that closes the detector magnetic field. The μ-RWELL chambers provide 2D space point measurements with a few hundred micron precision. In order to benefit from industrial production capabilities of this technology, a modular design is adopted with basic μ-RWELL 'tiles' with an active area of 50 × 50 cm² and a readout strip pitch of about 1 mm, enabling a sufficient spatial resolution of about 400 μm while limiting the number of readout channels to 1000 per tile. The choices of detector tile size, strip pitch and width are a compromise between the largest μ-RWELL detector that can be industrially mass-produced and the maximum input detector capacitance that can be tolerated in terms of signal over noise ratio by the front-end electronics.

Table 17 lists the dimensions, the number of basic μ-RWELL tiles, and the readout channels of the three muon stations of the IDEA detector. In total, including the barrel and the end-cap muon stations, the system comprises about 5800 μ-RWELL tiles with about 6 million readout channels.

The geometries and material of both the barrel and the end-caps have been implemented in the GEANT4 full simulation of the muon system. The implementation of algorithms for digitisation and clustering will follow in the next step of the study. Since the μ-RWELL technology has not yet been used to build a full detector system, a vigorous R&D programme to study integration issues will be carried out in the coming years. The detailed layout of the detector, together with all its services, will have to be accurately developed. The optimisation of the basic μ-RWELL tile, including gas gap, diamond like carbon layer resistivity, and gas amplification, has started [748,749] and is expected to be finalised to match the requirements of the IDEA muon system by 2027. The μ-RWELL R&D is performed in synergy with the WP1 of DRD1 [750]. Another important
<table><caption>**Table 17** Dimensions of the three IDEA barrel muon stations, together with the number of detector tiles and the corresponding number of readout channels</caption><thead><tr><th>Station</th><th>Radius (m)</th><th>Length (m)</th><th>Strip pitch (mm)</th><th>Strip length (mm)</th><th>Area (m²)</th><th># of tiles</th><th>Channels</th></tr></thead><tbody><tr><td>1</td><td>4.52</td><td>9.0</td><td>1</td><td>500</td><td>260</td><td>1040</td><td>1,040,000</td></tr><tr><td>2</td><td>4.88</td><td>9.0</td><td>1</td><td>500</td><td>280</td><td>1120</td><td>1,120,000</td></tr><tr><td>3</td><td>5.24</td><td>10.52</td><td>1</td><td>500</td><td>350</td><td>1400</td><td>1,400,000</td></tr></tbody></table>

aspect of this R&D programme is the design and development of dedicated front-end electronics based on a custom-made ASIC.

## 6.13 Luminosity measurement

For the precise measurement of cross sections, the integrated luminosity must be determined with high precision. Ambitious goals have been formulated on the measurement precision: $10^{-4}$ or better on the *absolute* luminosity and $5 \times 10^{-5}$ or better on the *relative* luminosity between energy scan points. At FCC-ee, the wide-angle diphoton process, $e^{+}e^{-} \rightarrow \gamma\gamma$, is statistically relevant and provides a promising complement to the traditional low-angle Bhabha scattering process, $e^{+}e^{-} \rightarrow e^{+}e^{-}$. For both processes, the definition of the geometrical precision constitutes an important source of systematic uncertainty.

As discussed in Sect. 4.6.3, the $\gamma\gamma$ final state places a requirement on the accuracy of the lower limit of the polar angle acceptance at the 8 $\mu$rad level, corresponding to 20 $\mu$m at 2.5 m from the IP. For each of the proposed ECAL solutions, R&D is needed on how to obtain such construction precision. Complementary methods to determine the acceptance in-situ with this precision or better are under development and alluded to in Sect. 4.6.3. Likewise, studies are needed on how to ensure that the efficiency of observing the $\gamma\gamma$ final state can be understood to the required precision over the wide detector acceptance.

For the measurement of low-angle Bhabha scattering, the luminosity calorimeters (LumiCals) are located close to the beam pipe, where they are neighbouring the complex Machine Detector Interface region (Sect. 5). Placed in front of the compensating solenoids, the LumiCals are at only ~1.1 m from the IP. In this region, space is severely limited and a very compact design is called for. The Bhabha cross section falls very steeply, as $1/\theta^3$, with $\theta$ being the scattering angle, resulting in very challenging tolerances on the definition of the geometrical precision at the $O(1 \mu m)$ level.

### 6.13.1 LumiCal design

Based on experience from LEP [751,752] and from past linear collider studies [624,753,754], compact SiW sandwich calorimeters are proposed as luminosity monitors for the measurement of low-angle Bhabha scattering. The calorimeters are designed as cylindrical devices assembled from stacks of identical SiW layers. This simple geometry facilitates the control of construction and metrology tolerances to the necessary micron level, as emphasised by the OPAL experiment [751]. The monitors are centred around the outgoing beam directions in the severely limited space available, in front of the compensating solenoids, which extend to $|z| \simeq 1.2$ m from the IP. The monitor design is illustrated in Fig. 118, where the main physical dimensions are also given. The design includes 25 layers, each comprising a 3.5 mm tungsten plate, equivalent to one radiation length, and a Si-sensor plane inserted in the 1 mm gap. In the transverse plane, the Si sensors are finely partitioned into pads. The proposed segmentation features 32 divisions, both radially and azimuthally, for 1024 readout channels per layer, or 25,600 channels in total for each calorimeter. A solution with a four times finer azimuthal segmentation is also under consideration.

A 30 mm uninstrumented region at the outer circumference is reserved for services (front-end electronics, cables, and cooling), as well as for the physical structures (likely including precision dowels and bolts) needed for the assembly of the SiW sandwich. Overall, the proposed design is very compact, each calorimeter weighing only about 65 kg. An example of the integration of the LumiCals with the MDI and the detector system is shown in Figs. 86 and 88, in Sect. 5.

The Si-sensor pads are connected to front-end electronics positioned at radii immediately outside the sensors. To minimise the occurrence of pile-up events, it is desirable to read out the sensors at the bunch-crossing rate. This constraint calls for the development of readout electronics with an $O(20 \text{ ns})$ shaping time. From experience with similar electronics development [755], a power budget of 5 mW per readout channel has been estimated, for a total of 130 W per calorimeter, to be removed by cooling. For the required geometric precision, the temperature needs to be controlled to within a tolerance of 1 $^{\circ}$C.
<figure><img src="image_128.png" /><figcaption>**Fig. 118** Front view (left) and top view (right) of the luminosity calorimeter, centred around the outgoing beam direction (shown as a red arrow). A possible segmentation of the Si pads is seen in the front</figcaption></figure>

view. Surrounding the sensitive region are regions for front-end elec-
tronics (red), and for cables and cooling (blue). The top view shows the
interleaved silicon-tungsten layer structure

The goal of 10<sup>-4</sup> precision on the absolute luminosity measurements translates into a required precision of O(1 &mu;m) on the radial dimensions of the calorimeters and of O(100 &mu;m) on the distance between the two calorimeters.

First full simulation studies of the LumiCals have been performed using 45.6 GeV electrons. They show that the proposed geometry covers the polar angle region between 53 and 98 mrad for fully contained showers, corresponding to a cross section of 28 nb at the Z-pole energy. With a sampling fraction of 1.1%, the calorimeters have an energy resolution of 3.2%, corresponding to 22%/&radic;E. The intrinsic resolution on the radial coordinate of showers is found to be 75 &mu;m at a z = 1100 mm reference plane, considerably better than the contribution of about 120 &mu;m from multiple scattering of the primary electrons in the 2 mm of beam pipe material traversed at shallow angles.

The feasibility of the proposed design has been demonstrated in part, over the last two decades, by work of the FCAL R&D Collaboration, which had been specialising in technologies for very-forward calorimeters at linear colliders. A five-layer prototype with a similar sandwich structure was built and successfully tested in a beam test [754], and a dedicated readout system based on a custom-designed readout chip was prepared [755,756].

Much work is needed towards a consolidated LumiCal design that satisfies the many severe requirements. Important future
steps include:

- Engineering-level study of the proposed detector assembly method, which involves precision dowels and through-going bolts. This study must take into account the required O(1 µm) geometrical precision on the radial coordinate.

- Realistic estimate of the space needed for services at radii outside the sensitive region. This region shall be kept as transparent as possible by the use of lightweight materials, to minimise particle interactions.

- Design of a procedure for maintaining and monitoring the geometric accuracy of the monitors via precise metrology and alignment.

- Design of a cooling system allowing control of a constant and uniform temperature over the monitors. The required tolerances have to be developed.
- Re-evaluation of the expected radiation dose based on the final collider parameters and assessment of whether existing sensor technologies are adequate or further sensor R&D is required.

- Design of compact low-power readout electronics that preferentially allows readout at the 50 MHz bunch-crossing rate, including transmission of signals away from the detectors. The system developed by the FCAL Collaboration may be a good starting point.

- Further full simulation studies to optimise the design of the detector.

## 6.14 Outlook

During the Feasibility Study, the detector designer community confirmed and enhanced its engagement and commitment to support a few complete detector concepts and to develop innovative detectors capable of delivering the required physics performance. The FCC-ee detectors have to meet unprecedented performance requirements in order to match the expected statistical precision and discovery physics potential. These requirements are, in many respects, complementary to what was needed at HL-LHC: while radiation tolerance is not an issue, with few exceptions close to the beams, the demands on precision, efficiency, purity, transparency of trackers, and compactness of calorimeters are considerably more challenging. Even though the readout bandwidth requirements appear relaxed when compared to the situation at HL-LHC, the required rate capabilities far exceed those from past linear collider studies. These constraints significantly magnify the system design and integration challenges especially if material budget and dead space are to be kept at minimum.

The detector R&D community has undergone a restructuring process, leading to the formation of DRD Collaborations to address these demands. While it is clear that these Collaborations will only be able to unfold their potential with an adequate ramp-up of resources, it is also important to emphasise that they must benefit from proper guidance through the detector conceptual activities in the FCC effort. In particular, it is crucial to continue to develop and maintain a powerful common software framework (Sect. 8), including full-simulation tools, in view of establishing and evolving the link between the detector concepts, on the one hand, and technological R&D, prototype design and construction, and ultimately test-beam data analysis, on the other. It will be essential that this common framework be adopted by the DRD teams, to optimise the subsystem inclusion in the FCC-ee detector simulation studies. Indeed, realistic geometries and digitizers will be essential to assess physics performance, as well as to compare with prototypes and test-beam data.

The detector community is well connected worldwide. The US and European roadmap processes, for example, have been well informed of each other and led to the formulation of overarching themes that are aligned to a large extent. This process is reflected in the ongoing integration of international groups and projects into the new DRD structure. Many of the proposals submitted to the DRD Collaborations target future Higgs factories and, among those, many specifically target FCC-ee. Given the current FCC-ee timeline, the R&D in the 2025–2027 period will give priority to conceptual and component studies, with system aspects in focus from the beginning, preparing the way to the possible development of prototypes and demonstrators during the subsequent 3-year period (2028–2030), followed by the construction and test of realistic modules by 2035.

The next phase of the FCC study will first capitalise on the developments made during the Feasibility Study regarding the full-simulation of the existing proto-detector concepts, to confront their simulated performance with the detector requirements from physics. This work will clarify if those physics-driven requirements are matched by the current proto-detector concepts and will point the way to alternative detector solutions. Different detector configurations will then be studied to optimise both performance and cost. In parallel, the links to the DRD Collaborations will be tightened. Work towards the common goal of developing FCC-ee detector concepts will be encouraged, by giving the R&D groups the necessary inputs and requirements from the FCC Feasibility Study, and by identifying their needs in terms of guidance and software tools.

Several challenges, specifically needed for FCC-ee but maybe not included in the DRD programme, will also need to be addressed. For example:

- How to monitor the time-stability of the magnetic field map in the experiments at the $10^{-7}$ level (taking into account all magnetic elements, including compensating solenoids, etc.)?

- How to achieve, possibly using a set of geometry systems, the accuracy on the knowledge of the alignment and surveying fiducials required for precision measurements (such as the luminosity measurement at low angles, the dilepton/diphoton cross section measurements at large angles, or the tau lepton lifetime measurement)?

- Can cosmic-ray muons continue to be used for the global alignment of FCC detectors, despite the fact that they will operate in much deeper caverns than those of previous colliders?
- Are there new detector technologies or configurations that would be particularly well-suited for specific FCC-ee measurements or that would be beneficial in view of improving the performance-to-cost ratio?

In the next few years, regular workshops will be organised with the DRD Collaborations, to evaluate possible design choices for detector subsystems, including their simulation, optimisation, demonstrators, and key engineering aspects, as well as to foster interactions and cross-fertilisation between interested institutes. Issues ranging from low-level readout architectures and engineering resources to larger-scale system integration, full-simulation-based optimisation, and high-level event reconstruction, will be addressed. The goal will be to quantify the cost and performance (including flexibility aspects) of each specific design choice, always retaining a physics-driven perspective, towards the timely delivery of conceptual design reports and full detector concepts proposals shortly after 2030. Reaching this ambitious goal will require an appropriate re-organisation and a significant injection of more (human and financial) resources in the project.

# 7 FCC cavern infrastructure

## 7.1 Introduction

Four experiment caverns are foreseen at FCC. During the FCC-ee operation, all these caverns will house general-purpose detectors, with various degrees of specialisation, aimed at exploiting the full physics potential of this collider. During the FCC-hh operation, a layout similar to the present LHC is foreseen: two caverns will house general-purpose detectors that cover the entirety of the proton-proton physics programme, similar to ATLAS and CMS, and the other two will house detectors more specialised to dedicated physics topics, on the model of ALICE and LHCb. It would be highly inefficient, impractical, and costly to modify the caverns at the end of the FCC-ee phase. A common cavern infrastructure that will serve equally well FCC-ee and FCC-hh must therefore be designed ahead of time.

Most aspects of the FCC experimental cavern infrastructure are defined by requirements for the FCC-hh detectors, given their much larger size, the extreme radiation environment and related shielding, as well as larger magnetic stray fields. A reference detector, conceived as a general-purpose detector able to fully exploit the physics potential of FCC-hh, was studied in detail in Ref. [703]. A cavern size of L66m × W35m × H35m with a shaft diameter of 18m is deemed sufficient to install and house such a detector. The cross section of this cavern is very similar to that of the ATLAS experiment. Two caverns of this size and two smaller caverns for the specialised experiments have therefore been assumed to define the corresponding civil-engineering operations and costs.

To evaluate their size, the two smaller caverns were assumed to house a detector specialised in B-physics, on the one hand, and a detector specialised in heavy-ion physics, on the other. Preliminary studies [757,758] have shown that a detector with transverse and longitudinal sizes not significantly larger than the dimensions of LHCb (10m and 20m, respectively) would have the same acceptance and resolutions as LHCb, in spite of the much larger energies. A more compact design, inspired from that of the BTeV detector [759], would allow a two-arm spectrometer to be built in the same spatial envelope. Similarly, a heavy-ion experiment would need to be more granular and have better performance, but its overall size would not have to be different from that of ALICE (the ALICE cavern dimensions are L53.5m × W15.5m × H22.7m).

A transverse cavern size similar to that of the CMS experiment would therefore be sufficient for both specialised detectors, leading to a L66m × W25m × H24.5m cavern and a shaft diameter of 15m for those two caverns. Such four caverns will definitely be more than adequate to house the FCC-ee detectors, which have typical diameters and lengths of 12–14m. The possibility of detector opening for maintenance in these caverns, especially the smaller ones, still need to be fully understood and ascertained.

In the following sections, the specifications and the layout of the FCC-hh reference detector are summarised, and more details on the cavern layout are given.

## 7.2 The FCC-hh reference detector

The FCC-hh parameters allow the direct exploration of particles with mass up to around 40–50 TeV [288], approximately an order of magnitude over the LHC sensitivity to heavy resonant states. During its lifetime, the FCC-hh is also expected to produce trillions of top quarks and tens of billions of Higgs bosons, allowing for rich SM precision measurement campaign [10,760] and rare-decay study programme [263]. Most importantly, FCC-hh is the only machine under study today that can provide a few per-cent level measurement of the Higgs boson self-coupling [85,760].
<figure><img src="image_129.png" /><figcaption>Fig. 119 Schematic of the FCC-hh reference detector</figcaption></figure>

An experimental apparatus that operates at FCC-hh must, hence, perform optimally on two main fronts (see Ref. [703] for a thorough discussion). Firstly, physics at the EW and Higgs boson scale will produce objects in the detector with momenta in the $p_T$ range 20–100 GeV; the LHC detectors were built to produce an optimal response in such an energy range. Secondly, a new regime, at the energy frontier, will be characterised by the energy scale of decay products originating from highly boosted SM particles and heavy resonances (potentially with mass as high as 50 TeV). An FCC-hh detector must therefore be capable of reconstructing leptons, jets, top quarks, and Higgs and W/Z bosons with momenta as large as $p_T = 20$ TeV. In short, the detector must provide accurate measurements in the full energy range between tens of GeV and tens of TeV.

Figure 119 shows the layout of the FCC-hh reference detector. This detector concept does not represent the final design, but rather a concrete example that suits the performance and physics requirements, and allows the identification of areas where dedicated further R&D efforts are needed. The detector has a diameter of 20 m and a length of 50 m, comparable to the dimensions of the ATLAS detector but much heavier. The central detector, with a pseudorapidity coverage of $|η| < 2.5$, houses the tracking, electromagnetic calorimetry, and hadron calorimetry, inside a 4 T solenoid with a free bore diameter of 10 m. In order to reach the required performance over the $2.5 < |η| < 6$ pseudorapidity range, the forward parts of the detector are displaced along the beam axis by 10 m from the interaction point. Two forward magnet coils with an inner bore of 5 m provide the required bending power. These forward magnets are also solenoids with 4 T field, providing a total solenoid

<figure><img src="image_130.png" /></figure>
<figure><img src="image_131.png" /><figcaption>**Fig. 120** Radial magnetic field for the FCC-hh reference detector, without magnet yoke. The stray field is around 100 mT at the cavern wall, while in the service cavern (50 m from the experimental cavern wall), it amounts to less than 3 mT</figcaption></figure>

volume with a length of 32 m for high precision momentum spectroscopy up to $|η| \approx 4$ and tracking up to $|η| \approx 6$. As an option, replacing the forward solenoids with two forward dipoles is also being considered. The tracker cavity has a radius of 1.7 m with the outermost layer at around 1.6 m from the beamline in the central and forward regions, providing the full spectrometer arm up to $|η| = 3$. The electromagnetic calorimeter (ECAL) has a thickness of around 30 radiation lengths ($X_0$). The overall calorimeter thickness, including the hadron calorimeter (HCAL), exceeds 10.5 nuclear interaction lengths ($\lambda$), ensuring 98% containment of high energy hadron showers and limiting punch-through to the muon system. The ECAL is based on liquid argon (LAr) given its intrinsic radiation hardness. The barrel HCAL is a scintillating tile calorimeter with steel and lead absorbers that uses wavelength shifting (WLS) fibres and silicon photomultipliers (SiPMs) for the readout. It is divided into a ‘central barrel’ and two ‘extended barrels’. The HCALs for the endcap and forward regions are also based on LAr. The requirement of calorimetry acceptance up to $|η| \approx 6$ translates into an inner active radius of only 8 cm at a z-distance of 16.6 m from the IP. The transverse and longitudinal segmentation of both the electromagnetic and hadronic calorimeters is ~4 times finer than the present ATLAS calorimeters.

The muon system is placed outside the magnet coils. The barrel muon system provides muon identification, stand-alone muon spectroscopy by measurement of the angle of the muon track, as well as precision muon spectroscopy by combining the tracker measurement with the measured space points in the muon chambers. The forward muon system can only provide spectroscopy if forward dipoles are used.

