down quark masses as mentioned above, and Yukawa unification is only consistent with low-energy data in a restricted region of SUSY parameter space, with important consequences for SUSY searches [116, 118]. More recent analyses of Yukawa unification after LHC Run-I are found in Ref. [119].

Gauge coupling unification is also successful in the scenario of split supersymmetry [80], in which squarks and sleptons have mass at a scale $\tilde{m} \gg m_Z$, while gauginos and/or Higgsinos have masses of order the weak scale. Unification of $b-\tau$ Yukawa couplings requires $\tan\beta$ to be fine-tuned close to 1 [101]. If by contrast, $\tan\beta \gtrsim 1.5$, $b-\tau$ Yukawa unification only works for $\tilde{m} \lesssim 10^4$ GeV. This is because the effective theory between the gaugino mass scale and $\tilde{m}$ includes only one Higgs doublet, as in the standard model. As a result, the large top quark Yukawa coupling tends to increase the ratio $\lambda_b/\lambda_\tau$ due to the vertex correction, which is absent in supersymmetric theories, as one runs down in energy below $\tilde{m}$. This is opposite to what happens in the MSSM where the large top quark Yukawa coupling lowers the ratio $\lambda_b/\lambda_\tau$ [110].

### 93.7.2 Beyond leading order: three-family models

Simple Yukawa unification is not possible for the first two generations. Indeed, the simplest implementation of $SU(5)$ implies $\lambda_s = \lambda_\mu$, $\lambda_d = \lambda_e$ and hence $\lambda_s/\lambda_d = \lambda_\mu/\lambda_e$. This is an RG-invariant relation which extrapolates to $m_s/m_d = m_\mu/m_e$ at the weak scale, in serious disagreement with data ($m_s/m_d \sim 20$ and $m_\mu/m_e \sim 200$). An elegant solution to this problem was given by Georgi and Jarlskog [120] (for a recent analysis in the SUSY context see [121]).

More generally, we have to recall that in all of the previous discussion of Yukawa couplings, we assumed renormalizable interactions as well as the minimal matter and Higgs content. Since the GUT scale is close to the Planck scale, higher-dimension operators involving the GUT-breaking Higgs may modify the predictions, especially for lower generations. An example is provided by the operators $10\bar{5}5_H 24_H$ with $24_H$ the GUT-breaking Higgs of $SU(5)$. We can fit parameters to the observed fermion masses with these operators, though some fine-tuning is introduced in doing so. The SM Higgs doublet may come in part from higher representations of the GUT group. For example, the **45** of $SU(5)$ includes an $SU(2)_L$ doublet with appropriate $U(1)_Y$ charge [120]. This **45** can, in turn, come from the **120** or **126** of $SO(10)$ after its breaking to $SU(5)$ [122, 123]. These fields may also have renormalizable couplings with quarks and leptons. The relations among the Yukawa coupling constants in the SM are modified if the SM Higgs doublet is a linear combination of several such doublets from different $SU(5)$ multiplets. Finally, the SM fermions may not be embedded in GUT multiplets in the minimal way. Indeed, if all quarks and leptons are embedded in **16s** of $SO(10)$, the renormalizable interactions with $10_H$ cannot explain the observed CKM mixing angles. This situation improves when extra matter multiplets, such as **10**, are introduced: After $U(1)_X$, which distinguishes the **5s** coming from the **16** and the **10** of $SO(10)$, is broken (e.g. by a VEV of $16_H$ or $126_H$), the r.h. down quarks and l.h. leptons in the SM can be linear combinations of components in **16s** and **10s**. As a result, $\lambda \neq \lambda'$ in $SU(5)$ [124].

To construct realistic three-family models, some or all of the above effects can be used. Even so, to achieve significant predictions for fermion masses and mixing angles grand unification alone is not sufficient. Other ingredients, for example additional global family symmetries are needed (in particular, non-Abelian symmetries can strongly reduce the number of free parameters). These family symmetries constrain the set of effective higher-dimensional fermion mass operators discussed above. In addition, sequential breaking of the family symmetry can be correlated with the hierarchy of fermion masses [125]. One simple, widely known idea in this context is to ensure that each $10_i$ enters Yukawa interactions together with a suppression factor $e^{3-i} (\epsilon$ being a small parameter). This way one automatically generates a stronger hierarchy in up-type quark Yukawas as compared to down-type quark and lepton Yukawas and no hierarchy for neutrinos, which agrees with observations at the $O(1)$-level. Three-family models exist which fit all the data, including neutrino masses and mixing [27, 126].

Finally, a particularly ambitious variant of unification is to re-

quire that the fermions of all three generations come from a single representation of a large gauge group. A somewhat weaker assumption is that the flavor group (e.g. $SU(3)$) unifies with the SM gauge group in a simple gauge group at some energy scale $M \ge M_G$. Early work on such ‘flavor-unified GUTs’, see e.g. [124, 127], has been reviewed in [128, 129]. For a selection of more recent papers see [130]. In such settings, Yukawa couplings are generally determined by gauge couplings together with symmetry breaking VEVs. This is reminiscent of heterotic string GUTs, where all couplings come from the 10d gauge coupling. However, while the $E_8 \to SU(3) \times E_6$ branching rule $248 = (8, 1) + (1, 78) + (3, 27) + (3, 27)$ looks very suggestive in this context, the way in which most modern heterotic models arrive at three generations is actually more complicated.