The reference detector does not assume a magnet yoke, i.e., there is no shielding of the magnetic field. Figure 120 shows the magnetic stray field as a function of radial distance from the beamline. The stray field still amounts to 100 mT at the cavern wall ($R = 17.5$ m), which has to be considered for the implementation of access structures and services. The 5 mT level is achieved at a distance of 55 m from the beamline, still outside of the service cavern. Clearly, it would be more convenient to have a shield for the magnetic field, but to arrive at a level of 5 mT at the cavern wall, which was the specification for CMS, an iron yoke of 4 m thickness would be required, weighing a total of 52 kt.

As can be seen in Fig. 119, embedding the muon system inside a yoke of 4 m radial thickness would lead to a total detector radius of around 11 m, similar to the ATLAS detector. Such a yoke is probably excessive in terms of cost and construction. With the radial extent of around 10 m for the FCC-hh reference detector, a cavern cross section of 35 m × 35 m is appropriate. If needed, such a cavern could even house the magnet yoke. For illustration, Fig. 121 shows an FCC-ee detector and the FCC-hh reference detector in this large cavern, while Fig. 122 shows an FCC-ee detector and a specialised FCC-hh detector of 14 m-diameter, similar to CMS, in the smaller caverns.

In FCC-hh, the longitudinal extent of the detector is limited by the machine elements and the related shielding. The last magnetic elements in the final focusing magnets of FCC-hh are at $ℓ^* = 40$ m from the interaction point. In order to shield these magnets from the collision debris originating from the interaction point, the so-called ‘TAS absorbers’ are placed at a
**Fig. 121** An FCC-ee detector (left, diameter 12 m) and the FCC-hh reference detector (right, diameter 17 m) in a large cavern of 35 m × 35 m cross section

<figure><img src="image_132.png" /></figure>

**Fig. 122** An FCC-ee detector (left, diameter 12 m) and a smaller, specialised FCC-hh reference detector (right, ø 14 m) in a small cavern of 24.5 m × 25 m cross section

<figure><img src="image_133.png" /></figure>

**Fig. 123** Total radiation load for the FCC-hh detector and the final focusing magnets in the machine tunnel, with a possible ultimate integrated luminosity of 30 ab⁻¹

<figure><img src="image_134.png" /></figure>

distance of around 35 m. The absorption of these high energy hadrons produces a significant amount of neutrons that ‘diffuse’ out of this absorber, as can be appreciated in Fig. 123. The concrete cavern wall at z = 33 m stops these neutrons from entering the cavern, defining the maximum possible cavern length to be 66 m. Altogether, these basic considerations converge to a cavern size of L66 m × W35 m × H35 m for the FCC-hh reference detector.

## 7.3 FCC cavern infrastructure

The FCC-hh cavern infrastructure is shown in Fig. 124. Since the service cavern is at a distance of around 50 m from the detector cavern and between 60 and 70 m away from the beamline, the stray field therein is below 5 mT (Fig. 120) and standard equipment can be placed at this location. Besides, the radiation shielding provided by this distance suffices to allow
<figure><img src="image_135.png" /><figcaption>**Fig. 124** FCC-hh cavern infrastructure. The bypass tunnels are required to enable transport vehicles to pass around the experimental area</figcaption></figure>

<table><caption>**Table 18** Requirements and key numbers for the FCC-ee and FCC-hh detectors</caption><thead><tr><th>Item</th><th></th></tr></thead><tbody><tr><td>Size of large caverns</td><td>L66 m W35 m H35 m</td></tr><tr><td>Shaft diameter of large caverns</td><td>18 m</td></tr><tr><td>Size of small caverns</td><td>L66 m W25 m H24.5 m</td></tr><tr><td>Shaft diameter of small caverns</td><td>14 m</td></tr><tr><td>FCC-hh reference detector diameter without yoke</td><td>20 m</td></tr><tr><td>FCC-hh reference detector diameter with yoke</td><td>22 m</td></tr><tr><td>Stray field at cavern wall (R = 17.5 m)</td><td>100 mT</td></tr><tr><td>Distance for stray field < 5 mT</td><td>55 m</td></tr><tr><td>FCC-ee detector diameter</td><td>12–14 m</td></tr></tbody></table>

permanent access to the service cavern. A main shaft of 18 m diameter gives access from the surface to the experiment cavern. It houses only some ventilation pipes but no other services or elevators, and is only foreseen for the transport of equipment. The personnel access and the detector services are housed in the service shaft, which connects to the service cavern. Three connection tunnels, represented in Fig. 124, connect the service and experiment caverns: a central one, of 10 m diameter, for services, and two others, of 5.5 m diameter, placed on each of the two ends of the detector. They are complemented by two evacuation tunnels, also represented in the figure.

The principal dimensions of the FCC cavern infrastructure are summarised in Table 18.

## 8 Software and computing

Ever since the launch of the FCC conceptual design study in 2014, one of the primary objectives has been to design and develop a unified, synergistic, and adaptable software ‘ecosystem’, to serve as a foundation for all future experiments at FCC-ee and FCC-hh. With its data processing framework and all the necessary tools inspired by the advanced software of running experiments and ongoing R&D initiatives, the resulting ecosystem is aiming at addressing all future experiment’s use cases, based on modern software technology.

In 2019, in the new development phase following the conceptual design study, pursuing the idea of a common software ecosystem for future projects was further motivated by the need to pool efforts in a phase of limited resources. In the short
to medium term, the minimal goal is to provide the teams forming around detector concepts with a starting point that is as complete as possible. The broader vision, however, remains unchanged: to encourage the community to adopt common software wherever feasible, relying on experiment-specific solutions only when strictly necessary. Even in those cases, such developments should, where possible, be framed as extensions of the core components. Adopting this approach from the outset also has clear benefits for long-term data preservation and sustainability, an aspect that future projects should take into account from the very beginning.

While this transformative approach required significant time to gain general acceptance, and even if the level of completeness is not anywhere close to that of running experiments, this new ecosystem is now regularly used by the FCC particle physicists in their daily work. The performance of some tools, such as flavour tagging algorithms, already far surpasses that of the algorithms used for past linear collider studies [761]. Needless to say, further work is needed to fully enable all studies targeted by the FCC-ee scientific programme. For example, the following tasks (among many other necessary developments) were identified as priorities for the FCC Feasibility Study:

- Proceed with the full and parametrised simulations (and their interplay) of the sub-detectors currently considered (Sect. 6), including digitisation and sub-detector interchange with a 'plug-and-play' framework, towards enabling the study of the performance (Sect. 4) of a large variety of detector concepts.

- Develop and implement the various reconstruction and analysis tools for use by all collaborators, reaping the benefits from LHC experience and, whenever relevant, from past linear collider studies.

- Complete the simulation of the interaction region, also known as machine detector interface (MDI, Sect. 5), in view of the final evaluation and mitigation of beam-related backgrounds in the detectors. This task includes streamlining the access to the Monte Carlo codes that simulate the relevant backgrounds.

- Provide the technology needed to improve the accuracy of the simulation of beam-related quantities (such as the beam-energy spread, crossing-angle spread, bunch length and transverse size, final state particle deflection by the colliding bunches, etc.) as well as initial state and final state radiation (and their interference) to match the statistical precision expected at FCC-ee, in particular at the Z pole. Ensure that these technologies are usable in all Monte Carlo generator codes relevant for FCC-ee, in close interaction with the code authors.

- Continue to drive the development of the common software framework (KEY4HEP) and common data format (EDM4HEP), ensuring that they meet the requirements of FCC, both in terms of functionality and of infrastructure building, testing and deployment.

- Evaluate the need for computing resources and proceed with regular simulated data production. The computing needs for FCC-ee are dominated by the Z-pole run, both online and offline. The corresponding demands are significant, even when compared to HL-LHC. By the time FCC-ee operations start, it will be crucial to leverage the advances and insights gained from HL-LHC, also in terms of resource sustainability. Even during the next phase of the study, the needs for fully simulated and reconstructed event samples, and for their analysis, are potentially challenging and require detailed identification, evaluation, and purchase of the necessary computing resources. Coordination with resource providers, which include CERN, WLCG grid sites involved in FCC research, and HPC centres, is required to identify ways to guarantee access to these resources.

- Last but not least, provide the users with detailed documentation and regular pedagogical tutorials, as has been the case in the past decade.

This section reviews the progress made towards achieving the tasks listed above. The results presented and discussed reflect the collaborative efforts of the 'Software and Computing work package', in conjunction with other work packages within the FCC PED feasibility study. A key factor in this progress has been the strong software core team at CERN, which provides the overall vision, delivers the daily technical coordination, and ensures the timely development of essential common tools.

## 8.1 The FCC software ecosystem

During the FCC feasibility study, the focus has been to deliver the components deemed essential to meet the challenges of FCC-ee and to assess the physics potential of the proposed experimental infrastructure: a comprehensive suite of $e^{+}e^{-}$ event and beam-background generators; a proper handling of the complex interaction region and associated backgrounds; an infrastructure that facilitated the implementation of detector subsystems and detector concepts (i.e., their geometries,
<figure><img src="image_136.png" /><figcaption>**Fig. 125** Workflows to be supported during the project design and FCC Feasibility Study</figcaption></figure>

their simulation, and the development of versatile reconstruction algorithms); and tools for event analysis, visualisation, and resource management. The corresponding workflows are illustrated in Fig. 125.

Because this ambitious plan required human resources far beyond those available during this phase of the project, a proposal was made to other e⁺e⁻ particle physicist communities to join forces and explore the possibility of developing a common software solution that could be adapted to the needs of all collider and detector geometries. Based on the initial FCC software framework developed during the Conceptual Design Study, nicknamed FCCSW, and driven by the belief that the high-energy physics community was ready to further expand the number and role of shared components between experiments, the KEY4HEP initiative was launched after two founding workshops held in 2019 and early 2020 [762,763].

Like any other large-scale software development, KEY4HEP is inherently a collaborative effort. It builds on the experience of the LHC experiments, is integrated with community R&D projects, and maximises the reuse of established solutions and packages, allowing experiments to benefit from existing community developments. Notable examples include the common core framework GAUDI [764]), developed and used by LHCb and ATLAS, the DD4HEP [765] and PODIO [766] R&D projects for, respectively, detector description and event data model definition, and other well-known packages like ROOT [767] or GEANT4 [768]. By leveraging and contributing to these experiment-independent software packages, the KEY4HEP initiative aims at fostering a broader ecosystem of HEP software, enhancing collaboration and innovation across the field.

After recalling the main concepts of KEY4HEP in Sect. 8.2, the current status in each of the main areas is summarised in the following sections: common event data model (Sect. 8.3); event generators (Sect. 8.4); parametrised (Sect. 8.5) and full (Sect. 8.6) simulation; digitisation (Sect. 8.7) and reconstruction (Sect. 8.8); event analysis (Sect. 8.9); visualisation (Sect. 8.10); and resources (Sect. 8.11).

## 8.2 The main components of KEY4HEP

The KEY4HEP ecosystem has been designed to address core requirements common to all experiments in a sufficiently robust manner, while allowing specific extensions to meet individual demands. High-energy physics data processing consists of several basic components that need to be chosen carefully, the most important of which are listed below.

1. A data processing framework provides the structure for integrating and steering all other components. For example, past linear collider studies used the MARLIN [769] framework for many years. In KEY4HEP, as mentioned above, GAUDI [764] was selected for its adoption by two LHC experiments, its broad user and developer communities, and its maturity as a framework that has evolved to be experiment-agnostic. Its potential for further evolution, including support for heterogeneous computing resources, multiple architectures, and task-based concurrency, was also considered an asset, although, in this respect, the experience developed by CMS with CMSSW and possibly by ALICE with O2 (Refs. [770,771] and references therein) will also be leveraged in future developments<fnref n="26" />.

<footnote n="26">²⁶ The evaluation of CMSSW as a replacement of GAUDI has already been listed as part of possible future R&D programs for the evolution of the common software ecosystem.</footnote>
2. A detector geometry description tool, chosen to be DD4HEP [765] because of its already use in the relevant communities. In addition to providing a comprehensive detector description for event simulation, reconstruction, and analysis, DD4HEP is now also used in production by the CMS and LHCb collaborations. This adoption drives a consolidation and development process that is highly advantageous for future experiments, in particular in critical areas, such as alignment and calibration.

3. A common event data model, called EDM4HEP (Sect. 8.3).

4. An infrastructure to build, test, and deploy the required software with minimal effort, automating the installation and ensuring a consistently linked set of packages with correct dependency resolution. The LHC Collaborations addressed this challenge independently, without converging on a unified solution. The HEP Software Foundation's packaging working group identified the scientific package manager SPACK [772] as a potentially promising common solution worth further exploration for use in HEP. In line with the KEY4HEP philosophy, SPACK was evaluated and successfully used to build KEY4HEP, despite certain limitations [704]. These challenges include limited support for development workflows and deployment capabilities, requiring custom in-house workarounds, such as those required to deploy build artifacts on CERNVM-FS, the widely-adopted technology for software distribution in HEP.

## 8.3 The event data model EDM4HEP

The event data model defines the structures needed to describe the required event information in the persistent store. While, in principle, this model can be different from what is used in the transient store seen by the data processing algorithms, and also from algorithm to algorithm, adopting the same event model everywhere reduces the need for conversions, enhances generality, and improves interoperability.

Since the launch of the FCC studies, the choice has been for an event data model managed by PODIO [766], a toolkit that generates the data model implementation from templates. With this choice, the high-level description in YAML files using Plain-Old-Data (POD) simple types are separated from the low-level persistency layer, which can be optimised according to the back-end. Once the required classes are defined in the YAML file, the PODIO tool creates the source code automatically. The same technology has been chosen for KEY4HEP, with an event data model referred to as EDM4HEP, initially based on the event data models used in past linear collider studies (LCIO [773]) and in the FCC conceptual studies (FCCEDM [11]) classes, and improved from there as needed.

The underlying assumption is that the same event data model can be used for all types of HEP experiments, which is well-suited to the integrated FCC programme, with a lepton collider followed by a hadron collider. This requirement appears to be fulfilled by EDM4HEP, although a more definitive assessment will become available only when the FCC-hh investigations are extended to more use cases.

### 8.3.1 A specific use case: LEP data in EDM4HEP

In the context of the LEP data preservation efforts, an initiative has been launched to migrate those data to EDM4HEP, in a pioneering attempt to analyse these real, non-simulated data in the FCC software ecosystem. Beyond the clear advantage of preserving the ability to extract new scientific insights from LEP data for future generations, this effort has several key objectives relevant to FCC-ee. Most interestingly, LEP and FCC-ee share the same collision type and several centre-of-mass energies. This initiative therefore opens a unique opportunity to FCC physicists to gain hands-on experience with real data, thereby preparing them for future analyses within the FCC-ee scientific programme. It can also provide a platform to validate and improve simulation, reconstruction, and analysis tools, thus enhancing their reliability for future collider studies.

A preliminary migration feasibility study is currently underway with data from the ALEPH experiment. The project aims at establishing a conversion workflow that integrates both the experiment legacy software, executed within dedicated containers with the latest operating systems and validated by the experiment, and KEY4HEP-based applications. The initial approach involves extracting data at the analysis level<fnref n="27" /> into an operating system-agnostic ASCII format, which can then be used to reconstruct the EDM4HEP structures for FCC analyses. Additionally, the project seeks to recreate a bookkeeping database containing relevant ALEPH metadata.

The status of the project was presented in the autumn of 2024 [775, 776]. The current findings provide encouraging evidence of the overall feasibility of the approach, despite difficulties in recovering comprehensive documentation, retrieving detailed information about the data that are often hardcoded within the legacy software, and reconstructing detailed metadata about the

<footnote n="27">²⁷ For ALEPH, the initial focus is on the MINI format [774] however, the methodology under development is designed to be adaptable and could also be extended to the more comprehensive DST data format.</footnote>
<caption>**Table 19** List of generators and related tools available in KEY4HEP at the time of writing. Most of the generators are available in the upstream SPACK repository; the ones added by the KEY4HEP-SPACK repository</caption>

are indicated with an asterisk. Some additional details on the way the tools are built can be found in Ref. [623]

<table><thead><tr><th colspan="7">Generators</th></tr></thead><tbody><tr><td>BABAYAGA*</td><td>BAURMC</td><td>BHLUMI*</td><td>CRMC</td><td>EVENTGEN</td><td>GENIE</td></tr><tr><td>GOSAM</td><td>GUINEA-PIG*</td><td>HERWIG3</td><td>HERWIGPP</td><td>KKMC*</td><td>MADGRAPH5AMC</td></tr><tr><td>PHOTOS</td><td>PYTHIA6</td><td>PYTHIA8</td><td>SHERPA</td><td>STARLIGHT</td><td>SUPERCHIC</td></tr><tr><td>TAUOLA</td><td>VBFNLO</td><td>WHIZARD</td><td></td><td></td><td></td></tr></tbody><thead><tr><th colspan="6">Generator tools</th></tr></thead><tbody><tr><td>AGILE</td><td>ALPGEN</td><td>AMPT</td><td>APFEL</td><td>CCS-QCD</td><td>CHAPLIN</td></tr><tr><td>COLLIER</td><td>CUBA</td><td>DIRE</td><td>FEYNHIGGS</td><td>FORM</td><td>HEPMC</td></tr><tr><td>HEPMC3</td><td>HEPPDT</td><td>HOPPET</td><td>HZTOOL</td><td>LHAPDF</td><td>LHAPDFSETS</td></tr><tr><td>LOOPTOOLS</td><td>OPENLOOPS</td><td>PROFESSOR</td><td>PROPHECY4F</td><td>QD</td><td>QGRAF</td></tr><tr><td>RECOLA</td><td>RIVET</td><td>SYSCALC</td><td>THEPEG</td><td>UNIGEN</td><td>YODA</td></tr></tbody></table>

data samples. These findings highlight the importance of generalising this effort as part of a more structured and systematic project.

## 8.4 Integration of event generators

Event generators are a crucial component of the software infrastructure in any HEP experiment, to design optimal data analysis strategies, evaluate detector performance requirements, and compare them with the response of different detector solutions, ultimately maximising the physics potential of the project. The richness of the FCC physics programme introduces new challenges for event generators across multiple dimensions. The unprecedented statistical precision expected at the Z pole for FCC-ee, and the expanded energy range of FCC-ee and FCC-hh, call for substantial theoretical advances (Sect. 3). These very precise calculations need to be translated into similarly accurate, computationally efficient, and easily maintainable software packages.

Many event generators are already included in KEY4HEP through the integration of the upstream SPACK repository. At the start of the FCC studies, when SPACK was not yet in use, the initial set of event generators was derived from the 'LCG stacks', i.e., software stacks developed and maintained in the EP-SFT group at CERN targeting the cases of ATLAS and LHCb. These stacks are, however, more and more used by non-LHC projects, and have been progressively expanded to include event generators not used at the LHC, such as WHIZARD [777], a general purpose event generator used for past linear collider studies. Today, KEY4HEP includes an extended set of generic event generators, able to cover most of the initial needs of future projects, such as PYTHIA8 [778].

The increasing interest for FCC-ee has brought in the need for more specific and more accurate event generators. State-of-art generators for high-energy $e^{+}e^{-}$ collisions, however, date from the LEP era and have been minimally maintained since. One of the first tasks to be addressed in the FCC feasibility study was the recovery of the still very relevant LEP event generators, such as KKMC [779], BHLUMI [780], and BABAYAGA [781]. The generators and related tools available in KEY4HEP at the time of writing are listed in Table 19.

### 8.4.1 Event generators as packages

Within the software ecosystem, generators are software packages that come with their own build, test, and deploy recipes. The recipes allow KEY4HEP to build in share installation mode, run the built-in test programs, and install the binaries into a distributed shared file system (CernVM-FS).

The generated events need to be injected into the simulation workflow, which requires a low level of interoperability between the event generator and the rest of the chain, named *Common Data Formats*. This level ensures that the applications
exchange information files that are understood by all relevant processes, even on different hardware.<fnref n="28" /> The event generators are indeed typically stand-alone applications producing files with the generated events, in ASCII or binary data format. These event data formats have evolved in time following the requirements set by the community and are briefly reviewed in the next section. Some recent event generators offer enhanced interoperability with *Callable Interfaces*, i.e., an API of functions streamlining the exchange of information among various components and increasing flexibility. These APIs can also be used as interface to a framework, as is described in the next section.

### 8.4.2 Common data formats

The data formats produced by event generators provide structures to store the lists of particles per event, with their momenta and type, information relevant to the event, such as its weight(s), and information relevant to the run, such as the configuration and version of the generator. Several formats serving similar purposes appeared in the years ahead of the LHC. Among these, `STDHEP` [782] and `HEPEVT` [783] are first attempts to create standards, a challenge that has been taken on by `HEPMC` [784], the latest version of which (version 3) includes readers for most of the available formats. The complexity of the generators developed for LHC brought in new needs, essentially to store information about matrix elements and alike. They have been included in the ‘Les Houches Event format’ (LHEf). This format had initially been designed to transfer the matrix-element information to the parton shower component, but has since been used as a generic format at LHC and beyond, including `FCC`.

To handle the plethora of formats, `KEY4HEP` ensures that readers for all the formats required by the event generators of interest are available for all the simulation chains in use, based either on `GAUDI` or with standalone applications. For `GAUDI` applications, such as those using the framework components provided by `K4SIMDELPHES` [785] and/or `K4SIMGEANT4` [786], the readers are implemented as `GAUDI` algorithms and transform the input from the files into `EDM4HEP` structures in memory that can be parsed by the next simulation algorithm. For standalone applications, such as those provided by `K4SIMDELPHES` (Sect. 8.5) or `DDSIM` (Sect. 8.6.1), support for the formats is implemented within the applications.

In the context of the ongoing `ECFA` activities for electroweak and Higgs factories, the `HEPMC3` and `EDM4HEP` formats were recommended for the next versions of event generators, and the latter is deemed more suitable to meet the needs of the community. These recommendations were discussed at a dedicated event in June 2024 [787].

### 8.4.3 Configuration

The configuration of generators for Monte Carlo simulations often involves redundant efforts, as different generators aim at the same physics processes. To streamline this process and improve efficiency, the `K4GENERATORCONFIG` [788] package provides a unified approach to generator inputs. This package, which is already included in `KEY4HEP`, addresses essentially two challenges: lack of standardisation (each generator requiring a specific input format despite simulating, in principle, the same physics processes), and author involvement (relying on authors to adopt a common input format is impractical, as they are unlikely to change existing workflows or agree on a unified approach). The proposed solution consists in the creation of a master input card defining the required parameters and configuration for simulations, which is then converted by a dedicated Python module into generator-specific runcards, ensuring compatibility across different MC tools. This approach will automate the creation of inputs tailored to each generator while maintaining consistency with the master card.

The targetted benefits are reproducibility and error minimisation, as a unified configuration process inherently reduces discrepancies and manual errors in input preparation, and minimises the potential for mistakes that can arise from manual handling of generator-specific configuration cards. The solution also provides a way to improve legacy preservation, as the system also supports the older ‘LEP era generators’, ensuring continued usability, even when there is no active development by the original authors.

An initial set of generators has already been integrated in the system and an infrastructure has been set up to enable running and comparing benchmarks of the tools. A status report was presented at the 3rd `ECFA` workshop, in October 2024 [789].

## 8.5 Parametrised simulation

The `DELPHES` parametrised simulation toolkit [790] is integrated into `KEY4HEP`. By applying resolution and efficiency functions to generator-level objects, `DELPHES` offers a high-level approximation of the detector response in a highly flexible and

<footnote n="28">²⁸ Passing information through files might impact performance. However, reading Monte Carlo events from files is not a limiting factor at the LHC and will likely not be at `FCC` either.</footnote>
lightweight tool. Its capabilities encompass the propagation of charged (and neutral) particles in a magnetic field, the modelling of electromagnetic and hadronic calorimeters, and the parametrisation of muon identification efficiencies. Basic elements like charged-particle tracks and calorimeter energy clusters are reconstructed from the simulated detector response. A simplistic particle-flow reconstruction combines tracks and calorimeter information to form a list of particle candidates in a global event description. These particles are then used as input to form higher-level objects such as isolated leptons, jets, and total/missing energy and momentum. Although the physics performance obtained from DELPHES represents the best that could be achieved with nominal sub-detector resolutions, this tool shows a reasonable agreement with the more detailed full simulation, as discussed in Sect. 4.10, and can thus be used to establish detector requirements and to provide rather robust estimates of the FCC-ee physics potential.

The DELPHES toolkit was enhanced with several new features, which include an algorithm reconstructing the charged-particle track parameters and covariance matrix for arbitrary tracking geometries; a module for deriving time-of-flight measurements; and a tool that parametrises the number of ionisation clusters associated with the trajectory of a charged particle in a gaseous detector, based on simulations from GARFIELD [720]. These tools have been incorporated into the central DELPHES package and are employed, in particular, to train a jet-flavour-identification algorithm [791] based on deep neural networks.

A DELPHES configuration card simulating the expected performance of the IDEA detector concept, with a detailed layer-by-layer description of its tracking system, has been implemented and added to the central repository [792]. An alternative version of this parametrisation, featuring a full silicon tracking system, was also developed to emulate physics performance closer to what is anticipated from the CLD detector concept. The integration of CLD calorimeter parametrisations into this card is under development. More information on these parametrisations can be found in Ref. [623].

The DELPHES integration into KEY4HEP is achieved through the K4SIMDELPHES package [785], which wraps the core components of DELPHES and adds the functionality to convert its output into the EDM4HEP data model. Several command-line tools (DELPHES\*_EDM4HEP) simplify the use of these extensions in stand-alone mode, while the K4SIMDELPHESALG GAUDI algorithm enables full integration of DELPHES simulations within a KEY4HEP workflow, allowing users to benefit from features such as the generator functionalities described in Sect. 8.4.

To enhance flavour physics studies in parametrised simulations, an interface between PYTHIA8 and EVTGEN is implemented, and is fully integrated with the DELPHES applications. This interface enables efficient generation of background contributions in regions of phase space where specific signals are expected (e.g., rare hadron decays or long-lived particles). Users must apply a posteriori normalisations ‘manually’ to ensure consistency between the generated number of events and the reported cross sections.

## 8.6 Full simulation

Some applications require simulations with a higher level of detail than DELPHES. For example, R&D efforts and physics analyses that access detector-level information demand a more detailed description of the detector geometry and response. To address these needs (and, incidentally, to validate the detector parametrisation outlined in the previous section), a detailed modelling of all the (sub-)detectors considered for FCC is actively being developed. This section provides an overview of the current status of geometry implementation, along with existing examples of full detector configurations using different combinations of sub-detectors.

### 8.6.1 Detector description and simulation strategy

The DD4HEP toolkit [765] (Sect. 8.2) is used to model FCC detector geometries. This modern community standard hides the geometry complexity and allows high-level aspects (such as sub-detector dimensions, shape and materials, or the list of sub-detectors to be combined into a complete detector concept) to be configured by non-expert users with simple XML ('compact') files in a flexible plug-and-play approach, crucial for detector optimisation efforts. This approach allows for the optimisation of (sub-)detector variants without the need for recompilation and without an in-depth understanding of the technical details of the geometry implementation. It is essential, however, that the developer of the C++ detector builder (also called 'detector driver') incorporates the necessary prescriptions and safeguards to ensure that a 'sane' geometry be implemented under all circumstances. Several tools are available in DD4HEP to validate the resulting geometries, such as checks to ensure that detector volumes do not overlap.

While implementing a completely new sub-detector geometry is a more complex task, numerous examples and a wealth of community expertise greatly facilitate this process. Adding the newly created sub-detector to an existing concept, or building a new concept using existing sub-detectors, is straightforward using the 'master' XML files that manage the list of sub-detectors
and their envelope dimensions. This, again, assumes that the C++ drivers are designed to adapt dynamically to changes in outer envelope dimensions. A policy has been set in place to document XML parameters that require additional prescriptions before modification, complementing the sanity check tools to reduce the risk of creating ill-defined geometries.

The DD4HEP framework is also well-suited for the modelling of individual modules used in test beams. Implementing test-beam geometries into this framework for the upcoming R&D activities would be highly advantageous, as it would provide a basis for preparing complete sub-detectors, in view of their integration into full detector concepts. Occasionally, the availability of complete sub-detector geometries predates the test-beam campaigns. In such cases, R&D teams could simplify and adapt the more complex full geometry to create the individual module.

The GEANT4 simulations are run on these models through the DDSIM tool provided by DD4HEP. This tool provides many functionalities that help the simulation configuration through command-line arguments or Python steering files (or a combination thereof), and can be run with simple particle guns or by providing input files containing the particles from Monte Carlo generators. Most common formats are supported: HEPMC(3), HEPEVT, STDHEP, and the so-called 'pair' files produced by GUINEAPIG++ (in addition to the LCIO format). The output format can be EDM4HEP, LCIO, or the DD4HEP native format.

### 8.6.2 Sub-detector models

Sub-detector geometries are available in the K4GEO GITHUB package [793]. The currently available DD4HEP drivers, relevant for FCC-ee, are listed below. A more thorough description of their implementation details can be found in Ref. [623].

- **Beam-pipe and related MDI components.** Two different models exist: one based on 'native' GEANT4 shapes with a simplified geometry and the other exploiting the ability of DD4HEP to directly import the CAD-based technical drawings, thus providing a much higher level of detail at the expense of poorer computing performance.

- **Vertex detectors.** The driver used to model, for instance, the CLD vertex barrel detector, builds an arbitrary number of layers made of staves parallel to the z axis with two different materials (one for the sensitive layers and the other for the support). The endcaps are constructed with simple octagonal plates perpendicular to the z axis, made of an arbitrary number of slices with different thicknesses and materials. Another detector builder was recently developed to model the IDEA vertex detector. This driver offers a higher level of detail: it accounts for non-sensitive edges of the modules and includes staves/petals internal structures, together with support components. A switch in this driver allows the modelling of a geometry with almost support-free curved sensors.

- **Main trackers.** Two versions are available: the former modelling a full silicon tracker, following an approach similar to that of the CLD vertex detector builder, described above, and the latter modelling a full stereo gaseous drift chamber. The latter features hyperboloid layers and twisted tubes to emulate the cell volume hosting the sense and field wires. The full geometry is built with a handful of user-provided parameters: global dimensions, number of (super)layers, number of cells in the first layer and its increment from one layer to the next, etc. A third model, describing a straw-tube tracker, is under preparation.

- **Dedicated particle identification detector.** A first version of the Array of RICH Cells (ARC) concept, described in Sect. 6, is implemented. The driver builds both the barrel and the endcaps, and omits, for now, the cells in the transition region, given their higher complexity. This detector builder includes the radiator gas and aerogel, the mirrors, the sensitive silicon sensors, the cooling plates and the outer vessel. The mirror positions and inclinations are set according to Ref. [642]. The material budget of the full sub-detector implementation corresponds to approximately 5% of a radiation length and can be easily tuned.

- **Calorimeters.** The following drivers are available: SiW luminosity calorimeter, noble liquid calorimeter with inclined absorber/readout planes, scintillating tile calorimeter ('tileCal'), and two fibre dual readout calorimeters, one with a capillary tube-based geometry and one where the fibres are directly inserted into metallic towers. A detector driver modelling a segmented crystal-based dual readout calorimeter is being integrated in KEY4HEP. The simulation of dual readout calorimeters is especially challenging, in particular because of the number of scintillating photons generated, and requires special prescriptions [623]. The high-granularity calorimeters proposed for CLD are built with the generic driver described below.

- **Generic detector builders.** Some drivers have been designed generically to serve multiple purposes. For example, GENER-ICCALBARREL_O1_V01 and GENERICCALENDCAP_O1_V01, are used, e.g., to build the ECAL, HCAL, and muon system of CLD. These drivers arrange user-defined layer sequences, either radially or along the z-axis, forming a polyhedron with a customisable number of sides, set in the compact file. Another example of a generic detector builder is MUONSYSTEM-
<figure><img src="image_137.png" /><figcaption>**Fig. 126** Illustration of the flexibility provided by the detector driver that builds µRWELL-based muon systems: different barrel implementations with 6, 12, and 4 sides (from left to right). The grey layers represent the sensitive detector components, while the return yokes are shown in red</figcaption></figure>

<figure><img src="image_138.png" /><figcaption>**Fig. 127** Pictures of three detector concepts (ALLEGRO, CLD, and IDEA) implemented in DD4HEP</figcaption></figure>

MURWELL_01_v01, which defines stacks of layers made of user-defined tiles (e.g., PCB's) and also provides flexibility on the number of sides, as illustrated in Fig. 126.

This flexibility is an appealing feature at this stage of the project, as it allows the software implementation to smoothly and rapidly adapt to detector R&D choices. Unlike the formerly described drivers building the CLD calorimeters and muon system, MUONSYSTEMMURWELL_01_v01 allows the user to define some overlap between the tiles (e.g., to account for their possibly non-sensitive edges) and stagger each side of the polyhedron to ensure a fully hermetic coverage. This constructor is used to model the IDEA µRWELL-based muon system and pre-shower sub-detectors.

### 8.6.3 Full detector models

The availability of these sub-detector geometries along with the plug-and-play philosophy of DD4HEP facilitates the creation and implementation of full detector concept alternatives. These models are hosted in the K4GEO GitHub package [793] and take the MDI components (beam-pipe, compensating solenoids, shields, LumiCal, etc.) from a central place, to ease the software maintenance. Pictures of three detector concepts introduced in Sect. 6, as they are currently implemented in DD4HEP, are shown on Fig. 127.

A complete model of the CLD detector is available [794]. The main change with respect to the original geometry is the adaptation of the vertex detector to the most recent beam-pipe design (Sect. 5). Based on this model, an alternative option including the ARC subsystem, was prepared. This version of CLD features a reduced-size outer tracker in order to fit the ARC between the main tracker and the (unchanged) ECAL, as shown in Fig. 128. This enables comprehensive studies to evaluate the benefits of enhanced particle identification capabilities, as well as any potential impact on the performance of the particle-flow reconstruction.

A first complete model of the IDEA detector is also available. It consists of a detailed inner vertex detector with straight staves; a full stereo drift chamber with all wires included; a silicon wrapper constructed with the same driver as that used for the inner vertex detector;<fnref n="29" /> a solenoid and an end-plate absorber described as simple cylinders with a thickness 0.75%X₀; a pre-sampler; a fibre-based 'monolithic' dual-readout calorimeter; and a µRWELL-based muon system. Based on this

<footnote n="29">²⁹ With the options of changing the definition of the staves in the compact file to have sensitive components on both sides, using strips instead of pixels, and a reduction in the level of details being modelled to reach a computationally affordable description.</footnote>
<figure><img src="image_139.png" /><figcaption>**Fig. 128** Picture of the CLD detector concept model with enhanced particle identification capabilities. This variant of CLD includes the ARC sub-detector between the outer tracker and the ECAL. The other subsystems (HCAL, muon chambers, etc.) are present in the model but not shown here</figcaption></figure>

implementation, an alternative version of the IDEA detector, featuring an additional crystal-based ECAL, is now being
developed.

The ALLEGRO detector concept is implemented as follows: a tracking system (inner vertex detector, drift chamber, and silicon wrapper) directly imported from the IDEA implementation; a noble liquid ECAL inside a lightweight cryostat whose outer wall also accounts for the solenoid material budget; and a tile HCAL, placed inside a muon system place-holder made of two nested layers of sensitive cylinders.

The GEANT4 toolkit is used to simulate the passage of particles through matter. Its raw simulation output requires further processing to create data objects suitable for analysis. The processing workflow includes two key stages: digitisation, which transforms simulated detector hits into realistic detector responses, and reconstruction, which interprets these responses to identify and characterise the underlying physics objects. The next two sections provide an overview of the capabilities currently available in the central FCC software, with ongoing developments and future directions. A more detailed discussion can be found in Ref. [623].

8.7 Digitisation

For silicon trackers and muon systems, a straightforward and generic digitisation approach is currently implemented. The simulated hit positions and time are smeared with Gaussian uncertainties, keeping the digitised hit position within the sensitive volume and applying an optional time window cut. The spatial smearing is performed in the local coordinate system of the sensitive module and allows for two distinct Gaussian widths. For strip-based sensors, a uniform probability distribution is assumed, such that the position is set in the middle of the sensor with an uncertainty along the strip direction equal to the wafer length divided by $\sqrt{12}$. This simple method allows a flexible and generic software implementation, making it applicable to various sub-detector types. An enhanced digitisation model that includes, in particular, charge-sharing effects, is under development. This new model will enable more detailed studies and simulations.

The digitisation of the drift chamber sub-detector follows a similar methodology. In this case, the two variables subject to Gaussian smearing are the distance from the simulated hit to the nearest wire and the position along the wire. In addition to producing digitised hits with smeared positions, the algorithm calculates the associated number of interactions (clusters) and the number of electrons emitted per interaction. This calculation is based on a parametrised model using the GARFIELD++ simulation framework [795]. A more detailed drift chamber digitisation, which will include the generation and analysis of full waveforms, is under development. This evolution will enable more reliable assessments of, e.g., the impact of beam-induced backgrounds on the drift chamber occupancy and on track reconstruction efficiency and purity.

A different approach is required for calorimeters: the simulated energy deposits corresponding to the same readout cell are aggregated and a calibration factor (sampling fraction) is applied alongside other specific processes, as outlined below.

- The digitisation of CLD calorimeters is based on the original ILCSOFT implementation, interfaced with GAUDI wrappers and data format converters to EDM4HEP. This implementation supports per-layer sampling fractions, operates in both analogue and digital modes, and includes zero-suppression emulation.

- The ALLEGRO calorimeter digitiser is a ‘KEY4HEP-native’ solution (i.e., a GAUDI algorithm with EDM4HEP input and an output that does not require wrappers or converters) that handles radial-layer-dependent calibration, zero suppression, noise addition, and cross-talk emulation. The cross-talk emulation is performed in two steps: (1) the derivation of a detector-specific map that encodes which cells ‘communicate’ with each other and the associated cross-talk coefficients (sourced
from measurements for the ALLEGRO ECAL); (2) the detector-agnostic energy distribution across cells, following the guidelines set by the map.

- The fibre dual-readout calorimeter digitiser accurately emulates the response of the silicon photomultiplier, generating full waveforms based on photon arrival times using the SIMSiPM [796] package. This digitisation depends on parameters that can be obtained from vendors' data sheets and accounts for a variety of effects, including wavelength-dependent efficiency, dark counts, after-pulsing, and cross-talk.

## 8.8 Reconstruction

The EDM4HEP digitised objects produced by the algorithms mentioned in the previous section are subsequently processed through various reconstruction routines. Two tracking solutions are currently used in the FCC software: one based on a conformal tracking implementation from ILCSOFT [797], suitable for silicon tracking systems, and another based on a Geometric Algebra Transformer [667] called via ONNX RUNTIME [798], successfully applied to both silicon and gaseous trackers, as detailed in Sects. 4.10 and 4.3.3. The machine learning solution currently covers only track finding; ongoing developments will extend its capabilities to track fitting. Other 'classical' approaches are also investigated, both for gaseous and silicon-based tracking systems.