## 93.8 Neutrino masses

We see from atmospheric and solar neutrino oscillation observations, along with long baseline accelerator and reactor experiments, that neutrinos have finite masses. By adding three “sterile” neutrinos $\nu_i^c$ with Yukawa couplings $\lambda_{\nu,ij}$ ($\nu_i^c L_j H_u$) ($i, j = 1, 2, 3$), one easily obtains three massive Dirac neutrinos with mass $m_\nu = \lambda_\nu v_u$, analogously to quark and charged lepton masses. However, in order to obtain a $\tau$ neutrino with mass of order 0.1 eV, one requires the exceedingly small coupling ratio $\lambda_{\nu\tau}/\lambda_\tau \lesssim 10^{-10}$. By contrast, in GUTs the seesaw mechanism naturally explains such tiny neutrino masses as follows [2–4]: The sterile neutrinos have no SM gauge quantum numbers so that there is no symmetry other than global lepton number which forbids the Majorana mass term $\frac{1}{2}M_{ij} \nu_i^c \nu_j^c$. Note also that sterile neutrinos can be identified with the r.h. neutrinos necessarily contained in complete families of $SO(10)$ or Pati-Salam models. Since the Majorana mass term violates $U(1)_X$ in $SO(10)$, one might expect $M_{ij} \sim M_G$. The heavy sterile neutrinos can be integrated out, defining an effective low-energy theory with only three light active Majorana neutrinos with the effective dimension-five operator

$$-\mathcal{L}_{eff} = \frac{1}{2} c_{ij} (L_i H_u) (L_j H_u), \qquad (93.17)$$

where $c = \lambda_\nu^T M^{-1} \lambda_\nu$. This then leads to a $3 \times 3$ Majorana neutrino mass matrix $m = m_\nu^T M^{-1} m_\nu$.

The seesaw mechanism implemented by r.h. neutrinos is sometimes called the type-I seesaw model. There are variant models in which the dimension-five operator for neutrino masses is induced in different ways: In the type-II model, an $SU(2)_L$ triplet Higgs boson $\Sigma$ is introduced to have couplings $\Sigma L^2$ and also $\Sigma H_u^2$ [122, 131]. In the type-III model, an $SU(2)_L$ triplet of fermions $\tilde{\Sigma}$ with a Yukawa coupling $\tilde{\Sigma} L H_u$ is introduced [132]. In these models, the dimension-five operator is induced by integrating out the triplet Higgs boson or fermions. Such models can also be implemented in GUTs by introducing Higgs bosons in the **15** or fermions in the **24** in $SU(5)$ GUTs or the **126** in $SO(10)$ GUTs. Notice that the gauge non-singlet fields in the type-II and III models have masses at the intermediate scale. Thus, gauge coupling unification is not automatic if these variant mechanisms are implemented in SUSY GUTs.

Atmospheric neutrino oscillations discovered by Super-Kamiokande [133] require neutrino masses with $\Delta m_\nu^2 \sim 2.5 \times 10^{-3}$ eV$^2$ with maximal mixing [64], in the simplest scenario of two neutrino dominance. With hierarchical neutrino masses this implies $m_{\nu\tau} = \sqrt{\Delta m_\nu^2} \sim 0.05$ eV. Next, we can try to relate the neutrino Yukawa coupling to the top quark Yukawa coupling, $\lambda_{\nu\tau} = \lambda_t$ at the GUT scale, as in $SO(10)$ or $SU(4) \times SU(2)_L \times SU(2)_R$ models. This gives $M \sim 10^{14}$ GeV, which is remarkably close to the GUT scale.

Neutrinos pose a special problem for GUTs. The question is why the quark mixing angles in the CKM matrix are small while there are two large lepton mixing angles in the PMNS matrix. Global fits of neutrino masses and mixing angles can, for example, be found in Refs. [134] and [135]. For SUSY GUT models which fit quark and lepton masses, see Ref. [136, 137] for reviews. Finally, for a compilation of the range of SUSY GUT predictions for neutrino mixing, see [138].
We should also note that, both within and independently of the GUT framework, much work has been devoted to neutrino-mass and more generally flavor model building on the basis of discrete symmetries (see e.g. [137,139]). A more recent interesting twist in this context is the use of the (non-linearly realized) modular group $SL(2, \mathbb{Z})$ as a discrete flavor symmetry [140]. This group plays a key role in string theory as the group of large diffeomorphisms of the 2-torus, the latter appearing as the string worldsheet and, more relevant in the present context, as part of the compactification space of torus orbifold models (cf. also Sect. 93.4). For a selection from the recent significant activity in these directions see e.g. [141].

## 93.9 Selected topics

### 93.9.1 Global symmetries

As we discussed, global symmetries are frequently introduced to control higher-dimension operators in GUT models. This is particularly important in the context of nucleon decay but also plays a role in GUT-based flavor model building and cosmological applications, such as baryogenesis and inflation. However, we should note that appealing to global symmetries to suppress specific interactions may not be as straightforward as it naively seems. Indeed, there are two possibilities: On the one hand, the relevant symmetry might be gauged at a higher scale. Effects of the VEVs responsible for the spontaneous breaking are then in principle dangerous and need to be quantified. On the other hand, the symmetry might be truly only global. This must e.g. be the case for anomalous symmetries, which are then also violated by field-theoretic non-perturbative effects. The latter can in principle be exponentially small. It is, however, widely believed that global symmetries are always broken in quantum gravity (see e.g. [142]). One then needs to understand which power or functional form the Planck scale suppression of the relevant interaction has. For example, dimension-five baryon number violating operators suppressed by just one unit of the Planck or string scale are completely excluded in the supersymmetric models.

In view of the above, it is also useful to recall that in string models 4d global symmetries generally originate in higher-dimensional gauge symmetries [40, 143]. Here ‘global’ implies that the gauge boson has acquired a Stückelberg-mass. This is a necessity in the anomalous case (Green-Schwarz mechanism [144]) but can also happen to non-anomalous symmetries. One expects no symmetry violation beyond the well-understood non-perturbative effects. Discrete symmetries arise as subgroups of continuous gauge symmetries, such as $\mathbb{Z}_N \subset U(1)$. In particular, non-anomalous subgroups of Stückelberg-massive $U(1)$s represent unbroken discrete gauge symmetries and as such are non-perturbatively exact (see e.g. [145]). Of course, such discrete gauge symmetries may also arise as remnants of continuous gauge symmetries after conventional 4d spontaneous breaking.