Calorimeter clustering can be performed using three different KEY4HEP-native solutions: one based on a fixed-size sliding window for finding local maxima, another based on ATLAS topological clustering [799], and the third using the CMS CLUE algorithm, which has been ported to KEY4HEP in the K4CLUE package [800]. A fourth option for calorimeter clustering, used by the CLD detector, is available through the particle flow algorithm described below.

A particle-flow-based global event reconstruction is available in the PANDORASDK [669] framework, which is integrated into ILCSOFT and accessible in KEY4HEP via wrappers and converters. A complete particle-flow-algorithm sequence is in place for the CLD detector, adapted from the ILD solution [668]. While this implementation already demonstrates excellent performance [794], further optimisation is underway. The particle flow approach is expected to deliver the highest performance, in particular for jet energy and angular resolutions, making it the preferred tool for detector optimisation. Consequently, dedicated efforts are focused on several key areas:

- re-implementing the interface to PANDORASDK as a GAUDI algorithm with EDM4HEP input and output, eliminating the reliance on data converters and wrappers;

- developing PANDORASDK sequences for the ALLEGRO and IDEA detectors, adapted to and exploiting the specificities of their trackers and calorimeters;

- implementing machine learning-based particle flow algorithms, as described in Ref. [620].

The clustering of EDM4HEP::RECONSTRUCTED PARTICLECOLLECTION particle-flow particle candidates into jets is managed through a standard interface to the FASTJET [801] package. An additional FASTJET-based interface is available for the clustering of calorimeter-only objects and can be used for detector setups that do not yet provide reconstructed particle candidates.

Several particle identification algorithms are, or will be, developed to further extend particle-flow capabilities with additional particle identification algorithms. These algorithms include a RICH pattern recognition [802] for the ARC detector (Sect. 6.7.2), a cluster-counting technique for gaseous trackers with $dN/dx$ measurement (Sect. 6.6), and a deep-learning-based jet flavour tagging using ParticleNet [803]. The latter is already implemented for the IDEA detector within the analysis framework described in the next section and is being migrated to a GAUDI algorithm for integration into the central reconstruction chain. This GAUDI algorithm will need to be flexible to accept detector-dependent features in the training model.

## 8.9 Analysis tools

To maximise synergies and enhance the productivity of the FCC particle physicist teams, the analysis tools are centrally developed and maintained in KEY4HEP. The samples generated for FCC studies are stored using the ROOT-based EDM4HEP data model, both for the parametrised and full simulation workflows. Since this data model is built with the PODIO library, EDM4HEP files can be analysed using the automatically generated helper methods (Sect. 8.3) in C++ or through the associated PYTHON bindings. Although this is not the intended usage, those files can also be processed using 'plain' (PY)ROOT, i.e., without going through the PODIO layer. A third solution, relying on RDATAFRAMES [804], is available through KEY4HEP. This package, called FCCANALYSES, has been central to most of the physics analyses presented in this report and is described below.
The FCCANALYSES package equips analysers with a comprehensive and efficient toolkit built around RDATAFRAME. By leveraging the RDATAFRAME framework, it provides automatic multi-threading, with object relations from EDM4HEP maintained in a structured tabular format through an RDATASOURCE instance implemented in PODIO. Event selection and high-level computations follow the standard RDATAFRAME syntax, while FCCANALYSES includes a set of general-purpose functions for added convenience. Samples and their metadata (cross sections, event counts, normalisation factors, etc.) are managed via JSON files, with centrally-produced samples browsable through a web interface [805] and available on EOS. A plotting utility facilitates process normalisation, stacked histograms, and background vs. signal comparisons. In FCCANALYSES, histograms can be produced directly from input samples in a single step, but a 'staged' workflow, allowing resource-intensive steps to be isolated for efficiency, is also supported. To enhance analysis capabilities, FCCANALYSES provides additional features, including the following ones.

- **Job submission** through HTCONDOR [806] to CERN batch system.

- **Jet clustering** via FASTJET [801] and functionalities to perform jet-parton matching.

- **Machine learning integration** using ONNX RUNTIME [798], TMVA [807] or XGBOOST [808].

- **Flavour tagging** with the deep-learning based PARTICLENET [803] model trained for the IDEA detector DELPHES simulation.

- Automated **yield table production** for arbitrary cut-flows.

- Direct creation of ROOT files and associated data cards in a format suitable for the COMBINE [809] statistical analysis and combination tool.

- **Smearing tools** to generate new object collections from existing DELPHES samples under different detector performance assumptions.

A more detailed overview is given in Ref. [623].

In addition to this well-established toolkit, new initiatives aim at expanding the technology options offered to the analysers. For instance, the COFFEA [810] PYTHON-based framework, known for scalable, efficient processing of large HEP datasets, now supports EDM4HEP. The FCC software team is also exploring future-proof solutions, acknowledging shifts in paradigms akin to the HEP community's transition from Fortran to C++. In this regard, the Julia [811] language, celebrated for its speed, ease of use, and expressive syntax, could address the 'two-language problem' (i.e., the reliance on C++ for performance-intensive tasks and Python for user interface). To test Julia's suitability, an EDM4HEP format reader was developed as part of the JULIAHEP [812] project, which aims to consolidate Julia-based tools for HEP.

## 8.10 Visualisation

Visual renderings of the software processes and outputs are crucial for purposes such as debugging, validation, physics interpretation, and outreach. A variety of related tools have been developed or integrated into the FCC software ecosystem, as described below.

To enable visualisation of FCC events and detectors, an experiment-independent web-based event display tool, Phoenix [813], was extended to support the EDM4HEP data model. Leveraging this technology, a dedicated web interface, PHOENIX@FCC [814], was created to host the central versions of FCC detector geometries. This interface allows users to overlay event data onto a 3D view of the detector, with the flexibility to easily incorporate custom detectors. An example of an event display generated with this tool is shown in Fig. 129.

Beyond the FCC-specific implementation, several other tools are available for displaying detector geometries and event content. These include the JSROOT web interface [815], the QT plugin integrated with GEANT4 (accessible through DDSIM), and the CED event display from ILCSOFT [816].

Another visualisation tool was developed as part of the FCC studies, to render the content and relationships between objects in EDM4HEP-based events. This tool, called the EDM4HEP Event Data Explorer (EEDE) [817], visualises EDM4HEP objects as boxes that display the values of their various fields and are connected to related objects (e.g., a calorimeter cluster will be linked to its associated individual cells). The displayed content can be tuned by applying filters on the objects. Figure 130 shows a screenshot of this tool in use, with an excerpt of a Monte Carlo generator particle tree.
<figure><img src="image_140.png" /><figcaption>**Fig. 129** Visualisation of a t̄ event within the CLD detector, displayed using the PHOENIX@FCC web-based event display</figcaption></figure>

<figure><img src="image_141.png" /><figcaption>**Fig. 130** Visualisation of the Monte Carlo particle tree for an $e^+e^- \to Z \to b\bar{b}$ event, generated using the EDM4HEP Event Data Explorer [817]</figcaption></figure>

## 8.11 Computing resources

The computing resource requirements of a project include the processing power necessary to manage the data generated by its activities and the storage capacity needed to maintain those data samples at various stages of processing. During the Feasibility Study, the work of particle physicists has primarily focused on ‘offline’ activities, which correspond to the
<table><caption>**Table 20** Resources available at CERN for FCC physics, experiments and detectors studies as of October 2024. The (old) benchmark HepSpec06 (HS06) is still used to facilitate comparison with LHC numbers; for the purpose of this analysis, HS06 and HS23 are numerically equivalent</caption><thead><tr><th></th><th>Storage on EOS</th></tr></thead><tbody><tr><td>600 TB</td><td>For central productions</td></tr><tr><td>100 TB</td><td>For analysis</td></tr><tr><td></td><td>Processing power</td></tr><tr><td>9000 HS06/HS23</td><td>CPU on lxbatch</td></tr><tr><td>3 GPU</td><td>Nodes on CERN Openstack</td></tr><tr><td>Some GPU</td><td>Nodes on EuroHPC (via CERN OpenLab)</td></tr></tbody></table>

workflows in Fig. 125. These activities are expected to remain central during the next phase of the study. An initial analysis of the FCC offline computing needs is presented in Ref. [818]. This section builds upon and expands that analysis, with further insights.

The FCC PED activities to date have primarily relied on resources provided by CERN, as displayed in Table 20. These resources represent approximately 0.1% of those currently available to the LHC experiments, and will need to substantially increase. The main purpose of this section is to give enough elements to provide reasonable projections of the needs, as a function of parameters that will be better defined as the project progresses. Current ideas to ensure that an adequate amount of resources is available for the studies are also presented. The target timescale is that of the next phase of the study (2025–2027), possibly extending to the first years of the proto-collaboration forming phase (2028–2030). A projection to the needs of the actual Z-pole operations, in two decades from now, is also presented.

### 8.11.1 Resource modelling

Reliable projections require a model for the resource needs. When discussing the computing resource needs, it is necessary to treat the two main phases of the project separately: design and preparation on the one hand, and data taking on the other. During the design and preparation phase, the studies are performed with simulated and test-beam data, with needs increasing with time, based on expected integrated luminosities that define the statistical framework, and with many moving targets and unstructured activities (such as the number and type of detector concepts, data formats, algorithms, and levels of software optimisation). During collider operation, detector and data formats are fixed, and the integrated luminosity of collected data is known. At this stage, most resources are devoted to producing the necessary samples of simulated events, reconstructing both collected and simulated data, possibly with updated versions of core software and calibration constants, and to prepare the data for the optimisation of quasi-stable algorithms and for end-user analyses.

The significant and sustained effort dedicated to modelling the computing resource needs in ATLAS and CMS has been thoroughly documented, and has quantified both the short- and long-term projections for the high-luminosity LHC programme. An example can be found in Ref. [819]. The most recent update is shown in Fig. 131, from the latest CMS [820] and ATLAS [821] approved figures, with similar real and simulated data samples. Not surprisingly, the projected needs are shown to decrease with more aggressive R&D efforts. In particular, past investments in R&D, software quality/performance improvement, and optimal use of storage in the past decade, have proven to be critical in reducing the HL-LHC computing needs of the experiments. The projected needs are compared to the extrapolated available computing capacities under a sustainable flat budget model. From these numbers, it is possible to derive that both ATLAS and CMS will have storage needs of the order of a few EB and computing needs of the order of a few MHS06.<fnref n="30" />

The basic concepts of resource modelling employed by the LHC experiments can be applied to the FCC case, which boils down to identifying the activities and the corresponding set of objectives and required workflows. The detailed activities and objectives depend on the phase of the project, although macro-activities can be present at all stages. Today, and in the near future, the identified macro-activities include data analysis, sub-detector development and optimisation, and algorithm design and optimisation.

<footnote n="30">³⁰ An HS06 = HEPSpec06 is a benchmark to measure the computing capacity of a Computing Element. The rule of thumb 'core = 10 HS06' is used for the hardware available (at the time of writing) at, for example, the CERN facilities.</footnote>
<figure><img src="image_142.png" /><figcaption>**Fig. 131** Projections of CMS (left) and ATLAS (right) computing (top) and storage (bottom) resource needs for HL-LHC. In both cases, the demands in case of no or conservative R&D and planned or aggressive R&D are compared with projections of future pledged resources. From Refs. [820,821]. For ATLAS and CMS, the data and Monte Carlo samples have roughly the same size [822]</figcaption></figure>

## Data analysis

This activity will always be present, in all phases of the project. During the design phase, the goal is to study the potential of the project with a level of accuracy that depends on the aspect being investigated. A first feasibility study of a measurement is typically done using a parametrised simulation of the response of a given detector concept, to identify critical points that would require a more accurate simulation. Parametrised (or fast) simulation will likely remain necessary during data taking, e.g., to enable a faster optimisation of a reconstruction tool, to efficiently evaluate an analysis potential, or to quickly scan larger regions of parameter space. As the studies progress, the need for accuracy increases, which calls for fully-simulated and properly-reconstructed events. Therefore, the analysis activity will always bring requirements for adequate samples of parametrised and fully simulated-reconstructed events, their relative importance depending on the phase of the project. An example of a presently ongoing analysis macro-activity with full simulation is discussed in Sect. 4.10.

## Sub-detector development and optimisation

This activity is specific to the design phase, during which the detector response is simulated, primarily using particle guns to generate particles of a specific type, within a given region of phase space. Additionally, samples of simulated events may prove useful and serve as benchmarks for the design process. While the size of these samples is usually not enormous, they may require a higher level of detail than is typical for standard physics analyses, potentially resulting in large data volumes. Examples of such activities are discussed in Sect. 6.

## Algorithm design and optimisation

This activity is present during all phases of a project. During the design phase, a minimal set of algorithms is identified to evaluate the performance of the proposed (sub)detectors, and to subsequently improve and tune their design. During later stages, when the detector design is frozen (or when the detector is built), the algorithms are continuously developed for improved performance. This activity makes use, in particular, of particle guns and simulated events enriched in certain
<table><caption>**Table 21** Baseline event sizes and processing times. Parametrised simulation and full simulation with GEANT4 are denoted DELPHES and FULL, respectively. For FULL, the values are extrapolated from measure-</caption><thead><tr><th rowspan="2">Process<br>e<sup>+</sup>e<sup>-</sup> →</th><th rowspan="2">√s (GeV)</th><th colspan="2">Size/event</th><th colspan="2">Processing time/event</th></tr><tr><th>DELPHES (kB)</th><th>FULL (MB)</th><th>DELPHES (ms)</th><th>FULL (s)</th></tr></thead><tbody><tr><td>Z → q<span style="text-decoration: overline;">q</span>, ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>91.18</td><td>8.3, 1.2</td><td>1.1, 0.16</td><td>14, 0.5</td><td>11, 1.6</td></tr><tr><td>W<sup>+</sup>W<sup>-</sup> → all, v<span style="text-decoration: overline;">v</span>ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>157–163</td><td>9.5, 1.2</td><td>1.3, 0.16</td><td>16, 0.5</td><td>13, 1.6</td></tr><tr><td>HZ → v<span style="text-decoration: overline;">v</span>b<span style="text-decoration: overline;">b</span>, b<span style="text-decoration: overline;">b</span>b<span style="text-decoration: overline;">b</span></td><td>240</td><td>8.9, 13</td><td>1.2, 1.8</td><td>15, 23</td><td>12, 18</td></tr><tr><td>ZZ → all</td><td>240</td><td>10</td><td>1.4</td><td>17</td><td>13</td></tr><tr><td>t<span style="text-decoration: overline;">t</span> → all</td><td>365</td><td>18</td><td>2.3</td><td>30</td><td>23</td></tr></tbody></table>

ments performed with Z → q<span style="text-decoration: overline;">q</span> events, under the assumptions described in the text

topologies. Examples of such activities are presented in Sect. 4. Advanced AI approaches, such as ML-based tracking and particle flow algorithms, are complementary to more classical approaches in both the design and production phases. During the design phase, they offer a rapid re-optimisation of varying designs and concepts; during the production phase, they are expected to deliver better performance.

### 8.11.2 Modelling resources for FCC-ee

At this stage, quantitative predictions are only possible for the analysis macro-activity. The necessary basic ingredients are the event sizes and the event processing time. The current activities mostly use parametrised simulations, hereafter labelled DELPHES, for which rather complete sets of events have been produced. The numbers presented in the following are taken from the Winter 2023 production campaign. For the full simulation, some measurements have been performed with the simulation of selected samples with CLD, taken as a reference. It is assumed that the event sizes and the event processing times scale in the same way as for DELPHES. This assumption is based on the fact that these numbers depend mostly on the number and type of particles, and that they affect the sizes and processing time in the same way in DELPHES and full simulation. The resulting event sizes and processing times are reported in Table 21. In the future, the simulated hits (currently stored for development activities) might not be fully recorded.

To project the needs in the years to come, an assumption on the needs in terms of sizes of the simulated samples has been made. A rule of thumb often used to get approximate values is to assume simulated samples corresponding to the expected integrated luminosity at each centre-of-mass energy, as displayed in Table 1 of this report. Table 22 shows the corresponding needs, for one experiment, in terms of computing resources.

Reconstruction and analysis requirements are not included in Table 22 because of the lack of sufficient quantitative information. However, the size of the DELPHES output, designed to emulate the reconstruction process, can serve as a basis for estimating the reconstruction needs. While the actual reconstruction may require more detailed information than what is currently provided by DELPHES, it is unlikely to significantly impact the overall resource demands. This conclusion is even clearer for the final analysis tuples, which represent a condensed version of the DELPHES output. The processing power needs are more difficult to quantify. For reference, at LEP and Belle II, the reconstruction step took about 30% of the full simulation CPU time [818], which can be taken as a conservative estimate, given that (opportunistic) heterogeneous resources can play a relevant role in here. The numbers reported for one experiment in Table 22 give therefore a reasonable estimate of the scale of the problem.<fnref n="31" /> These numbers show that the computing needs for the Z run are of the same order of magnitude as those of ATLAS and CMS for HL-LHC. For the other runs, instead, the table shows that full nominal integrated luminosity samples are achievable today.

### 8.11.3 Minimal baseline working scenario

These considerations enable the design of a minimal working scenario to serve as a baseline target. This scenario includes, as a minimum, full nominal integrated luminosity samples for the W, HZ, and t<span style="text-decoration: overline;">t</span> datasets, as well as ‘sufficiently large’ samples for the Z run, where the precise definition of ‘sufficiently large’ remains to be determined. Table 23 reports the values, assuming

<footnote n="31">³¹ It should be noted that, for DELPHES, in principle the sample can be reused for a different *detector concept* on the fly with minimal use of additional processing resources.</footnote>
<table><caption>**Table 22** Projected needs for the nominal integrated luminosity, for one experiment. The amount of HS06 is shown for a reference period of 3 years, i.e., roughly the duration of the next phase of the study</caption><thead><tr><th rowspan="2">Run</th><th rowspan="2">Process</th><th rowspan="2">Number of events</th><th colspan="2">DELPHES</th><th colspan="2">FULL</th></tr><tr><th>Storage (PB)</th><th>CPU (HS06)</th><th>Storage (PB)</th><th>CPU (HS06)</th></tr></thead><tbody><tr><td rowspan="2">Z</td><td>q̅q</td><td>1500 G</td><td>12.5</td><td>2.2 k</td><td>1650</td><td>2 M</td></tr><tr><td>ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>225 G</td><td>0.275</td><td>12</td><td>40</td><td>40 k</td></tr><tr><td>W</td><td>W<sup>+</sup>W<sup>-</sup></td><td>60 M</td><td>~ 10<sup>-3</sup></td><td></td><td>0.075</td><td>72</td></tr><tr><td rowspan="2">HZ</td><td>HZ</td><td>500 k</td><td>~ 10<sup>-5</sup></td><td></td><td>~ 10<sup>-3</sup></td><td>~ 1</td></tr><tr><td>VBFH</td><td>16 k</td><td>~ 10<sup>-6</sup></td><td></td><td>~ 10<sup>-3</sup></td><td></td></tr><tr><td rowspan="3">top</td><td>t̅t</td><td>500 k</td><td>~ 10<sup>-5</sup></td><td></td><td>~ 10<sup>-2</sup></td><td>~ 1</td></tr><tr><td>HZ</td><td>90 k</td><td>~ 10<sup>-6</sup></td><td></td><td>~ 10<sup>-3</sup></td><td></td></tr><tr><td>VBFH</td><td>23 k</td><td>~ 10<sup>-6</sup></td><td></td><td>~ 10<sup>-3</sup></td><td></td></tr><tr><td>Total</td><td></td><td>1725 G</td><td>13</td><td>2.2</td><td>1690</td><td>2 M</td></tr></tbody></table>

<caption>**Table 23** Projected needs for one experiment, for the scenario with nominal integrated luminosity samples for the W, HZ and t̅t runs, and event samples 100 times larger than the LEP samples for the Z run. The last row corresponds to four experiments requiring the same resources.</caption>

The amount of HS06 is shown for a reference period of 3 years, i.e., roughly the duration of the next phase of the study. The totals in the Full case are beyond today's availability

<table><thead><tr><th rowspan="2">Run</th><th rowspan="2">Process</th><th rowspan="2">Number of events</th><th colspan="2">DELPHES</th><th colspan="2">FULL</th></tr><tr><th>Storage (TB)</th><th>CPU (HS06)</th><th>Storage (TB)</th><th>CPU (HS06)</th></tr></thead><tbody><tr><td>Z</td><td>q̅q</td><td>400 M</td><td>3.25</td><td>~ 1</td><td>440</td><td>475</td></tr><tr><td>(100×LEP)</td><td>ℓ<sup>+</sup>ℓ<sup>-</sup></td><td>42.5 M</td><td>0.05</td><td></td><td>6.5</td><td>7</td></tr><tr><td>W</td><td>W<sup>+</sup>W<sup>-</sup></td><td>60 M</td><td>0.6</td><td></td><td>75</td><td>72</td></tr><tr><td rowspan="2">HZ</td><td>HZ</td><td>500 k</td><td>0.0065</td><td></td><td>1</td><td>~ 1</td></tr><tr><td>VBFH</td><td>16 k</td><td>~ 0.001</td><td></td><td>0.25</td><td></td></tr><tr><td rowspan="3">top</td><td>t̅t</td><td>500 k</td><td>0.009</td><td></td><td>9</td><td>~ 1</td></tr><tr><td>HZ</td><td>90 k</td><td>~ 0.001</td><td></td><td>0.2</td><td></td></tr><tr><td>VBFH</td><td>23 k</td><td>~ 0.001</td><td></td><td>0.25</td><td></td></tr><tr><td>Total</td><td></td><td>500 M</td><td>4</td><td>~ 1</td><td>530</td><td>550</td></tr><tr><td>4 experiments</td><td></td><td>2000 M</td><td>16</td><td>~ 4</td><td>2100</td><td>2200</td></tr></tbody></table>

that 'large enough' means 100 times the LEP event samples. The total values per detector and for all four detector concepts are also provided, assuming that they have similar average demands. These numbers are not far from the resources currently available and are well within the range of what can be realistically achieved, as discussed later. Consequently, the baseline '100×LEP' scenario appears to be a realistic and achievable target.

Efficiently managing limited computing resources requires a three-fold optimisation approach for the software, the analysis techniques, and the workload and data management. A proactive approach to resource management is essential for securing ongoing support from official bodies, especially as computing needs continue to grow. The following paragraphs discuss the current (or planned) pertinent investigations.

### 8.11.4 Optimising resources: software

#### Software quality and efficiency improvements

Upgrading the code quality and efficiency is fundamental, though it often involves a considerable investment in time and expertise. By continually using the latest software versions, projects can leverage optimisations and new capabilities. For instance, recent updates to GEANT4 have nearly doubled the speed of simulation for the ATLAS experiment, illustrating the potential performance gains achievable through modernised codebases. Moreover, new, faster simulation techniques
are emerging and being integrated in the software frameworks for use in production,<fnref n="32" /> and may offer further efficiency improvements. End-to-end fast simulation based on Machine Learning techniques are also being developed, which could provide interesting ways to test very large event samples [823].

### Selective and filtered simulation approaches

Another opportunity for optimisation lies in selective or filtered simulations. By applying filters at the generation stage, simulations can focus only on event components relevant to specific analyses, reducing unnecessary computation. For example, simulating only sub-detectors relevant for a given study could save substantial processing power. This strategy requires a careful balance between computational savings and scientific accuracy, but could significantly improve throughput.

### Leveraging heterogeneous resources for reconstruction and analysis

Heterogeneous computing environments, combining CPUs, GPUs, and other accelerators, offer significant opportunities for resource optimisation, particularly for computationally intensive tasks such as reconstruction and analysis. This approach has already proven highly valuable at the LHC, where the use of GPUs and specialised hardware for suitable tasks has improved efficiency, freeing traditional CPU resources for other activities. Extensive R&D programmes are underway to develop the potential of these technologies in view of HL-LHC.<fnref n="33" /> Integrating these advances into the FCC software ecosystem to ensure seamless compatibility and optimal performance across diverse processing architectures is of critical importance for the FCC project.

### 8.11.5 Optimising resources: analysis techniques

#### Enhanced interplay between full and parametrised simulation

In scenarios where full simulation is unnecessary, parametrised simulations, such as those provided by DELPHES, can produce sufficiently accurate results with far lower resource demands. Facilitating interaction between full and parametrised simulations allows researchers to switch between these approaches as needed, optimising resource use for each stage of an analysis. Developing automated or optimised configurations for DELPHES would further support this flexibility, making it easier to adapt simulations based on the specific needs of each analysis.

#### Advancing beyond traditional statistical methods

By default, HEP analyses rely on a straightforward rule of thumb: generating MC samples at least as large as the expected data sample. While simple, this approach is resource-intensive, particularly in scenarios with high data volumes and complex simulations. Alternative statistical methodologies that allow similar statistical power with fewer simulated events are already explored in some fast simulation domains with promising results [825]; these variance reduction techniques should be further investigated to optimise computational resources.

### 8.11.6 Optimising resources: workload and data management

A home-made solution effectively supported the production on the local CERN HTCONDOR and EOS resources until the time of writing. The increasing complexity and scale of FCC projects necessitate a more robust and distributed infrastructure. The primary requirements for the updated system include: a centralised file catalogue to organise and track data; data replication to ensure redundancy and accessibility across sites; and remote access capabilities to facilitate seamless interaction with distributed resources.

To address these FCC needs, ILCDIRAC, the instance of the DIRAC framework used in past linear collider studies, has been adopted. This framework is widely recognised for its workload management and file catalogue capabilities, and is already employed by several high-energy physics experiments, such as LHCb, Belle II, BES III, JUNO, etc. Through this integration, the FCC Virtual Organisation (FCC VO) has become part of ILCDIRAC. The CERN HTCONDOR and EOS resources have been associated with the FCC VO within ILCDIRAC. In addition, steering applications tailored to FCC workflows have been integrated into the framework to support specialised production needs.

<footnote n="32">³² Parts of the electromagnetic calorimeter of ATLAS are simulated with Machine Learning techniques.</footnote>

<footnote n="33">³³ An example is the Next Generation Trigger project [824].</footnote>
Production with iLCDIRAC has begun, marking significant progress in adopting the distributed model. Efforts to include external storage elements (SE) have been initiated with sites at CNAF, Bari, and Glasgow. While these integrations are still in the testing phase, they represent an essential step towards expanding the infrastructure capacity and flexibility. This approach ensures that FCC projects benefit from a scalable and distributed workload management system, ready to handle the challenges of future production and analysis tasks.

### 8.11.7 Increasing available resources: pledged resources

At CERN, FCC currently obtains computing resources from quotas reserved for the 'Small and Medium Experiments' (SME) projects. These resources, while sufficient for initial activities, are limited and cannot realistically be increased by a large factor in the SME context.

To address future needs, discussions are ongoing with the WLCG and CERN resource management teams to integrate FCC into the WLCG computational infrastructure. This integration, which should begin as early as 2025, would establish a reliable framework for resource allocation and enable a steady increase in computing and storage capacity over time. Current projections suggest that, by the end of the next phase of the study, in 2027, a tenfold increase in resources should be achievable, equivalent to approximately 5 PB of storage and 100 kHS06 of CPU power. These resources would be sufficient to support the minimal baseline '100 × LEP' scenario discussed earlier, while also providing contingency for targeted studies requiring larger data samples.

### 8.11.8 Increasing available resources: opportunistic resources

To enhance resource availability for FCC projects, leveraging opportunistic resources is a key strategy, which includes high-performance computing (HPC) facilities, national resources, and advanced development initiatives.

On the HPC front, discussions are ongoing with CERN OpenLab to exploit EuroHPC resources for FCC needs. The focus is on providing transparent access through the CERN OpenLab interface, which is being developed to support diverse hardware architectures, such as AMD, Intel, and ARM CPUs, as well as NVIDIA and AMD GPUs. Initial estimates suggest access to substantial computing resources over periods ranging from 6 months to 1 year, which would support specific, time-limited studies requiring intensive computational power. Investigations are underway to integrate these HPC resources into DIRAC, ensuring streamlined access for FCC workflows. The HPC resources are particularly suitable for specialised use cases that demand intense but temporary computational efforts, such as AI and machine learning (ML) developments, and physics-specific simulations or statistical studies requiring short-term bursts of computing power.

Resources available at individual institutes or through national departments could significantly contribute to FCC workloads. These resources can potentially be included within the FCC VO through integration with the DIRAC framework, enhancing the overall pool of accessible computational power.

### 8.11.9 Projecting to the Z run

All the above provides a basis for understanding the computing needs during the Z run. The analysis focuses on storage requirements, likely to be the most critical aspect. The squares in Fig. 132 show the projected FCC storage requirements for the real data collected during the Z-pole run,<fnref n="34" /> with four experiments and the assumption of four identical runs in 4 years. Also shown are the projections for simulated data with size identical to the real data (triangles), four times larger than the real data (stars) and ten times larger than the real data (circles). The horizontal band indicates the HL-LHC’s projected storage requirements, as derived from Fig. 131 assuming that ATLAS and CMS account for approximately 90% of the total.

The storage resources required for FCC-ee data during the Z run are comparable to the projected requirements of the LHC. If the LEP model of retaining SIM-level data for all official simulated samples were to be adopted, the storage requirements would substantially increase, even under the minimal assumption that simulated samples are comparable in size to real data. Alternative strategies for storing simulated data may therefore need to be developed, drawing on approaches already explored at the LHC, such as eliminating the need to retain the largest simulated samples. By the time of the Tera-Z run, the aforementioned end-to-end technologies may also have matured sufficiently to significantly reduce the storage requirements for simulated events. In any case, a dedicated computing infrastructure, similar to the World LHC Computing Grid (WLCG)

<footnote n="34">³⁴ A similar situation applies to CPU needs, though it is important to consider the previously mentioned challenge of adapting to heterogeneous resources. Nonetheless, it is anticipated that by 2045 this issue will likely no longer be a significant obstacle.</footnote>
**Fig. 132** Projection of the current storage resources to the FCC-ee Z-pole run with four experiments collecting equal amounts of data in four successive years (squares) and varying amounts of simulated data (triangles, stars, circles). The figure also includes the projected resource needs of the LHC and a hypothetical evolution of WLCG resources, under different scenarios for sustained annual budget increases

<figure><img src="image_143.png" /></figure>

for the LHC, is therefore required to meet the computing demands of the FCC. As previously mentioned, this could possibly be a natural extension of the WLCG. The projected storage capacity of the WLCG during the years of the FCC-ee Z-pole run, under various assumptions regarding sustained annual budget increases, is also shown in Fig. 132. While provided for illustrative purposes only, this projection suggests that a natural evolution of the current model could effectively supply the required resources.

## 8.12 Human resources: status and needs

The substantial progress achieved in the software ecosystem during the FCC Feasibility Study has demonstrated that a dedicated software core team at CERN is pivotal in driving and coordinating the majority of FCC activities. This team has evolved over time, initially operating within the CERN EP-SFT group and then, in September 2024, moved to the newly-established CERN EP-FCC group. The current workforce at CERN includes (in FTEs) 1.4 staff members, providing leadership and continuity, 3 fellows, and 3 students (technical and doctoral). Additionally, the CERN EP R&D program has been instrumental in providing fellow support, particularly for the development and advancement of KEY4HEP, a critical component for the FCC activities. Contributions from external institutes have increased, in particular from collaborators in France, Italy, and the United States. This expanding network of external contributors strengthens the FCC effort by bringing diverse expertise, resources, and perspectives, complementing the core team's efforts at CERN.

Consolidating and expanding the team is essential to sustain progress, address emerging challenges, and capitalise on synergies with other initiatives. To strengthen this team, efforts are being made to secure two additional staff positions for long-term stability and expertise; two continued fellows to retain knowledge and maintain operational continuity; two technical students, providing critical support for development tasks and creating a pipeline of future talent. In addition, a dedicated IT contact would be beneficial to foster strong relationships with the CERN IT service groups, and ensure streamlined access to IT services and infrastructure critical to the FCC activities.

The software ecosystem central to FCC workflows, KEY4HEP, requires permanent development, consolidation, and maintenance. Establishing long-term support mechanisms is crucial to ensure the continued relevance and effectiveness of KEY4HEP. Discussions with CERN EP management are underway, to secure a sustainable future for the project as it evolves from its current R&D phase into a baseline activity.

## 8.13 Outlook

Before and during the Feasibility Study, a constant concern has been to overcome the challenges of limited resources, while being able at all times to evaluate the FCC detector requirements and physics potential, with a robust software and computing infrastructure. It was therefore strategically decided to maximize the use of already existing solutions in a common software framework, while broadening the applicability of common tools and frameworks to meet the evolving needs of the project.
The resulting KEY4HEP ecosystem is now routinely used by FCC particle physicists in their daily work. To fully reap the rewards of such a transformative approach, it will be essential to further generalise its use, in particular in the scope of the ongoing DRD efforts and, later, within the experimental Collaborations.

The long-term viability and adaptability of the framework will require continuous consolidation and harmonisation, to efficiently support the required workflows. To maximise the effectiveness of the available computing resources, robust support for multi-threading must be guaranteed, and mechanisms to handle heterogeneous resources should be implemented wherever applicable. These efforts are closely aligned with HL-LHC developments, making it imperative to ensure the seamless integration of these advances into KEY4HEP. As KEY4HEP transitions out of the R&D phase, it will be crucial to establish a sustainable support model with contributions from collaborating institutes.

Significant progress has been made in the development of full simulation tools, including the essential plug-and-play capability, but much remains to be accomplished in this domain. A critical task will be the implementation of detailed signal digitisers, where the DRD teams are expected to play an important role. To consolidate the conclusions of the Feasibility Study, from beam-induced background simulations to detector requirements and physics potential, the complete SIM-DIGI-RECO chain must be established for all present and future detector subsystems and concepts. As new sub-detector technologies emerge, new detector configurations, distinct from those studied during the Feasibility Study, will be explored. More flexible geometry implementations and improved sub-detector interoperability will be required. The generalisation of common reconstruction algorithms, e.g., for tracking, particle identification, and particle-flow reconstruction, will empower the community to identify optimal detector designs with a minimal investment of human resources. Advanced AI approaches will play a pivotal role in this effort.

Future full simulation studies will demand a significant increase of both computing and human resources. Meeting these growing computational needs involves pursuing multiple avenues inspired by the LHC model, with integration into the WLCG resource pool, leveraging HPC calls, and exploring opportunistic use of available resources. Should the acquisition of additional resources prove challenging, mitigation techniques have been identified and will need to be implemented. Improving the interface between centrally-produced samples and analysis frameworks, including Python-based frameworks, is essential.

Closer ties with the LHC community will need to be developed, as they can unlock mutual benefits, by leveraging shared technologies that advance both the FCC and LHC objectives. In this respect, promoting positions shared between LHC and FCC might foster joint development efforts and enhance expertise exchange. Finally, to broaden the project resource base, continued efforts are required to attract more external contributors from institutes worldwide, to raise awareness and interest in FCC among the broader scientific community, and to encourage partnerships and resource sharing.

# 9 Energy calibration, polarisation, monochromatisation

## 9.1 Overview

Excellent knowledge of the collision energy, $\sqrt{s}$, is vital for many of the most important measurements that will be performed at FCC-ee, in particular the determination of the Z-resonance parameters, and the mass and width of the W boson. To achieve this goal requires calibrating the mean energy of each beam around the ring, $E_b$, in principle not identical for electrons and positrons but here designated with a single symbol for simplicity. The collision energy $\sqrt{s}$ can then be calculated, provided there is sufficiently good knowledge of the crossing angle of the two beams and all effects that give rise to local shifts of the energy at each interaction point.

Circular colliders have the unique attribute that transverse polarisation naturally accumulates through the Sokolov-Ternov effect, and the spin tune, which is the ratio of the precession frequency to the revolution frequency, is directly proportional to $E_b$. The spin tune can be directly measured by the procedure of resonant depolarisation (RDP), in which the frequency of a depolarising kicker magnet is adjusted until the polarisation is found to vanish. This technique, which has an intrinsic relative precision of $10^{-6}$ or better, has been exploited at many facilities, most notably at LEP in scans of the Z resonance [826] and more recently at VEPP4 in the determination of the $J/\psi$ and $\psi(2S)$ masses [827]. Alternatively, in a free spin precession (FSP) measurement the depolariser may be used to rotate the spin vector into the horizontal plane, and the precession frequency measured directly. The self-polarisation of the beams can be used for these measurements, but this will only be possible for Z-pole operation and at energies up to and including the $W^+W^-$ threshold. At energies higher than these, the polarisation level will be too small for RDP and FSP measurements to be practical and the energy scale will have to be determined from
physics processes at the experiments, such as $e^{+}e^{-} \rightarrow Z(\gamma)$, ZZ and $W^{+}W^{-}$ production. Here, the Z and W masses measured with high precision at lower energies with RDP provide a normalisation that can then be applied at higher energies.

The calculation of $\sqrt{s}$ at each interaction point requires good knowledge of the crossing angle of the two beams, which must be measured by the experiments in real time. In addition, it is necessary to account for local energy variations from synchrotron radiation, the RF system and impedance, and to consider the effects of opposite-sign vertical dispersion.

The knowledge of $E_b$ at LEP was ultimately limited by the sampling rate of RDP measurements, which were performed outside physics operation with a periodicity of around once per week. The energy was found to vary significantly between measurements due to several effects, for example earth tides and stray ground electric currents [826]. In order to enable the much greater degree of systematic control that the vastly larger event samples at FCC-ee warrant, the operational strategy will be very different to LEP. Measurements of $E_b$ will be performed several times per hour on non-colliding pilot bunches. In Z running, around 160 pilot bunches will be injected at start of fill, and wiggler magnets will be activated to speed up the polarisation time. One to two hours will be required for the polarisation to build, after which the wigglers will be turned off and physics (colliding) bunches injected. The RF frequency will be continually adjusted to keep the beams centred in the quadrupoles, thus suppressing tide-driven energy changes, which would otherwise be $O(100 \text{ MeV})$. A model will be developed to track residual energy variations between measurements.

A more detailed discussion on the machine aspects concerning the $\sqrt{s}$ calibration can be found in the Volume 2 of this Report [18]. The contribution of the experiments to those studies and the current level of understanding of the expected performance are summarised here. Also included below is a brief discussion of the studies that are underway for monochromatisation of the collision energy when operating at $\sqrt{s} \approx 125 \text{ GeV}$, corresponding to the mass of the Higgs boson. Monochromatisation is motivated by the need to reduce the spread of $\sqrt{s}$ to a value similar to the Higgs width (around 4 MeV), thereby improving the sensitivity to direct Higgs production and allowing tight constraints to be placed on the electron-Yukawa coupling.