### 93.9.2 Anomaly constraints vs. GUT paradigm

As emphasized at the very beginning, the fact that the SM fermions of one generation fill out the $10+\bar{5}$ of $SU(5)$ appears to provide overwhelming evidence for some form of GUT embedding. However, one should be aware that a counterargument can be made which is related to the issue of ‘charge quantization by anomaly cancellation’ (see [146,147] for some early papers and [148] for a more detailed reference list): Imagine we only knew that the low-energy gauge group were $G_{SM}$ and the matter content included the $(3, 2)_Y$, i.e. a ‘quark doublet’ with $U(1)$-charge $Y$. One can then ask which possibilities exist of adding further matter to ensure the cancellation of all triangle anomalies. It turns out that this problem has only three different, minimal$^{10}$ solutions [147]. One of those is precisely a single SM generation, with the apparent ‘$SU(5)$-ness’ emerging accidentally. Thus, if one randomly picks models from the set of consistent gauge theories, preconditioning on $G_{SM}$ and $(3, 2)_Y$, one may easily end up with ‘$10+\bar{5}$’ of an $SU(5)$ that is in no way dynamically present. This is precisely what happens in the context of non-GUT string model building [149].

### 93.9.3 Topological defects and phase transitions

Of the various topological defects which may exist in the broken phase of GUT models, the most famous ones are magnetic monopoles. These are typically localized classical solutions carrying magnetic charge under an unbroken $U(1)$ symmetry [150]. These magnetic monopoles with mass of order $M_G/\alpha_G$ can be produced during a possible GUT phase transition in the early Universe. The flux of magnetic monopoles is experimentally found to be less than $\sim 10^{-16} \text{ cm}^{-2} \text{ s}^{-1} \text{ sr}^{-1}$ [151]. Many more are however predicted, hence the GUT monopole problem. In fact, one of the original motivations for inflation was to solve the monopole problem by exponential expansion after the GUT phase transition [152] and hence dilution of the monopole density. Other possible solutions to the monopole problem include: sweeping them away by domain walls [153], $U(1)$ electromagnetic symmetry breaking at high temperature [154] or GUT symmetry non-restoration [155]. Parenthetically, it was also shown that GUT monopoles can catalyze nucleon decay [156]. A significantly stronger bound on the monopole flux can then be obtained by considering X-ray emission from radio pulsars due to monopole capture and the subsequent nucleon decay catalysis [157].

Note that the present upper bound on the inflationary vacuum energy density is very close to the GUT scale, $V_{inf}^{1/4} = (1.88 \times 10^{16} \text{ GeV}) \times (r/0.10)^{1/4}$, with the scalar-to-tensor ratio constrained to $r < 0.036$ [158]. This guarantees that reheating does not lead to temperatures above $M_G$ and hence the monopole problem is solved by inflation (unless $M_G$ is unexpectedly low).

As already noted, topological defects other than monopoles are also common, see e.g. [159]. They can be cosmologically relevant in GUT models based on a gauge group larger than $SU(5)$, say, $SO(10)$, where an intermediate gauge theory may appear. The breaking of this intermediate gauge symmetry can a priori occur anywhere between the GUT and the electroweak scale. Right-handed neutrino masses favor a value near $\mathcal{O}(10^{14}) \text{ GeV}$ and non-SUSY coupling unification may profit from such a two-step GUT breaking scheme (cf. Sect. 93.5). Crucially for the present context, the last breaking step may occur after inflation, generating topological defects (like cosmic strings) which are not diluted. Their signature can be probed through gravitational waves [160], with the metastable string case being of particular phenomenological interest [161, 162]. Metastability arises because the nucleation of a monopole-anti-monopole pair, each of which serves as an endpoint for the string, allow the cosmic string to break. The lifetime becomes long and hence the string stable as the ratio between monopole mass and the square root of the string tension grows. This is related to the ratio of scales of the two symmetry breaking steps. It is of phenomenological interest that metastability allows the string network to evade the recent bound of $G\mu \lesssim 10^{-10}$ (or $\sqrt{\mu} \lesssim 10^{14} \text{ GeV}$) [162]. Moreover the spectrum is blue-tilted compared to the stable string case. Finally, we note that if the intermediate gauge symmetry breaking proceeds with a (strong) first order phase transition, this could also generate gravitational waves [162, 163]. However, due to the relatively high energy scales involved the peak frequency tends to be high, with signals hopefully to be explored in future gravitational wave experiments.

### 93.9.4 Flavor violation

Yukawa interactions of GUT-scale particles with quarks and leptons may leave imprints on the flavor violation induced by SUSY breaking parameters [164]. To understand this, focus first on the MSSM with universal Planck-scale boundary conditions (as e.g. in gravity mediation). Working in a basis where up-quark and lepton Yukawas are diagonal, one finds that the large top-quark Yukawa coupling reduces the l.h. squark mass squares in the third generation radiatively. It turns out that only the l.h. down-type squark mass matrix has sizable off-diagonal terms in the flavor basis after CKM-rotation. However, in GUTs the color-triplet Higgs has flavor violating interactions from the Yukawa coupling $\lambda_{ij} (10_i, 10_j, 5_H)$, such that flavor-violating r.h. slepton mass terms are radiatively generated in addition [165]. In $SU(5)$ extension of the type-I seesaw model, where r.h. neutrinos are introduced as $SU(5)$ singlets with interactions $\lambda_{ij}'' (1_i, \bar{5}_j, 5_H)$, the doublet and color-triplet Higgses acquire another type of Yukawa

<footnote>$^{10}$ Adding extra vector-like sets of fields, e.g. two fermions which only transform under $U(1)$ and have charges $Y$ and $-Y$, is considered to violate minimality.</footnote>
coupling, respectively. They then radiatively generate flavor-
violating l.h. slepton [166] and r.h. down squark masses [167].
These flavor-violating SUSY breaking terms induce new contri-
butions to FCNC processes in quark and lepton sectors, such as
$\mu \to e\gamma$ and $K^0-K^0$ and $B^0-B^0$ mixing. Note that even if the
flavor-universal SUSY breaking terms are generated at $M_G$, the
r.h. neutrino Yukawa coupling may induce sizable flavor violation
in l.h. slepton masses due to the running between $M_G$ and the
right-handed-neutrino mass scale.