## 9.2 Input from the experiments

The experiments operating at FCC-ee will themselves provide measurements that are essential input to the calibration of the collision energy and related quantities. A full discussion of these measurements can be found in Ref. [22]. Here, a brief summary is given, together with some recent updates. The principal data set for performing these measurements is the very large sample of dimuon events that each experiment will collect, arising from the process $e^{+}e^{-} \rightarrow \mu^{+}\mu^{-}(\gamma)$, where $\gamma$ indicates the possible presence of initial-state radiation (ISR). Analysis of the topology of these events, constrained by the total energy and momentum conservation in the final state, allows several important quantities to be determined. This analysis is, in general, based on the knowledge of the muon directions, which in turn imposes demands on the performance of the tracking system (see Sect. 4.2).

### 9.2.1 The crossing angle $\alpha$

The nominal value of the crossing angle is $\alpha = 30 \text{ mrad}$, but the true value must be determined throughout data-taking so that the collision energy can be calculated to the required precision. At the Z pole, more than $10^6$ dimuon events will be collected every 10 min in each detector, which will allow this parameter to be measured with a statistical uncertainty of 0.3 $\mu$rad, which is sufficient for the physics goals, since a precision of 15 $\mu$rad leads to an uncertainty of 10 keV on $\sqrt{s}$. The statistical precision will be worse at higher energies, where the production rate is lower, but will not compromise the physics measurements that are targeted in these regimes.

There is an important subtlety in the crossing-angle determination that must be accounted for. The electron and positron bunches experience mutual electric and magnetic fields that accelerate (decelerate) the bunches before (after) the collision and also increase (decrease) the crossing angle. The collision energy is invariant, but the change in crossing angle from this effect (estimated to be a relative 0.6% modification) must be known so that the measured crossing angle can be corrected back to the unaffected quantity and used together with beam energies as determined from RDP to calculate $\sqrt{s}$.

The magnitude of the variation in $\alpha$ depends on parameters such as the bunch population and the spread in collision energy $\delta_{\sqrt{s}}$. It is found empirically, from simulation studies, that $\alpha$ is proportional to $\mathcal{L}^{1/2} / \delta_{\sqrt{s}}^{1/6}$. By measuring $\mathcal{L}$, $\alpha$, and $\delta_{\sqrt{s}}$ from dimuon events for different bunch intensities, it will be possible to extrapolate to zero intensity and determine the value of $\alpha$ in the absence of these effects. A good opportunity to perform these measurements would be in the period that top-up injection is taking place. It is therefore important that the detector can operate during this period and that the beams are stable. A simulated study of the measurement of $\alpha$ against $\mathcal{L}^{1/2} / \delta_{\sqrt{s}}^{1/6}$ is presented in Fig. 133.
<figure><img src="image_144.png" /><figcaption>**Fig. 133** Change in the measured crossing-angle $\alpha$ vs. $\mathcal{L}^{1/2} / \delta_{\sqrt{s}}^{1/6}$, at various points during the top-up injection. Extrapolation down to $\mathcal{L}^{1/2} / \delta_{\sqrt{s}}^{1/6} = 0$ allows the crossing-angle to be determined in the absence of bunch-bunch effects [22]. Both the luminosity, $\mathcal{L}$, and the spread in collision energy, $\delta_{\sqrt{s}}$, are here normalised to their nominal values</figcaption></figure>

<figure><img src="image_145.png" /><figcaption>**Fig. 134** Fitted value of longitudinal boost from one million dimuon events at one of the FCC-ee IPs [22]. Once the ISR is unfolded, this distribution can be used to measure the energy spread. The magenta line shows the impact of a centre-of-mass boost on the distribution. The shift can be measured with a statistical precision of 40 keV. The other curves indicate the impact of beamstrahlung (BS), angular resolution ($\sigma_{\theta,\phi}$) on the track directions, and ISR</figcaption></figure>

### 9.2.2 The longitudinal boost and the collision-energy spread

The dimuon topology allows the longitudinal boost to be determined on an event-by-event basis. When averaged over a suitable sample size, this provides invaluable information to constrain the model of the energy loss around the ring and to calculate the local collision energy at each interaction point. The width of this distribution (Fig. 134) is a measure of $\delta_{\sqrt{s}}$, which is an essential input to the measurement of certain observables, such as the Z and W widths. Again, the foreseen statistical precision on these quantities is excellent. For example, the energy spread can be measured to one part in a thousand with one million dimuon events. Recent work [828] has investigated how sensitive the determination of $\delta_{\sqrt{s}}$ is to the knowledge of the ISR corrections in dimuon production. The conclusion is that the measurement is robust; even if it is assumed that the second-order corrections from ISR are unknown (which is not the case), the resulting bias on the extraction of $\delta_{\sqrt{s}}$ is far smaller than the statistical uncertainty.

### 9.2.3 Relative $\sqrt{s}$ determination in the Z-resonance scan

The reconstructed peak position of the dimuon invariant-mass distribution provides an excellent proxy for the collision energy. The difference in this reconstructed position between the points of the Z-resonance scan provides a measure of the change
<figure><img src="image_146.png" /></figure>

**Fig. 135** Left: example fit to the dimuon invariant-mass distribution at $\sqrt{s} = 94.3$ GeV, where the peak is modelled with the superposition (blue) of a Gaussian function (red) and two exponential functions (black). Right: the difference (bias) between the $\sqrt{s}$ extracted from the dimuon invariant-mass fit and the true value. Results are shown for the simulated performance of the IDEA detector (red symbols), including

ISR/FSR effects, and for the expected dependence, including (black symbols) or not (black curve) ISR/FSR effects. Each set of results also has an overall overset of a few MeV, which is energy independent and, hence, not relevant for the determination of the Z width. A single shift has been applied to the bias, to correct for these offsets, so that the bias is zero at 87.9 GeV, for all sets of results

in collision energy, which is a critical input for several analyses, in particular the measurement of the Z boson width. The distribution is fitted in bins of the polar angle for back-to-back events. An example fit is shown in Fig. 135 (left). The statistical precision on this pseudo-$\sqrt{s}$ measurement, when summing the samples from four experiments, is around 20 keV for each of the two off-peak running points, assuming the momentum resolution of the IDEA detector. So that the detector does not introduce a bias in the measurement larger than the statistical precision, the momentum scale stability must be controlled at this level.

The field stability can be tracked with NMR probes and the momentum scale can be directly monitored through the reconstruction of low-mass resonances. However, even with a perfect detector, there is a bias in the pseudo-$\sqrt{s}$ measurement in the Z resonance scan arising from ISR/FSR effects, and from the product of the Breit-Wigner shape of the resonance and the Gaussian distribution of the energy spread of the colliding beams. The value of this bias varies by about 8 MeV when going from $\sqrt{s} = 87.9$ to 94.3 GeV, as can be seen in Fig. 135 (right). This difference must be corrected for in the measurement, which requires a good understanding of the ISR/FSR effects. In a generator-level study, disabling ISR/FSR changes the difference in the bias between the two off-peak points by around 500 keV. Therefore, the theoretical prediction of these ISR/FSR effects to the 1% level would be sufficient to render their impact negligible for the Z-width measurement.

### 9.2.4 Absolute $\sqrt{s}$ determination

At collision energies above the Z boson mass, the dimuon events may be used to provide an absolute measurement of $\sqrt{s}$. Radiative returns, in which the emission of an initial-state photon means that the dimuon has the Z mass, allows for the calibration of events unaffected by ISR. The method can be extended to also include multihadron final states. This method can be calibrated at the W-pair production threshold with RDP, and is of great value for physics studies in the regime where no RDP is possible, i.e., collision energies above 200 GeV. This approach also provides a useful complementary measurement of $\sqrt{s}$ in the intermediate energies where RDP is possible but challenging. The foreseen statistical uncertainty is around 280 keV for $6 \text{ ab}^{-1}$ of integrated luminosity at $\sqrt{s} = 125$ GeV and 260 keV for $20 \text{ ab}^{-1}$ at $\sqrt{s} = 160$ GeV. The performance of the tracking system must be sufficiently good that the precision is not compromised.

## 9.3 Expected precision on EW observables from the collision energy and its spread

Several of the most important electroweak observables are expected to have a dominant or significant systematic uncertainty associated with the knowledge of the collision energy and collision-energy spread. The collision-energy uncertainties can
<table><caption>**Table 24** Current projected $\sqrt{s}$-related uncertainties on selected electroweak observables</caption><thead><tr><th rowspan="2">Uncertainty</th><th colspan="5">Observable</th></tr><tr><th>m<sub>Z</sub> (keV)</th><th>Γ<sub>Z</sub> (keV)</th><th>sin<sup>2</sup> θ<sub>W</sub><sup>eff</sup> (×10<sup>-6</sup>)</th><th>Δα<sub>QED</sub>(m<sub>Z</sub><sup>2</sup>) / α<sub>QED</sub>(m<sub>Z</sub><sup>2</sup>) (×10<sup>-5</sup>)</th><th>m<sub>W</sub> (keV)</th></tr></thead><tbody><tr><td>Absolute</td><td>100</td><td>2.5</td><td>–</td><td>0.1</td><td>150</td></tr><tr><td>Point-to-point</td><td>14</td><td>11</td><td>1.2</td><td>0.5</td><td>50</td></tr><tr><td>Sample size</td><td>1</td><td>1</td><td>0.1</td><td>–</td><td>3</td></tr><tr><td>Energy spread</td><td>–</td><td>5</td><td>–</td><td>0.1</td><td>–</td></tr><tr><td>Total √s-related</td><td>101</td><td>12</td><td>1.2</td><td>0.5</td><td>158</td></tr><tr><td>FCC-ee statistical</td><td>4</td><td>4</td><td>1.2</td><td>3.9</td><td>180</td></tr></tbody></table>

be classed in three distinct categories, itemised below. These uncertainties propagate to the physics results in an observable-dependent manner, as discussed in Ref. [22].

- Uncertainties that are fully correlated between measurements propagate to the knowledge of the absolute energy scale. Examples include the values of the anomalous magnetic moment and the mass of the electron, the frequency of the RF system, and any other systematic bias that occurs at all times and all energies. At this stage in the studies, it is estimated that this uncertainty will be around 100 keV on the collision energy at the Z pole and 300 keV at the $W^+W^-$ threshold. This contribution is expected to be the dominant systematic uncertainty in the measurements of the Z and W boson masses.

- A point-to-point contribution comprises biases that occur at all times, or lead to an average shift, but are different for each energy setting. The principal method of determining this uncertainty will be based on the dimuon invariant-mass distribution, as reconstructed by the experiments. The estimated magnitude of this uncorrelated uncertainty is 20 keV for each off-peak point of the Z-resonance scan. The understanding gained at the Z pole and complementary measurements will lead to a corresponding uncertainty of around 100 keV at the $W^+W^-$ threshold. The point-to-point uncertainty is expected to be the dominant contribution in the measurement of the Z width.

- The uncertainty on each individual RDP measurement is dominated by an uncertainty that is set by the frequency of the polarimeter sampling or the size of the energy bins where the depolarisation can be located. A reasonable estimate of this uncertainty is 200 keV at the Z pole and 300 keV at the $W^+W^-$ threshold. As this component is statistical in nature, its impact decreases with the square-root of the number of events. As it is planned to collect $\sim 10^4$ measurements at each energy point, the final uncertainty from this source will be essentially negligible, compared to other contributions. However, the importance of making each measurement as precise as possible, and of collecting the largest possible number of measurements, will become more evident when the data set is split into smaller samples to perform systematic checks.

The contributions from each uncertainty category, and their quadratic sum, are listed in Table 24 for several key electroweak observables. This table also shows the contribution from the uncertainty in the knowledge of the energy spread, which affects quantities with a strong quadratic dependence on the collision energy. Observables that are most susceptible to this uncertainty include the Z cross section and the Z width. A collision-energy spread of 70 MeV, determined with a precision of $\pm 0.05$ MeV, leads to a sub-dominant systematic uncertainty in the measurement of these observables.

With the current expectations, it will be possible to reduce the uncertainty from energy-related quantities by an order of magnitude or more with respect to what was achieved at LEP, such that they will be smaller than, or similar to, the statistical uncertainty for all observables apart from $m_Z$. Indeed, the entries in Table 24 for the $\sqrt{s}$-related systematic uncertainties can be compared to the corresponding LEP values of 1.7 MeV for $m_Z$, 1.2 MeV for $\Gamma_Z$, and 9 MeV for $m_W$.

## 9.4 Prospects for monochromatisation and the measurement of the electron Yukawa coupling

This section describes the tantalising possibility, unique to FCC-ee, to observe the s-channel process $e^+e^- \to H$, and thereby determine the electron Yukawa coupling. The challenges are very demanding and progress is required from both the accelerator and the experimental analyses, but the current studies, described below, are encouraging.
**Fig. 136** Left: diagrams for the s-channel production of the Higgs boson decaying into two gluon jets (top) and reducible Z\* quark dijet backgrounds (bottom) in $e^+e^-$ at $\sqrt{s} = 125$ GeV. Right: resonant Higgs production cross section at $\sqrt{s} = 125$ GeV, including ISR effects, for several $e^+e^-$ collision energy spread values: $\delta_{\sqrt{s}} = 0, 4.1, 7, 15, 30, \text{ and } 100$ MeV [833]

<figure><img src="image_147.png" /></figure>

The electron Yukawa via resonant Higgs production at 125 GeV

Confirming the mechanism of mass generation for the stable visible elementary particles of the universe, composed of u and d quarks plus the electron (and neutrinos), is experimentally very challenging because of the low masses of the first-generation fermions and, thereby, their small Yukawa couplings to the Higgs field. (The neutrino mass generation remains a BSM problem in itself.) In the SM, the Yukawa coupling of the electron is $y_e = \sqrt{2} m_e / v = 2.8 \cdot 10^{-6}$, for $m_e(m_H) = 486$ keV and Higgs vacuum expectation value $v = (\sqrt{2} G_F)^{-1/2} = 246.22$ GeV. Measuring it via $H \to e^+e^-$ appears hopeless at hadron colliders because the decay has a tiny partial width, proportional to the electron mass squared,

$$ \begin{aligned} \Gamma(H \to e^+e^-) &= \frac{G_F m_H m_e^2}{4\sqrt{2}\pi} \left(1 - \frac{4m_e^2}{m_H^2}\right)^{3/2} \\ &= 2.14 \times 10^{-11} \text{ GeV}, \end{aligned} \qquad (10) $$

which corresponds to a branching fraction $B(H \to e^+e^-) \approx 5 \times 10^{-9}$ for the SM Higgs boson. At LHC and FCC-hh, such a final state is completely swamped by the Drell-Yan $e^+e^-$ continuum. The current LHC searches [829,830], exploiting about $140 \text{ fb}^{-1}$ of pp data at $\sqrt{s} = 13$ TeV, reach an observed upper limit on the branching fraction of $B(H \to e^+e^-) < 3.0 \times 10^{-4}$ at 95% CL. This value translates into the current upper bound on the Higgs boson effective coupling modifier to electrons of $|\kappa_e| < 240$. Assuming that the sensitivity to the $H \to e^+e^-$ decay scales simply with the square root of the integrated luminosity, the HL-LHC phase with a $\mathcal{L}_{\text{int}} = 2 \times 3 \text{ ab}^{-1}$ data sample (combining the ATLAS and CMS results) will result in $y_e \lesssim 100 y_e^{\text{SM}}$. Based on searches for the similar $H \to \mu^+\mu^-$ channel, one can expect upper limits on $B(H \to e^+e^-)$ to be further improved by factors of about four, by adding more Higgs production categories and using advanced multivariate analysis methods, eventually reaching $y_e \lesssim 50 y_e^{\text{SM}}$ at the end of the HL-LHC.

About 10 years ago, it was first noticed that the unparalleled integrated luminosities of $\mathcal{L}_{\text{int}} \approx 10 \text{ ab}^{-1}/\text{year}$ expected at $\sqrt{s} = 125$ GeV at the FCC-ee would make it possible to attempt an observation of the direct production of the scalar boson and, thereby, a direct measurement of the electron Yukawa coupling [831,832]. Subsequently, several theoretical studies [30,833–836], simulated data analysis [32], and accelerator studies [837–839] have explored the various aspects connected to the $e^+e^- \to H$ measurement.

The Feynman diagrams for s-channel Higgs production (and its statistically most significant decay at FCC-ee, $H \to \text{gg}$, see below) and dominant backgrounds are shown in Fig. 136 (left). The resonant Higgs cross section in $e^+e^-$ collisions as a function of $\sqrt{s}$ is theoretically given at Born level by the relativistic Breit–Wigner (BW) expression:

$$ \sigma_{ee \to H} = \frac{4 \pi \Gamma_H \Gamma(H \to e^+ e^-)}{(s - m_H^2)^2 + m_H^2 \Gamma_H^2}. \qquad (11) $$

An accurate knowledge of $m_H$ is, therefore, critical to maximise the resonant cross section. An $\mathcal{O}(4 \text{ MeV})$ precision on the Higgs boson mass can be achieved (Sect. 4.3) before any dedicated $e^+e^- \to H$ run. In addition, the FCC-ee beam energies will be monitored with a relative precision of $10^{-6}$, providing a sub-MeV accuracy on the exact point in the Higgs lineshape being probed at any moment.
For $m_H = 125$ GeV, Eq. 11 gives $\sigma_{ee \to H} = 4\pi B(H \to e^+e^-)/m_H^2 = 1.64$ fb as peak cross section. Two effects, however, lead to a significant reduction of the Born-level prediction: (i) ISR depletes the cross section and generates an asymmetry of the Higgs lineshape; and (ii) the actual beams are never perfectly monoenergetic, i.e., the collision $\sqrt{s}$ has a spread $\delta_{\sqrt{s}}$ around its central value, further leading to a smearing of the BW peak. For FCC-ee operating at 125 GeV, the natural spread in collision energy due to synchrotron radiation and beamstrahlung will be around 70 MeV. Monochromatisation aims at reducing $\delta_{\sqrt{s}}$ to the few MeV scale, while still delivering moderately large (few ab$^{-1}$) integrated luminosities, $\mathcal{L}_{\text{int}}$ [837–839]. The reduction of the BW cross section due to initial-state photon emission(s) alone is of a factor of 0.35 and leads to $\sigma_{ee \to H} = 0.57$ fb [833].

The additional impact of a given energy spread on the Higgs BW shape can be quantified through the convolution of BW and Gaussian distributions, i.e., a relativistic Voigtian function. Figure 136 (right) shows the Higgs lineshape for various $\delta_{\sqrt{s}}$ values. The combination of ISR plus $\delta_{\sqrt{s}} = \Gamma_H = 4.1$ MeV reduces the peak Higgs cross section by a total factor of 0.17, down to $\sigma_{ee \to H} = 0.28$ fb. Though tiny, the cross section for any other $e^+e^- \to H$ production process, through intermediate W or Z bosons, is much further suppressed by the electron mass for on-shell external fermions (chirality flip) [31] and is negligible as well as any other loop-induced Higgs production mechanisms at $\sqrt{s} = 125$ GeV that is not sensitive to $y_e$ [840].

The strategy to observe the resonant production of the Higgs boson [32] is based on identifying final states consistent with any of the H decay modes that lead to small (but statistically significant when combined together) excesses over the expected backgrounds (orders-of-magnitude more abundant than the signal). In Ref. [32], a detailed study was performed with large simulated event samples of signal and associated backgrounds generated with PYTHIA 8 [778] for eleven Higgs boson decay channels. A benchmark monochromatisation point of ($\delta_{\sqrt{s}}, \mathcal{L}_{\text{int}}$) = (4.1 MeV, 10 ab$^{-1}$), corresponding to 2800 Higgs bosons produced, was assumed for the signal. A simplified description of the expected experimental performance was considered for the reconstruction and (mis)tagging of heavy-quark (c, b), light-quark (uds), and gluon (g) jets, as well as photons, electrons, and hadronically decaying tau leptons. Generic preselection criteria were defined to suppress reducible backgrounds while keeping the largest fraction of the signal events. A subsequent multivariate analysis of $\mathcal{O}(50)$ kinematic and global topological variables, defined for each event, was carried out. Boosted Decision Tree (BDT) classifiers were trained on signal and background events to maximise the signal significance for each individual channel. The most significant Higgs decay channels are found to be $H \to gg$ (for a gluon efficiency of 70% and a uds-for-g jet mistagging rate of 1%), and $H \to WW^* \to \ell\nu jj$. The digluon final state is the most sensitive channel to search for the resonant Higgs boson production (Fig. 136 left, upper diagram) because it has a moderately large branching fraction ($B \approx 8\%$) while the $Z^* \to gg$ decay is forbidden by the Landau–Yang theorem. The most important experimental challenge is to reduce the light-quark for gluon mistagging rate to the 1% level (while maintaining the efficiency for the $H \to gg$ channel at 70%) to keep the overwhelming $Z^* \to u\bar{u}, d\bar{d}, s\bar{s}$ backgrounds (Fig. 136 left, lower diagram) under control. Such a mistagging rate is a factor of about seven times better than the current state-of-the-art for jet-flavour tagging algorithms [491], but it is a realistic goal given all the experimental and theoretical improvements in the understanding of parton radiation and hadronisation expected at the FCC-ee [841].

Combining all results for an accelerator operating at ($\delta_{\sqrt{s}}, \mathcal{L}_{\text{int}}$) = (4.1 MeV, 10 ab$^{-1}$), a 1.3$\sigma$ signal significance can be reached for the direct production of the Higgs boson, corresponding to an upper limit on the electron Yukawa coupling at 1.6 times the SM value: $|y_e| < 1.6 |y_e^{\text{SM}}|$ at 95% CL for each detector in 1 year. Based on this benchmark result and the dependence of the resonant Higgs cross section on $\delta_{\sqrt{s}}$ (Fig. 136, right), bidimensional maps of $e^+e^- \to H$ significance and electron-Yukawa sensitivities have been determined in the ($\delta_{\sqrt{s}}, \mathcal{L}_{\text{int}}$) plane.

Figure 137 shows the 95% CL upper limit contours on the electron Yukawa coupling strength as a function of the energy spread and integrated luminosity with the red star (on the red-dashed line corresponding to a reference monochromatised collision-energy spread equal to the Higgs boson width), indicating the result of this benchmark study. The next section discusses the results of the current monochromatisation simulation studies, shown with red and yellow squares in this figure.

## FCC-ee monochromatisation

Monochromatisation is necessary to reduce $\delta_{\sqrt{s}}$ to the few MeV level of the natural SM Higgs width and thereby increase the sensitivity of the electron-Yukawa measurement via $e^+e^- \to H$. This strategy was first proposed 50 years ago [844] and relies on creating opposite correlations between spatial position and energy deviations within the colliding beams with nominal beam energy $E_0$. Figure 138 shows a schematic of the principle of monochromatisation for beams that collide head on (left) and with a crossing angle $\alpha$ (right). The current baseline design of FCC-ee corresponds to the latter configuration. In both configurations, the correlations between transverse (either horizontal or vertical) position in the beam and energy lead to a lower spread in collision energy than in the uncorrelated case.
<figure><img src="image_148.png" /><figcaption>Fig. 137 Upper limit contours (at 95% CL) on the electron Yukawa $y_e$ (coloured bands) in the collision-energy spread $\delta_{\sqrt{s}}$ vs. integrated luminosity $\mathcal{L}_{\text{int}}$ plane. The red star over the $\delta_{\sqrt{s}} = \Gamma_H = 4.1$ MeV red-dashed line indicates the reference point assumed in the physics simulation analysis [32]. The black cross indicates the previously achieved working point with self-consistent parametric monochromatisation [839,842]. The red and yellow squares indicate the monochromatisation points based on simulations of the ‘GHC V22 Z’ and ‘GHC V22 t\bar{t}$’ optics, respectively (see text for details) [843]</figcaption></figure>

<figure><img src="image_149.png" /><figcaption>Fig. 138 Schematic of the principle of monochromatisation for head-on collisions (left) and collisions with a crossing angle (right). In both cases, opposite-sign correlations between the transverse position in the beam and the energy lead to a reduction in the collision-energy spread, compared with the uncorrelated case</figcaption></figure>

Monochromatisation can be achieved by adding dedicated components at the interaction region (IR) to generate a non-zero dispersion function with opposite signs for the two beams at the IP. A non-zero dispersion function at the IP in the horizontal and/or vertical directions ($D_{x,y}^* \neq 0$) enlarges the IP transverse beam size ($\sigma_{x,y}^*$), which in turn affects the luminosity, $\mathcal{L} \propto 1/(\sigma_x^* \sigma_y^*)$. The monochromatisation factor is defined as

$$ \lambda = \sqrt{1 + \sigma_{\delta}^{2} \left( \frac{D_{x}^{*2}}{\varepsilon_{x} \beta_{x}^{*}} + \frac{D_{y}^{*2}}{\varepsilon_{y} \beta_{y}^{*}} \right)}, \qquad (12) $$

where $\sigma_{\delta}$ is the relative beam energy spread due to synchrotron radiation and beamstrahlung, $\varepsilon_{x,y}$ the transverse emittances, and $\beta_{x,y}^*$ the betatron functions at the IP. For any value of $\lambda$ achieved, $\delta_{\sqrt{s}}$ and $\mathcal{L}$ in the monochromatisation operation mode are

$$ \delta_{\sqrt{s}} = \frac{\sqrt{2} E_0 \sigma_{\delta}}{\lambda} \quad \text{and} \quad \mathcal{L} = \frac{\mathcal{L}_0}{\lambda}, \qquad (13) $$

where $\mathcal{L}_0$ represents the luminosity for the same values of $\beta_{x,y}^*$ but without $D_{x,y}^*$. Consequently, the design of a monochromatisation scheme requires considering both the IR beam optics and the optimisation of other collider parameters to maintain the highest possible luminosity. Possible approaches to monochromatisation for FCC-ee have been studied for several years, starting from self-consistent parametric studies [837,839,842,845]. Recent developments [843,846] comprise a detailed study of the IP-region optics required for monochromatisation, exploring different potential configurations and their implementation in the FCC-ee global lattice, along with beam-dynamics simulations and performance evaluations including the impact of beamstrahlung.
<table><caption>**Table 25** Values of $\delta_{\sqrt{s}}$, $\mathcal{L}$, and $\mathcal{L}_{\text{int}}$ for five setups of the 'GHC V22 Z' monochromatisation IR optics [843]: without monochromatisation ('Std. ZES'), with $D_x^* \neq 0$ in four and two IPs ('ZH4IP' and 'ZH2IP'), with $D_y^* \neq 0$ ('ZV'), and with $D_{x,y}^* \neq 0$ ('ZHV')</caption><thead><tr><th></th><th>Std. ZES</th><th>ZH4IP</th><th>ZH2IP</th><th>ZV</th><th>ZHV</th></tr></thead><tbody><tr><td>CM energy spread δ<sub>√s</sub> (MeV)</td><td>69.52</td><td>26.80</td><td>24.40</td><td>25.25</td><td>20.58</td></tr><tr><td>Luminosity/IP L (10<sup>34</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>44.8</td><td>15.0</td><td>18.4</td><td>1.46</td><td>1.42</td></tr><tr><td>Integrated luminosity/IP/year L<sub>int</sub> (ab<sup>-1</sup>)</td><td>5.38</td><td>1.80</td><td>2.21</td><td>0.18</td><td>0.17</td></tr></tbody></table>

<table><caption>**Table 26** Same as previous table, but for the 'GHC V22 t̄' monochromatisation IR optics [843]</caption><thead><tr><th></th><th>Std. TES</th><th>TH4IP</th><th>TH2IP</th><th>TV</th><th>THV</th></tr></thead><tbody><tr><td>CM energy spread δ<sub>√s</sub> (MeV)</td><td>67.20</td><td>27.10</td><td>23.16</td><td>20.23</td><td>21.24</td></tr><tr><td>Luminosity/IP L (10<sup>34</sup> cm<sup>-2</sup>s<sup>-1</sup>)</td><td>71.2</td><td>17.9</td><td>24.5</td><td>1.37</td><td>1.42</td></tr><tr><td>Integrated luminosity/IP/year L<sub>int</sub> (ab<sup>-1</sup>)</td><td>8.54</td><td>2.15</td><td>2.94</td><td>0.16</td><td>0.17</td></tr></tbody></table>

The baseline FCC-ee standard lattice design is the so-called 'Global Hybrid Correction' (GHC) optics [676,847,848]. It allows for four IRs, where the $e^+$ and $e^-$ beams are brought to collision with an $\alpha = 30$ mrad angle in the horizontal plane, as well as a potential vertical crab-waist scheme. The results of the monochromatisation studies shown in Fig. 137 are based on two versions of this optics: 'GHC V22 Z', where the lattice is optimised for operation at the Z pole, and 'GHC V22 t̄', which is optimised for operation above the t̄ threshold. Three approaches to monochromatisation have been investigated. In the first, the horizontal dipoles used for the local-chromaticity-correction system are reconfigured to generate a non-zero $D_x^*$ of size ~ 10 cm, while maintaining the same $\alpha$ value. Given the values of the other parameters in Eq. (12) [847], it follows that monochromatisation factors in the range $\lambda = 5-8$ are achievable.

This study was performed both to provide monochromatisation in all four IRs and then repeated to give monochromatisation in only two IRs. The second method introduces a non-zero value of $D_y^*$ by adjusting the strengths of the skew quadrupoles in the interaction region. The very low vertical emittance in FCC-ee implies that similar monochromatisation factors as in the horizontal case can be achieved with $D_y^* \approx 1$ mm. Finally, schemes involving non-zero values of both $D_x^*$ and $D_y^*$ have been explored. In all cases, the layout of the components around the IR and the parameter values were adjusted to satisfy the boundary conditions in the machine and deliver optimum performance.

Simulations were performed with GUINEA-PIG [695] to determine the performance of the different monochromatisation schemes, taking into account the impact of beamstrahlung. The particle distribution at the IP was simulated as an ideal Gaussian distribution, comprising 40,000 particles and defined by the following global optical performance parameters: $E_0$, $\sigma_\delta$, $\epsilon_{x,y}$, $\beta_{x,y}^*$, $D_{x,y}^*$, $\sigma_z$, and $\alpha$. For each configuration, the $\delta_{\sqrt{s}}$ (from the distribution of the collision energy) and $\mathcal{L}$ were calculated. The results are presented in Tables 25 and 26 for the 'GHC V22 Z' and 'GHC V22 t̄' optics, respectively.

All the investigated monochromatisation schemes are successful in reducing $\delta_{\sqrt{s}}$ by a factor of two or more with respect to the value without monochromatisation. As expected, this reduction in energy spread is accompanied by a reduction in luminosity, which is more marked for the configurations with $D_y^* \neq 0$ and combined $D_{x,y}^* \neq 0$, where the beamstrahlung leads to a blow up in $\epsilon_y$. The corresponding physics performance is plotted as red (yellow) squares for the 'GHC V22 Z' ('GHC V22 t̄') setups in the ($\delta_{\sqrt{s}}, \mathcal{L}_{\text{int}}$) plane in Fig. 137, from which the corresponding 95% CL upper limit contours for the $\epsilon_e$ coupling can be read off. The physics performance of all designed monochromatisation IR optics with non-zero $D_x^*$ are comparable to, or even exceed, those of the previous FCC-ee self-consistent parameters (black cross). The 'MonochroM TH2IP' optics achieves the best $\delta_{\sqrt{s}}$ vs. $\mathcal{L}_{\text{int}}$ benchmark, with $\delta_{\sqrt{s}} = 23.16$ MeV and $\mathcal{L}_{\text{int}} = 2.94$ ab$^{-1}$. This corresponds to an upper limit (at 95% CL) of $|\epsilon_e| < 3.2 |y_e^{SM}|$ for the Higgs-electron coupling, for each detector in 1 year. With four experiments running at the same luminosity with the 'TH4IP' scheme in the 'GHC V22 t̄' optics with crossing angle, one should be able to set an upper limit (at 95% CL) of about 2.5 times the SM value in 1 year of operation. This is to be compared with about 4 times the SM value when operating without monochromatisation. Prospects for improvements in the monochromatisation performance are briefly alluded to in Sect. 9.5.
## 9.5 Outlook

The studies performed before and during the Feasibility Study established a baseline scheme for calibration of the collision energy, ensuring that the physics goals of FCC-ee can be met. Nevertheless, these studies must be refined in certain areas and alternative schemes should be considered to further improve performance and operational efficiency.

The absolute uncertainties in $\sqrt{s}$ arising from RDP are the dominant systematic uncertainties in the measurements of the Z and W masses. Future studies will investigate whether these uncertainties can be reduced beyond the currently assumed values: 100 keV at the Z pole and 300 keV at the $W^+W^-$ threshold.

The measurements of energy-related quantities made by the experiments using dimuon events are a critical ingredient in the $\sqrt{s}$ calibration, at all centre-of-mass energies. Recently, several of these studies have been deepened to validate their robustness with respect to the uncertainties in the knowledge of higher-order ISR/FSR effects; this work will be extended further. It is also important to consolidate the strategy for understanding how the measurement of the crossing angle is affected by changes in the bunch intensity. The impact of detector performance and the interplay with alignment studies will be another focus of attention. Finally, the use of other categories of physics events, beyond dimuons, will be investigated.

It is important to have a reliable procedure to accurately translate the mean beam energy, measured by RDP, to the local collision energy, relevant for the physics measurements. Full simulations of this procedure will be conducted, at each interaction point, incorporating the in-situ measurement of the longitudinal boosts of the collisions and the knowledge of the machine impedances. Attention will also be paid to the control of energy shifts from possible dispersion effects at each interaction point, as well as to the related requirements on the precision of the system of beam-position monitors.

More detailed simulations of the level and lifetime of transverse polarisation will be performed, in parallel with changes to account for any evolution in the proposed optics of the accelerator. A deeper understanding will be sought of any effects that might bias the assumed proportionality between the spin tune and the mean beam energy. It will be particularly important to monitor the expected level of polarisation at the $W^+W^-$ threshold and the RDP strategy in this challenging regime. Detailed technical designs will be made of the polarimeter and depolariser systems.

So far, the baseline strategy to get transversally polarised pilot bunches has been to inject unpolarised beams and to stimulate the growth of polarisation by activating wigglers at the start of each fill. This is a robust approach but has the disadvantage of introducing dead-time, during which no collisions are possible. To overcome this inconvenience, studies will investigate the possibility of injecting already-polarised pilot bunches, for which the design of the injection system must be modified. Simulations will be required to validate that the bunches retain their polarisation throughout the injection step and while travelling in the booster ring.

Further investigations will also take place regarding the feasibility of the electron Yukawa measurement. In particular, new and refined schemes will be investigated with the aim of improving the monochromatisation of the collision energy. It will also be necessary to develop and simulate a procedure to monitor and adjust the collision energy in real time, to ensure that it remains centred at the Higgs pole. Further physics studies will be performed to improve the signal yield and the signal-to-background discrimination. Investigations will be performed to evaluate if the significance of the signal can be improved with differential measurements, accounting for the expected correlations between the monochromatisation and the longitudinal coordinate of the $e^+e^-$ collision.

## 10 Community building

Community building is critical for the success of the FCC project, because it fosters political, public, and financial support, encourages scientific collaboration and interdisciplinary innovation, promotes education and outreach, and helps ensure the project's long-term impact and sustainability. By creating an engaged, well-informed, and enthusiastic community, FCC can position itself not only as a groundbreaking scientific endeavour but also as a global, inclusive project with far-reaching benefits for humanity. This aspect has been given high priority ever since the beginning of the Conceptual Design Study, in 2014, in several directions:

- **Global scientific networks:** The FCC project will be one of the largest scientific endeavours ever attempted and its success crucially depends on the cooperation of a broad international scientific community. Engaging researchers, engineers, and institutions worldwide in discussions and collaborations, early on, will ensure that FCC leverages the best scientific
expertise, knowledge, training, and innovation from across the globe, from the preparation of the theory and experimental tools to the actual operation of the collider and the detectors, culminating in the data analysis and interpretation.

- **Transdisciplinary collaboration:** The FCC project encompasses a wide range of disciplines, from particle physics theory to detector design and R&D, from computing to engineering, from accelerator physics to machine-detector interface, etc. A well-established community always encourages cross-disciplinary collaboration and cross-fertilisation, enabling experts from various fields to contribute their knowledge and solve complex problems together. It also provides the resilience necessary to overcome setbacks, adapt to new circumstances, keep pushing the project forward to its implementation.

- **Inspiring the next generation of scientists and engineers:** Community engagement will help inspire the next generation to pursue careers in high-energy physics. First by designing and building the future experiments, while participating in the HL-LHC data analysis and physics programme; and then by operating, exploiting and interpreting the results of the FCC experiments. To ensure success over the 15 years construction time, the FCC project must also be a focal point for educational programmes, workshops, and professional training that generate interest and excitement in scientific discovery. The work done today will likely benefit future generations in ways that cannot yet be predicted. By creating a strong, multi-generational community, the project ensures that these long-term benefits are recognised, advocated for, and maximised over time.

- **Funding:** Last but not least, the FCC project will require funding from multiple sources, including governments, private donors, and international organisations. A strong, active community can advocate for the project, raising awareness about its scientific and societal benefits. Demonstrating broad support and interests from the community and advocacy of the long-term scientific benefits is required to establish credibility and increase the likelihood of securing the necessary resources for the project.

As a matter of fact, the FCC feasibility study midterm review committees issued a number of recommendations to this effect. In particular, they recommended:

- to work with the scientific community, institutes, laboratories, and funding agencies to ensure support and resources for four experiments, facilitating the exploitation of the full scientific potential offered by the large investment in the FCC facility;

- to dedicate additional human and financial resources to the project, with a resource-loaded schedule of work and clear priorities;

- to develop the coordination and structure required to enable the theoretical progress needed to match the anticipated experimental precision of the FCC data, both at CERN (fellows, scientific associates, visitors) and by engaging collaborating institutes (including, for instance, the creation of European networks); and

- to establish a dedicated FCC team in the research sector at CERN, with specific new positions associated, and to quantify its size and makeup in terms of seniority so that the resources required can be estimated.

Such actions have been (at least partially) anticipated a decade ago during the Conceptual Design Study (2014-2019), and intensified during the Feasibility Study (2021-2025). The three volumes of the FCC Conceptual Design Report [10-12], released in January 2019, have been signed by 1364 authors, distributed in about 140 institutions, which had become members of the FCC Collaboration with the signature of Memoranda of Understanding (MoU) during this first phase. To comply with the recommendations of the 2021 European Strategy Update, the FCC Collaboration was reinforced by inviting more institutions to join and carry out the FCC Feasibility Study. One of the goals was to gather a majority of particle physicists behind the project, able to build a consensus in the community at the next European Particle Physics Strategy update that FCC is, indeed, the post-LHC collider option with the broadest scientific impact, at the intensity and the energy frontiers.

During the 5 years of the Feasibility Study, the expansion of the Collaboration was pursued in two different ways.

A. At the Collaboration level, the FCC Global Collaboration (FGC) Working Group continuously engages with current and new participants – national institutes, laboratories and universities, as well as industry – to encourage an expanded membership through Memoranda of Understanding. The FGC explores opportunities for future prospective participants, supports new participants in the application process, and assists the new participants in defining areas of collaboration, in particular for the accelerator. It then concludes relevant agreements to facilitate the integration process. It also prepares the foundations for R&D and contributions by industry, as well as fostering interest in geology, geodesy, logistics, materials
science, and other areas that, while not being at the core of CERN activities, are critical for the success of the FCC feasibility study and its implementation on the ground.