EDMs are also induced when both l.h. and r.h. squarks/sleptons
have flavor-violating mass terms with relative phases, as discussed
for SO(10) in [168] or for SU(5) with r.h. neutrinos in [169]. Thus,
such low-energy observables constrain GUT-scale interactions.

93.9.5 *From GUT baryogenesis to leptogenesis and B/L-violating transitions*

During inflation, any conserved quantum number is extremely
diluted. Thus, one expects the observed baryon asymmetry of the
Universe to originate at reheating or in the subsequent cosmolog-
ical evolution. In detail, the situation is slightly more involved:
Both baryon number B and lepton number L are global symme-
tries of the SM. However, (B+L) is anomalous and violated by
thermal fluctuations in the early Universe, via so-called sphaleron
processes. Moreover, it is violated in GUT models, as is most
apparent in proton decay. By contrast, (B-L) is anomaly free
and preserved by both the SM as well as SU(5) or SO(10) gauge
interactions.

Now, the old idea of GUT baryogenesis [170,171] is to generate a
(B+L) and hence a baryon asymmetry by the out-of-equilibrium
decay of the color-triplet Higgs. However such an asymmetry,
generated at GUT temperatures, is washed out by sphalerons<fnref n="11" />.
This can be overcome [173] using lepton-number violating inter-
action of neutrinos to create a (B-L) from the (B+L) asymmetry,
before sphaleron processes become sufficiently fast at T < 10¹²
GeV. This (B-L) asymmetry can then survive the subsequent
sphaleron dominated phase. Note that this does not work in the
minimal SUSY GUT setting, with the triplet Higgs above the
GUT scale. The reason is that a correspondingly high reheating
temperature would be required which, as explained above, is ruled
out by Planck data.

However, the most widely accepted simple way out of the
dilemma is to directly generate a net (B-L) asymmetry dynam-
ically in the early Universe, also using r.h. neutrinos. Indeed, we
have seen that neutrino oscillations suggest a new scale of physics
of order 10¹⁴ GeV. This scale is associated with heavy Majorana
neutrinos in the seesaw mechanism. If in the early Universe, the
decay of the heavy neutrinos is out of equilibrium and violates
both lepton number and CP, then a net lepton number may be
generated. This lepton number will then be partially converted
into baryon number via electroweak processes [174]. This mecha-
nism is called leptogenesis.

If the three heavy Majorana neutrino masses are hierarchical,
the net lepton number is produced by decay of the lightest one,
and it is proportional to the CP asymmetry in the decay. The
CP asymmetry is bounded from above, and the lightest neutrino
mass is required to be larger than 10⁹ GeV in order to explain the
observed baryon asymmetry [175]. This implies that the reheating
temperature after inflation should be larger than 10⁹ GeV so that
the heavy neutrinos are thermally produced<fnref n="12" />. In supersymmetric
models, there is a tension between leptogenesis and Big Bang
Nucleosynthesis (BBN) if gravitinos decay in the BBN era. The
gravitino problem gives a constraint on the reheating temperature
~ 10⁶⁻¹⁰ GeV though the precise value depends on the SUSY
breaking parameters [177]. Recent reviews of leptogenesis can be
found in Ref. [178].

One of the important tests of leptogenesis are searches for neu-
trinoless double-β (0νββ) decays<fnref n="13" />. In a 0νββ decay, only two

electrons but no (anti-)neutrinos are emitted by the decaying nu-
cleus. This is in contrast to ordinary double-β decay. Thus, 0νββ
decays are lepton-number-violating with ΔL = 2. At the nucleon
level, this is described by dimension-nine effective operators for
nn → ppee. These operators may in turn come from SM oper-
ators of with dimension less than nine, in combination with SM
weak interactions. The lowest one is the dimension-five opera-
tor generating the Majorana neutrino mass terms (Eq. (93.17)).
Thus, if the lepton-number violating effective interactions come
from physics at energies much above the weak scale, the 0νββ de-
cay rates are proportional to the Majorana neutrino masses. The
latest experimental results are reviewed in [64]. For recent studies
of the 0νββ decay including SM operators up to mass dimension
nine, see [179] and refs. therein.

In addition to L-violation, one can consider (B-L) and B vi-
olating phenomena. They are interesting in their own right and
may also be relevant to baryogenesis. The relevant operators have
higher mass dimension than the familiar dimension-six (B + L)-
violating operators (cf. Sec. 93.6). They may be predicted in
SO(10) GUTs with an intermediate scale, at which baryogene-
sis is realized, such as in [180]. First, one may have nucleon
decays with Δ(B-L) = 2, such as n → e⁻π⁺. This is in-
duced by dimension-seven effective operators in the SM, which
are suppressed by the SM Higgs VEV or derivatives. Second,
there are neutron-antineutron (n-n̄) oscillations, which are in-
duced by ΔB = 2 dimension-nine effective operators in the SM.
The upper bound on the mean time for n-n̄ transitions is directly
derived using free neutrons [181]. It is also constrained from the
lower limit on the lifetime for neutrons bound in ¹⁶O, derived by
Super-Kamiokande [182]. Their results are very similar. Super-
Kamiokande also searches for dinucleon decays with ΔB = 2, such
as pp → π⁺π⁺ and nn → π⁺π⁻ [183].

93.9.6 The QCD Axion

The axion is a hypothetical pseudoscalar particle which is capa-
ble of resolving the strong CP problem [184] and may potentially
be related to GUT physics. In particular, the strength of the
direct coupling of the QCD axion to photons, relative to its cou-
pling to gluons, may be seen as a phenomenological signature of
grand unification. It is quantified by the predicted anomaly ratio
E/N = 8/3 (see [185–187]). This ratio follows from the GUT nor-
malization of the relevant generators together with the complete-
ness of GUT multiplets contributing to the anomaly.<fnref n="14" /> It hence
arises in axion models of both DFSZ [188] and KSVZ [189] type
as long as the Peccei-Quinn symmetry commutes with the GUT
group (see e.g. [190]). Specifically in the case of a DFSZ axion, ex-
tra SU(2) multiplets contribute to the running of gauge couplings
between Peccei-Quinn and GUT scale, potentially affecting unifi-
cation. By contrast, the KSVZ axion can be implemented without
such effects.

We also note that, in bottom-up approaches and in the pres-
ence of split GUT multiplets, other anomaly ratios can appear
(cf. e.g. [191]). Their embedding in a UV GUT structure, pos-
sibly with explicit GUT symmetry breaking, requires case-by-
case study. The ratio E/N = 8/3 also arises in string-theoretic
GUTs [186,192]. In this case, the axion does not come from
the phase of a complex scalar but is a fundamental shift-symmetric
real field, coupling through a higher-dimension operator directly
to the product of the GUT field-strength and its dual.

93.10 Conclusion

Most conservatively, grand unification means that (some of) the
SM gauge interactions of U(1)Y, SU(2)_{L} and SU(3)_{C} become
part of a larger, unifying gauge symmetry at a high energy scale.
In most models, especially in the simplest and most appealing
variants of SU(5) and SO(10) unification, the statement is much
stronger: One expects the three gauge couplings to unify (up to
small threshold corrections) at a unique scale, M<sub>G</sub>, and the proton
to be unstable due to exchange of gauge bosons of the larger

<footnote n="11">¹¹ To be precise, if lepton flavor numbers $L_i$ ($i=1-3$) are nonzero and $(L_i-L_j) \neq 0$ ($i \neq j$), one may obtain nonzero values for B and L even if $(B-L) = 0$ [172].</footnote>

<footnote n="12">¹² This constraint may be avoided in resonant leptogenesis [176], in which the right-handed neutrinos are required to be almost degenerate in mass.</footnote>

<footnote n="13">¹³ Another important test of leptogenesis would be the observation of CP violation in neutrino oscillations. Strictly speaking, the CP phase in the</footnote>

<footnote>PMNS matrix does not contribute to $\epsilon_1$ in the seesaw model. Nevertheless, the observation of CP violation in neutrino oscillations would suggest that the seesaw mechanism is associated with a large CP violation, similarly to the quark sector.</footnote>

<footnote n="14">¹⁴See e.g. eq. (312) of [187]</footnote>
symmetry group. Supersymmetric grand unified theories provide, by far, the most predictive and economical framework allowing for perturbative unification. Many more details than could be discussed in the present article can be found in some of the classic reviews [128,193] and the four books [194] (see also [195] for two recent overviews).

Thus, the three classical pillars of GUTs are gauge coupling unification at $M_G \sim 2 \times 10^{16}$ GeV, low-energy supersymmetry (with a large SUSY desert), and nucleon decay. The first of these may be viewed as predicting the value of the strong coupling – a prediction which has already been verified (see Fig. 93.1). Numerically, this prediction remains intact even if SUSY partner masses are somewhat above the weak scale. However, at the conceptual level a continuously increasing lower bound on the SUSY scale is nevertheless problematic for the GUT paradigm: Indeed, if the independent, gauge-hierarchy-based motivation for SUSY is completely abandoned, the SUSY scale and hence $\alpha_3$ become simply free parameters and the first two pillars crumble. Thus, it is important to keep pushing bounds on proton decay which, although again not completely universal in all GUT constructions, is arguably a more generic part of the GUT paradigm than low-energy SUSY.

Whether or not Yukawa couplings unify is more model dependent. However, irrespective of possible (partial) Yukawa unification, there certainly exists a very interesting and potentially fruitful interplay between flavor model building and grand unification. Especially in the neutrino sector this is strongly influenced by the developing experimental situation.

It is probably fair to say that, due to limitations of the 4d approach, including especially remaining ambiguities (free parameters or ad hoc assumptions) in models of flavor and GUT breaking, the string theoretic approach has become more important in GUT model building. In this framework, challenges include learning how to deal with the many vacua of the ‘landscape’ as well as, for each vacuum, developing the tools for reliably calculating detailed, phenomenological observables. Finally, due to limitations of space, the present article has barely touched on the interesting cosmological implications of GUTs. They may become more important in the future, especially in the case that a high inflationary energy scale is established observationally.

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94. Leptoquarks

Revised October 2023 by S. Rolli (DOE) and M. Tanabashi (Nagoya U.; KMI, Nagoya U.).

Leptoquarks are hypothetical particles carrying both baryon number (B) and lepton number (L). The possible quantum numbers of leptoquark states can be restricted by assuming that their direct interactions with the ordinary Standard Model (SM) fermions are dimensionless and invariant under the SM gauge group. Table 94.1 shows the list of all possible quantum numbers with this assumption [1]. The columns of SU(3)$_C$, SU(2)$_W$, and U(1)$_Y$ in Table 94.1 indicate the QCD representation, the weak isospin representation, and the weak hypercharge, respectively. The spin of a leptoquark state is taken to be 1 (vector leptoquark) or 0 (scalar leptoquark).