B. From the side of the FCC Physics, Experiments, and Detectors (PED) group, one of the six pillars of the FCC Feasibility Study, contacts are established with all high-energy physics groups in Europe and around the world, to invite them to join and contribute to the FCC project, in parallel to their current activities. To this effect, an International Forum of National Contacts (IFNC) was created, chaired by two national contacts, with the mandate of attracting the different HEP groups, country by country. The quasi-complete list of European states (around 30) are represented in the IFNC, which meets regularly to reinforce the collaboration. The IFNC also reaches out to the rest of the world. The United States of America are now strongly involved in the Collaboration, following the recent Snowmass process and the positive recommendation of the U.S. Particle Physics Project Prioritization Panel (P5) to engage in an off-shore Higgs Factory. Most of the other large non-European countries are also active and represented in the IFNC (including Argentina, Brazil, Canada, Chile, India, Mexico, Pakistan, South Korea, Thailand, and Turkey) and the list continues expanding.

The cases of Japan and China, currently considering projects for colliders on their soil, are treated separately. With the goal to integrate teams from these countries in the near future, scientific exchanges with the Japanese and Chinese communities already occur in the FCC/CEPC/LC/ECFA and other national workshops. Informal discussions with early-career Japanese physicists have also been organised.

To build an extensive community of HEP physicists, the IFNC is also developing a finer structure, identifying institutional contacts for the participating institutes inside a country (up to 20 or 30 individuals for certain countries, such as France, Germany, Italy or the UK, and even more for the US), the goal being to have a vast majority of HEP institutes contributing, or on the verge of contributing, to the project by the end of the next European Strategy Update (2026).

In parallel, the PED group has also launched a call for Expressions of Interests (EoI's), in October 2024, to encourage the different institutes to get together and collaborate on innovative FCC sub-detector R&D within the DRD Collaborations, and on detector concept studies, with the FCC integration as main objective. A first version of these sub-detector EoI's will be submitted as input to the European Strategy Group by March 31st, 2025, and will be the basis for continuing development and consolidation during the next phase of the FCC study, until the end of 2027, with more R&D, prototype construction, detailed simulation, test beams, etc. Detector concepts EoI's will follow a similar development. Different combinations of sub-detectors will be integrated and tested in the common software to reach optimal performance, possibly as a function of the many physics objectives. Further steps are also envisioned, such as documenting, as an additional input to the European Strategy, the potential contribution of the different countries to FCC in the coming years, should the project be recommended and then approved.

The work with the scientific community progresses on a daily basis in the working groups of the PED pillar and gets a broader exposure twice a year during the 'FCC Collaboration Weeks' in Spring (2021 at CERN; 2022 in Paris; 2023 in London; 2024 in San Francisco; 2025 in Vienna) and the 'FCC Physics Workshops' in Winter (2022 in Liverpool; 2023 in Krakow; 2024 in Annecy; 2025 at CERN), allowing the community to be reinforced and new scientific collaborations to emerge. A strong FCC participation in the US Community Study on the Future of Particle Physics ('Snowmass 2021') acted as a decisive seed for the FCC effort in the US and was followed by three US-FCC workshops in 2023, 2024, and 2025. Besides, many national FCC Collaboration workshops have taken place, in essentially all large countries or regions of Europe and in the US, with active participation from the PED coordination group, yielding a significant growth of the PED part of the Collaboration in the past 5 years.

Several funding agencies have already reacted very positively to this evolution, decisively supported by substantive diplomatic work from the CERN management. The most resounding three examples are listed below.

1. In April 2024, the White House and CERN signed a joint statement of intent [849] saying, in particular, "*Should the member states determine that FCC-ee is likely to be CERN's next world-leading research facility, the US intends to collaborate on its construction and physics exploitation, subject to appropriate domestic approvals*".

2. In June 2024, the CERN Council approved the Medium Term Plan (MTP) for the period 2025-2029 [850], including the funding of a bottom-up resource request for FCC-specific new positions.

3. In September 2024, the EU Competitiveness Report [851] was publicly released, with the following statements: "*One of CERN's most promising current projects, with significant scientific potential, is the construction of the Future Circular Collider (FCC): a 90-km ring designed initially for an electron collider and later for a hadron collider. [...] Refinancing CERN and ensuring its continued global leadership in frontier research should be regarded as a top EU priority*".
Following the approval of the CERN MTP in June 2024, CERN created a dedicated FCC group in the EP department, effective since September 2024, with dedicated new positions (fellows, students, scientific associates, visitors) over the next 3 years. This sends another strong signal to the HEP community worldwide, regarding the host-lab commitment to FCC. Past experience has shown that even a moderately-sized host-lab group provides a significant leverage on contributions from the particle-physics community at other institutes. It is now anticipated that the creation of this group will be a strong incentive for CERN contract holders to reassign part of their time to the FCC project, starting with the supervision of the new recruits. As the project moves to the next phase, many more engineers and detector physicists will be needed soon. The current situation is being carefully monitored and it is expected that a significant pool of these engineers and physicists will transition to FCC detector development as the construction for the HL-LHC upgrades begins to wind down.

Assuming a positive recommendation of the CERN Council at around 2028, the FCC Collaboration expects that an FCC Committee (equivalent to the LHCC for the LHC experiments) will be formed by the CERN management and that a call for FCC detector Conceptual Design Reports will be issued soon after. Proto-collaborations (in particular, subsets of the FCC Collaboration, but not only) could then answer this call shortly after 2030 with full detector concept proposals.

Finally, the coordination and structuring of the theoretical work needed to match the anticipated experimental precision of the FCC data has started during the Feasibility Study. Several successful mini-workshops were organised (Targets and Tools, Flavour Physics Programme, BSM Physics Programme, Higgs/Top/EW Physics Programme, Parton Shower, Phenomenology) with between 100 and 350 participants. The CERN/TH FCC team currently consists of three physicists, with the occasional participation of up to eight staff members and fellows, reflecting a genuine academic interest in working on the FCC physics among theorists. Needless to say, more dedicated resources will be needed for a worldwide organisation during the next phases of the FCC study.

## 11 Outlook

The alignment of stars that led, in 2011/2012, to the concept of a ~100 km electron-positron collider in the same tunnel as a future 100 TeV proton-proton collider in the Geneva basin and, in 2020, to the update of the European Strategy for Particle Physics (ESPPU) endorsing the FCC feasibility study as a top priority for CERN and its international partners, has presented the global HEP community with a unique and exceptional opportunity to advance the field. After almost 5 years of Feasibility Study performed by a worldwide consortium of scientists and engineers, the particle physicists – including the early-career contingent – are now steadily coalescing around the initial-stage machine (FCC-ee) as the first priority for a post-LHC collider at CERN.

The FCC-ee offers ideal conditions (high luminosity, centre-of-mass energy calibration, possibly monochromatisation, and moderate beam-induced backgrounds) for the intensity-frontier study of the four heaviest particles of the Standard Model, accumulating enormous samples ($6 \times 10^{12}$ Z bosons at 88–94 GeV, $5 \times 10^8$ W bosons at and above 157 GeV, $2.8 \times 10^6$ Higgs bosons at and above 240 GeV, and $4 \times 10^6$ top quarks at and above 340 GeV) in only a few years of operation at each energy point. With a wealth of opportunities for precision electroweak, QCD, flavour, and Higgs measurements, searches for rare or forbidden processes, and the possible discovery of feebly coupled particles, FCC-ee is sensitive to essentially any kind of new physics from a few GeV up to scales of 10–100 TeV, over an extremely broad range of couplings. These studies may help address the most profound questions of particle physics today. What is the nature of dark matter? How did the antimatter disappear? What is responsible for the non-zero neutrino masses? Even if FCC-ee were to ‘only’ confirm the Standard Model with a precision up to three orders of magnitude better than today, theories that propose solutions to these fundamental questions would become very tightly constrained, thus guiding the development of new models and improving significantly the understanding of the creation of the Universe. It is instructive to recall that one of the foundation stones of modern physics is a null experiment: the absence of discovery of the Ether by the Michelson–Morley experiment in 1887.

The FCC-ee is also the perfect springboard for a $O(100)$ TeV hadron collider (FCC-hh), for which it provides a major fraction of the infrastructure. The complementary and synergistic exploratory physics programmes of these two machines offer a uniquely powerful long-term vision. In a way not too dissimilar from the discovery of Neptune in 1846, which was predicted by the precise measurement of the orbit of Uranus in 1843 (inconsistent with Newton’s laws applied to the solar system of the seven planets observed at that time), any deviation with respect to the Standard Model predictions observed at FCC-ee is testable directly with FCC-hh, up to a scale of 40 TeV. When a new physics signal is eventually observed at FCC-hh or elsewhere, the FCC-ee precision measurements – whether they agree or not with the Standard Model – will be an invaluable resource in establishing the nature of the underlying physics.

The FCC integrated project is also able to measure the Higgs boson interactions with fermions and gauge bosons with high precision (down to a part in a thousand) without theoretical hypotheses. The Higgs potential, modelled by the Higgs
<figure><img src="image_150.png" /><figcaption>**Fig. 139** Possible timeline of the FCC-ee project between the end of the feasibility study and the start of the first FCC-ee physics run, with key dates for the project as a whole (pink), and separately for the accelerator (left side, green) and for the detectors (right side, blue). (The acronym FC³ stands for 'FCC Committee'.)</figcaption></figure>

boson self interactions, plays a fascinating and central role in the cosmological history of the universe. A first determination of the trilinear Higgs boson self-coupling with a precision of the order of 25% will be provided by HL-LHC through the measurement of the Higgs-pair production cross section. A qualitatively different and complementary determination with a similar precision will exploit the per-mil-level measurement of the single-Higgs production cross section at FCC-ee, yielding a combined precision better than 20%. A unique per-cent level measurement of the trilinear Higgs self-coupling will only become available with FCC-hh.

To date, there is no other collider project that can even remotely compete with such an exploratory breadth and depth: the most complete understanding of the Higgs sector; the unique interplay between the electroweak, flavour, and Higgs measurements at the intensity frontier; the multiple synergies between FCC-ee and FCC-hh; the access to the smallest couplings and the highest energy scales; in all aspects, the FCC integrated programme offers outstanding physics prospects. The FCC project, with its four interaction points, therefore suits to perfection the scientific ambitions of CERN and of its worldwide community of 15,000 users. Comparison studies [14] indicate that the overall duration; the electricity consumption; the total cost; and the life-cycle carbon footprint of the FCC-ee construction and operation are all very significantly smaller than those of other (lower luminosity) Higgs factory options at CERN once normalised to their physics output (i.e., once the running time of these alternative projects is extended to match the same Higgs-coupling precision as FCC-ee, and yet, disregarding the richness of the remainder of the FCC-ee physics programme, which lies beyond these other options). Furthermore, the FCC integrated project minimises the carbon emissions on the road to the highest energies, as the FCC-ee infrastructure will be fully recycled for FCC-hh. The FCC infrastructure could also be repurposed to house a fast accelerator and injector for a very high energy muon collider in the LEP/LHC tunnel.

The delivery of this Feasibility Study marks the completion of the first phase of an extended and intensive programme of work. Even though the $e^+e^-$ collider is currently scheduled to deliver its first collisions in the second half of the 2040s, the timeline of the project, displayed in Fig. 139 for both the accelerator and the experiments, is tightly filled with important deadlines that must be met and critical milestones that cannot be missed.

The first of these milestones has been for the particle physics community to prepare expressions of interest (EoIs) for critical detector components towards the realisation of up to four experiments, in time for the forthcoming European Strategy Update. More EoIs are foreseen if FCC-ee is recommended as the preferred post-LHC project at CERN by the European Strategy Group. Should the project be approved by CERN Council on the basis of this recommendation, a formal call for the creation of experiment proto-collaborations will be launched, towards the submission of Detector Conceptual Design Reports (CDRs) a few years later, followed by detector Technical Design Reports (TDRs) in the mid-2030's. Achieving these

<figure><img src="image_151.png" /></figure>
ambitious goals will require an appropriate and timely re-organisation of activities over the coming couple of years, and a
significant injection of (human and financial) resources in the project.

In parallel with detector design, construction, installation, and commissioning, the road towards the first collisions is paved
with many other exigencies to respond to, a partial list of which follows.

- First and foremost, the effort towards the goal of matching theoretical calculation uncertainties to the expected statistical power of the collider (and propagating these calculations to technically accurate Monte Carlo generators), so as to optimally exploit the data from FCC-ee and, later, from FCC-hh, needs to be immediately structured and sustained with appropriate resources, from the clear roadmap established during the Feasibility Study.

- In the coming few years, the requirements from detailed physics case studies will continue to be the driving factor in efforts to design the most technologically-advanced (but also the most realistic) FCC-ee detector concepts, to ensure the full coverage of the wide and challenging physics programme. These efforts will have to be intensified, in particular at the Z pole, where the requirements from physics are expected to be the most demanding.

- These physics studies will need to be backed up with a versatile and reliable software ecosystem, from accurate Monte Carlo event generators to modern event reconstruction and analysis software, passing through detailed detector simulation. Achieving this will demand a significant increase of both computing and human resources, which were a limiting factor during the Feasibility Study. To broaden the project resource base, continued efforts are required to attract (many) more external contributors from institutes worldwide. Promoting positions shared between LHC and FCC will also foster joint development efforts and enhance expertise exchange.

- Regarding the interaction region, the integration strategy of the inner sub-detectors (e.g., vertex detectors, luminometers, superconducting pipes, supporting structures) with the accelerator components will be established, as their designs are finalised. Methods for opening and maintenance of the detector elements, together with their alignment with respect to the beams will be further developed, and possible consequences on the cavern dimensions will be evaluated. Most importantly, the studies of the impact of all beam-induced backgrounds on the detector performance and mitigation solutions will need to be consolidated for all sub-detectors.

- The measurement and monitoring of the centre-of-mass energy will be one of the cornerstones of the whole physics programme. The baseline scheme presented in this Volume must be refined and made fully reliable, and alternative schemes will be considered. Specifically, the possibility of injecting already polarised electron and positron bunches will be thoroughly investigated. Improved schemes for monochromatisation will be systematically studied in view of proposing a sustainable method for the electron Yukawa coupling measurement.

- Finally, detailed studies of the physics programme of FCC-ee on the one hand, and groundwork studies of physics and detectors at FCC-hh on the other, will continue to further extend the exploration of the standalone potential of each collider, and the synergies between them. These efforts will also reflect the guidelines that will emerge from the review of the Feasibility Study Report and from the ESPPU discussions.

While it will be years before all these goals are attained, there is no doubt that the recommendation of the FCC project by the forthcoming ESU will catalyse the engagement of the particle physics community at large on FCC-ee. The growing interest from young scientists in the project must be recognised with appropriate career opportunities.

The baseline choice of collision energies and running sequence (Z pole, WW threshold, ZH maximum, and $t\bar{t}$ threshold, as shown in Fig. 140) with four interaction points is sufficient to demonstrate that FCC-ee offers an extraordinary list of opportunities (and associated challenges) for milestone measurements with a real chance of discovery. Looking ahead, this list will only become richer as the investigations deepen, and it is already clear that more integrated luminosity and the extension of the programme to encompass additional energy points would increase the FCC science value still further [17]. In parallel, the FCC-ee machine parameters are now different from those that prevailed at the time of the CDR, and will continue to evolve in the next phase of the study, while the understanding of the physics performance of the experiments is progressing. This perspective may significantly modify, or enrich, the desirable scientific programme, as pictured in Fig. 140.

For example, the possibility to run at $\sqrt{s} = 125$ GeV, with a centre-of-mass energy spread of the order of the Higgs boson width, is under consideration, towards a 3σ evidence for the electron Yukawa coupling. Precision QCD studies with a few ab$^{-1}$ at centre-of-mass energies of 20, 30, 40, ..., 80 GeV are very appealing to a significant fraction of the HEP community. Because the study of the monochromatisation schemes required for the electron Yukawa measurement are not yet at a mature stage; and because Z-pole data with energetic initial-state radiation can in principle also explore lower centre-of-mass energies; no proposal is made yet to include these energy points in the baseline programme.
FCC-ee Physics Runs Ordered by Energy

<figure><img src="image_152.png" /><figcaption>**Fig. 140** Potential physics programme for FCC-ee, ordered by increasing centre-of-mass energy, without indication of a specific chronological sequence. The events highlighted in red indicate the minimal programme with 15 years of running, and with the corresponding integrated</figcaption></figure>

luminosities and physics outcome. The numbers of Z, WW, ZH, and $t\bar{t}$ events delivered to four interaction points are indicated. A possible wider physics programme, with additional centre-of-mass energies, is highlighted in blue

These additional possibilities and corresponding science value further demonstrates the flexibility and breadth of the FCC-ee physics potential. An increase of the FCC-ee specific luminosity would enable the physics programme to be extended to encompass at least some of these possibilities within the currently envisaged 15-year timescale. It will ultimately be up to the experimental collaborations and the relevant scientific committees to optimise the time flexibility and to tailor the FCC-ee operation scenario according to a number of factors that cannot be controlled today. For example, external events such as the FCC-hh magnet readiness or the CERN financial situation may call for a change in the overall duration of the FCC-ee running time. Furthermore, intriguing early results may motivate additional running at a given working point. Meanwhile, new avenues will be explored towards increasing the luminosities at all energies.

At the end of the HL-LHC operation, the LEP-LHC integrated programme will have delivered sustained scientific excellence for over 50 years, and greatly advanced our understanding of the fundamental interactions. The succession of FCC-ee and FCC-hh in a common tunnel will replicate and magnify this success, with vastly better precision and increased energies. The FCC integrated programme offers outstanding prospects for progress in a wealth of topics, including Higgs, electroweak, and flavour physics, as well as remarkable sensitivity in direct searches for both feebly coupled low-mass particles and those that may exist up to many tens of TeV. The upcoming ESPPU provides an opportunity for the global HEP community to endorse this vision, and then to work together so as to enable the first stage of this project, FCC-ee, to be realised in a timely fashion. Seizing this opportunity will be an important step forward in the journey towards a more complete understanding of the laws of nature.

**Acknowledgements** We would like to thank the **International Steering Committee** members: F. Gianotti (Chair), CERN; R. Bello, CERN; P. Chomaz, CEA, France; M. Cobal, INFN and University of Udine, Italy; B. Heinemann, DESY, Germany; T. Koseki, KEK, Japan; M. Lamont, CERN; L. Merminga, FNAL, United States; J. Mnich, CERN; M. Seidel, PSI and EPFL, Switzerland; C. Warakaulle, CERN; and the **Scientific Advisory Committee** members: A. Parker (Chair), Cambridge University, UK; R. Bartolini, DESY, Germany; A. Chabert, SFTRF, France; H. Ehrbar, Heinz Ehrbar Partners LLC, Switzerland; B. Gavela Legazpi, UAM Madrid, Spain; G. Hiller, TU Dortmund, Germany; S. Krishnagopal, FNAL, U.S.; P. Križan, University of Ljubljana, Slovenia; P. Lebrun, ESI, France; P. McIntosh, STFC, ATeV, UKRI, UK; M. Minty, BNL, U.S.; R. Tenchini, INFN Sezione di Pisa, Italy for their continued guidance and careful reviewing that helped to complete this report successfully.

<figure><img src="image_153.png" /></figure>

The research carried out by the international FCC collaboration hosted by CERN, which led to this publication, has received funding from the European Union's Horizon 2020 research and innovation programme under the grant numbers 951754 (FCCIS), 654305 (EuroCirCol),