If we do not require leptoquark states to couple directly with SM fermions, different assignments of quantum numbers become possible [2, 3].

Leptoquark states are expected to exist in various extensions of the SM. The Pati-Salam model [4] is an example predicting the existence of a leptoquark state. Leptoquark states also exist in grand unification theories based on SU(5) [5], SO(10) [6] which includes Pati-Salam color SU(4), and larger gauge groups. The existence of leptoquarks at TeV-scale also affect the renormalization group of the standard model gauge coupling strengths and may allow for the gauge coupling unification required by the grand unification theories [7]. Scalar quarks in supersymmetric models with R-parity violation may also have leptoquark-type Yukawa

couplings. The bounds on the leptoquark states can therefore be applied to constrain R-parity-violating supersymmetric models [8,9]. Scalar leptoquarks are expected to exist at the TeV scale in extended technicolor models [10, 11] where leptoquark states appear as the bound states of techni-fermions. Compositeness of quarks and leptons also provides examples of models which may have light leptoquark states [12].

Bounds on leptoquark states are obtained both directly and indirectly. Direct limits are from their production cross sections at colliders, while indirect limits are calculated from bounds on leptoquark-induced two-quark two-lepton interactions, which are obtained from low-energy experiments, or from collider experiments below threshold. The quantum number assignment of Table 94.1 allows several leptoquark states to couple to both left- and right-handed quarks simultaneously. Such leptoquark states are called non-chiral and may cause low-energy interactions

$$ (\bar{u}_R q_{L_i})(\bar{e}_R \ell_{L_j}) \epsilon^{ij} \qquad (\bar{d}_R q_{L_i})(\bar{\ell}_L^i e_R). \qquad (94.1) $$

Here i, j are indices for the weak isospin. These two-quark two-lepton interactions affect the $(\pi \to e\nu)/(\pi \to \mu\nu)$ ratio [13]. Non-chiral scalar leptoquarks also contribute to the anomalous magnetic moments of charged leptons [14, 15]. On the other hand, the exchanges of the chiral leptoquarks produce effective two-quark two-lepton interactions

$$ \begin{aligned} (\bar{q}_L^i \gamma^\mu q_{L_i})(\bar{\ell}_L^j \gamma_\mu \ell_{L_j}), \qquad &(\bar{q}_L^i \gamma^\mu q_{L_i})(\bar{e}_R \gamma_\mu e_R), \qquad &(\bar{q}_L^i \gamma^\mu (\bar{\sigma})_i^j q_{L_j}) \cdot (\bar{\ell}_L^k \gamma_\mu (\bar{\sigma})_k^l \ell_{Ll}), \\ (\bar{u}_R \gamma^\mu u_R)(\bar{\ell}_L^j \gamma_\mu \ell_{L_j}), \qquad &(\bar{u}_R \gamma^\mu u_R)(\bar{e}_R \gamma_\mu e_R), \qquad &(\bar{d}_R \gamma^\mu d_R)(\bar{\ell}_L^j \gamma_\mu \ell_{L_j}), \qquad &(\bar{d}_R \gamma^\mu d_R)(\bar{e}_R \gamma_\mu e_R) \end{aligned} \qquad (94.2) $$

below the leptoquark mass scale. Note that labels for the generations of quarks and leptons are suppressed in (94.1) and (94.2). If a leptoquark couples to quarks (leptons) belonging to more than a single generation in the mass eigenbasis, it can induce two-quark two-lepton interactions causing flavor-changing neutral currents (lepton-family-number violations). Since indirect limits provide more stringent constraints on non-chiral or flavor-violating leptoquarks, in the searches of leptoquark states at collider experiments, it is often assumed that a leptoquark state couples only to a single generation of quarks and a single generation of leptons in a chiral interaction, for which indirect limits become much weaker. Additionally, this assumption gives strong constraints on models of leptoquarks.

Refs. [16–18] give extensive lists of the bounds on the leptoquark-induced two-quark two-lepton interactions. For the isoscalar scalar and vector leptoquarks $S_0$ and $V_0$, for example, which couple with the first- (second-) generation left-handed quark, and the first-generation left-handed lepton, the bounds $\lambda^2 < 0.07 \times (M_{LQ}/1 \text{ TeV})^2$ for $S_0$, and $\lambda^2 < 0.4 \times (M_{LQ}/1 \text{ TeV})^2$ for $V_0$ ($\lambda^2 < 0.7 \times (M_{LQ}/1 \text{ TeV})^2$ for $S_0$, and $\lambda^2 < 0.5 \times (M_{LQ}/1 \text{ TeV})^2$ for $V_0$) with $\lambda$ being the leptoquark coupling strength, can be derived from the limits listed in Ref. [18]. See also Refs. [19, 20] for earlier studies. The $e^+e^-$ collider experiments are sensitive to the indirect effects coming from t- and u-channel exchanges of leptoquarks in the $e^+e^- \to q\bar{q}$ process. The HERA experiments give bounds on the leptoquark-induced two-quark two-lepton interaction. It should also be stressed that the measurements of the high-mass Drell-Yan cross sections, $pp \to \ell\nu$ and $pp \to \ell^+\ell^-$, are also sensitive to these leptoquark-induced interactions. For detailed bounds obtained in this way, see e.g., Ref. [17], and the Heavy Boson Particle Listings for “Indirect Limits for Leptoquarks” and their references.

Note that the two-quark two-lepton interactions arising from the leptoquark exchanges in Eq.(94.1) and Eq.(94.2) can also be regarded as a part of more general dimension-six operators in the context of low-energy standard-model effective field theory (SMEFT). For a complete list of SM gauge-invariant dimension-

six operators, see [21, 22]. A computation of the one-loop anomalous dimension matrix for SMEFT operators are found in Refs. [23–25]. The leptoquark induced two-quark two-lepton interactions often cause lepton-flavor non-universalities in heavy quark decays. The $R(D)$, $R(D^*)$ anomaly observed in the semileptonic $B$ decays [26] may be explained in models with TeV scale leptoquarks.

Collider experiments provide direct limits on the leptoquark states through limits on the pair- and single-production cross sections. The leading-order cross sections of the parton processes

$$ \begin{aligned} q + \bar{q} &\rightarrow \mathrm{LQ} + \overline{\mathrm{LQ}} \\ g + g &\rightarrow \mathrm{LQ} + \overline{\mathrm{LQ}} \\ e + q &\rightarrow \mathrm{LQ} \end{aligned} \qquad (94.3) $$

may be written as [27]

$$ \begin{aligned} \hat{\sigma}_{\mathrm{LO}} \left[ q\bar{q} \rightarrow \mathrm{LQ} + \overline{\mathrm{LQ}} \right] &= \frac{2\alpha_s^2 \pi}{27\hat{s}} \beta^3, \\ \hat{\sigma}_{\mathrm{LO}} \left[ gg \rightarrow \mathrm{LQ} + \overline{\mathrm{LQ}} \right] &= \frac{\alpha_s^2 \pi}{96\hat{s}} \\ & \times \left[ \beta(41 - 31\beta^2) + (18\beta^2 - \beta^4 - 17) \log \frac{1+\beta}{1-\beta} \right], \\ \hat{\sigma}_{\mathrm{LO}} \left[ eq \rightarrow \mathrm{LQ} \right] &= \frac{\pi\lambda^2}{4} \delta(\hat{s} - M_{\mathrm{LQ}}^2) \end{aligned} \qquad (94.4) $$

for a scalar leptoquark. Here $\sqrt{\hat{s}}$ is the invariant energy of the parton subprocess, and $\beta \equiv \sqrt{1 - 4M_{\mathrm{LQ}}^2/\hat{s}}$. The leptoquark Yukawa coupling is given by $\lambda$. The cross sections of the pair productions of scalar leptoquarks in pp collisions at the LHC energies have been computed in Refs. [28, 29] at the next-to-leading order in QCD. Leptoquarks are also produced singly at hadron colliders through $g + q \to \mathrm{LQ} + \ell$ [30], which allows extending to higher
<table><caption>**Table 94.1:** Possible leptoquarks and their quantum numbers.</caption><thead><tr><th>Spin</th><th>3B + L</th><th>SU(3)<sub>c</sub></th><th>SU(2)<sub>W</sub></th><th>U(1)<sub>Y</sub></th><th>Allowed coupling</th></tr></thead><tbody><tr><td>0</td><td>-2</td><td>3</td><td>1</td><td>1/3</td><td>q̄<sub>L</sub><sup>c</sup>ℓ<sub>L</sub> or ū<sub>R</sub><sup>c</sup>e<sub>R</sub></td></tr><tr><td>0</td><td>-2</td><td>3</td><td>1</td><td>4/3</td><td>d̄<sub>R</sub><sup>c</sup>e<sub>R</sub></td></tr><tr><td>0</td><td>-2</td><td>3</td><td>3</td><td>1/3</td><td>q̄<sub>L</sub><sup>c</sup>ℓ<sub>L</sub></td></tr><tr><td>1</td><td>-2</td><td>3</td><td>2</td><td>5/6</td><td>q̄<sub>L</sub><sup>c</sup>γ<sup>μ</sup>e<sub>R</sub> or d̄<sub>R</sub><sup>c</sup>γ<sup>μ</sup>ℓ<sub>L</sub></td></tr><tr><td>1</td><td>-2</td><td>3</td><td>2</td><td>-1/6</td><td>ū<sub>R</sub><sup>c</sup>γ<sup>μ</sup>ℓ<sub>L</sub></td></tr><tr><td>0</td><td>0</td><td>3</td><td>2</td><td>7/6</td><td>q̄<sub>L</sub>e<sub>R</sub> or ū<sub>R</sub>ℓ<sub>L</sub></td></tr><tr><td>0</td><td>0</td><td>3</td><td>2</td><td>1/6</td><td>d̄<sub>R</sub>ℓ<sub>L</sub></td></tr><tr><td>1</td><td>0</td><td>3</td><td>1</td><td>2/3</td><td>q̄<sub>L</sub>γ<sup>μ</sup>ℓ<sub>L</sub> or d̄<sub>R</sub>γ<sup>μ</sup>e<sub>R</sub></td></tr><tr><td>1</td><td>0</td><td>3</td><td>1</td><td>5/3</td><td>ū<sub>R</sub>γ<sup>μ</sup>e<sub>R</sub></td></tr><tr><td>1</td><td>0</td><td>3</td><td>3</td><td>2/3</td><td>q̄<sub>L</sub>γ<sup>μ</sup>ℓ<sub>L</sub></td></tr></tbody></table>

masses the collider reach in the leptoquark search [31], depending on the leptoquark Yukawa coupling. The next-to-leading order computations for the single production of the leptoquark states at the LHC energies have been performed in Refs. [32–35]. Since protons contain leptons inside, it is possible to target lepton-induced processes at high energy pp colliders. The single leptoquark production cross sections induced from the lepton-quark collisions at the LHC have been computed in Refs. [36,37]. Ref. [38] performed searches for the leptoquark states produced in lepton-quark collisions at the LHC.

See Ref. [17] for a comprehensive review on the leptoquark phenomenology in precision experiments and particle colliders.

Leptoquark states which couple only to left- or right-handed quarks are called chiral leptoquarks. Leptoquark states which couple only to the first (second, third) generation are referred as the first- (second-, third-) generation leptoquarks.

The LHC, Tevatron and LEP experiments have been searching for pair production of the leptoquark states, which arises from the leptoquark gauge interaction. Due to the typical decay of the leptoquark into charged and neutral leptons and quarks, the searches are carried on in signatures including high $p_T$ charged leptons, high $E_T$ jets and large missing transverse energy. Additionally, searches for pair produced LQs are often organized by the decay mode of the pair of LQs, via the decay parameter $\beta$, which represents the branching fraction into a charge lepton vs a neutrino: $\beta = 1$ for LQs decaying into a charged lepton with 100% branching fraction, $\beta = 0.5$ for LQs decaying into a charged lepton with 50% branching fraction. The gauge couplings of a scalar leptoquark are determined uniquely according to its quantum numbers in Table 94.1. Since all of the leptoquark states belong to color-triplet representation, the scalar leptoquark QCD-induced pair-production cross section at the Tevatron and LHC can be determined solely as a function of the leptoquark mass without making further assumptions. This is in contrast to the indirect or single-production limits, which give constraints in the leptoquark mass-coupling plane.

Older results from the Tevatron run can be found here: [39–42].

Since the previous version of this review, both ATLAS and CMS continue to update their results concerning searches for first, second, and third generation LQs and leptoquark states which couple only with the $i$-th generation quarks and the $j$-th generation leptons ($i \neq j$) without causing conflicts with severe indirect constraints. The datasets were almost all collected at center of mass energy of 13 TeV and corresponding to the latest integrated luminosity collected before the shutdown of the LHC occurring in 2019 and 2020.

It is worthy to note that organizing LQs by flavor quantum number first before organizing them by gauge quantum number is becoming more common and advantageous because it relates more closely to some of the experimental searches being performed. The traditional nomenclature for 1st, 2nd, and 3rd generation LQ encourages only looking for the diagonal elements in a flavor matrix of possibilities, which has been the traditional experimental search strategy.

Current results extend previous mass limits for scalar leptoquarks to > 1435 GeV (first generation, CMS, $\beta = 1, \sqrt{s} = 13$ TeV) and > 1270 GeV (first generation, CMS, $\beta = 0.5, \sqrt{s} = 13$ TeV) [43]; > 1800 GeV (first generation, ATLAS, $\beta = 1, \sqrt{s} =$

13 TeV) [44] and > 1290 GeV (first generation, ATLAS, $\beta = 0.5, \sqrt{s} = 13$ TeV) [45]; > 1530 GeV (second generation, CMS, $\beta = 1, \sqrt{s} = 13$ TeV) and > 1285 GeV (second generation, CMS, $\beta = 0.5, \sqrt{s} = 13$ TeV) [46]; and > 1700 GeV (second generation, ATLAS, $\beta = 1, \sqrt{s} = 13$ TeV) [44] and > 1230 GeV (second generation, ATLAS, $\beta = 0.5, \sqrt{s} = 13$ TeV) [45]. All limits are presented at 95% C.L.

As for third generation leptoquarks, CMS results are the following: 1) assuming that all leptoquarks decay to a top quark and a $\tau$ lepton, the existence of pair produced, third-generation leptoquark up to a mass of 1120 GeV ($\beta = 1, 13$ TeV) is excluded at 95% confidence level [47]; 2) assuming that all leptoquarks decay to a bottom quark and a $\tau$ lepton, the existence of pair produced, third-generation leptoquark up to a mass of 1020 GeV ($\beta = 1, 13$ TeV) is excluded at 95% confidence level [48]; 3) assuming that all leptoquarks decay to a bottom quark and a $\tau$ neutrino, the existence of pair produced, third-generation leptoquark up to a mass of 1185 GeV ($\beta = 0, 13$ TeV) is excluded at 95% confidence level [49]. In a recent paper [50] signatures of top quark $\tau$ lepton $\nu$ bottom and top $\tau \nu$ - not previously explored in dedicated searches, were analyzed in the context of searches for scalar leptoquark of charge $-1/3e$ coupling to a top quark plus a $\tau$ lepton ($t\tau$) or a bottom quark plus a neutrino ($b\nu$), or a vector particle of charge $+2/3e$, coupling to $t\nu$ or $b\tau$. These choices are motivated by models that can explain a series of anomalies observed in the measurement of B meson decays. The data are found to be in agreement with the standard model prediction. Lower limits at 95% confidence level are set on the LQ mass in the range 0.98–1.73 TeV, depending on the LQ spin and its coupling $\lambda$ to a lepton and a quark, and assuming equal couplings for the two LQ decay modes considered. These are the most stringent constraints to date on the existence of leptoquarks in this scenario.

In [51] ATLAS present the result of searches for pair production of third-generation scalar leptoquarks decaying into a top quark and a $\tau$-lepton, using 139 fb$^{-1}$ of data collected at 13 TeV. Scalar leptoquarks decaying exclusively into $t\tau$ are excluded up to masses of 1.43 TeV while, for a branching fraction of 50% into $t\tau$, the lower mass limit is 1.22 TeV. In two recent papers [52] and [53] ATLAS searched for pair-produced scalar or vector leptoquarks decaying into a b-quark and a $\tau$-lepton and single production of vector leptoquarks with electric charge of $2/3e$ and scalar leptoquarks with an electric charge of $4/3e$. For pair production of scalar leptoquarks, masses below 1490 GeV are excluded assuming a 100% branching ratio, while for vector leptoquarks the corresponding limit is 1690 GeV (1960 GeV) in the minimal-coupling (Yang–Mills) scenario. For single vector leptoquark production two models are considered: the Yang–Mills and Minimal coupling models. In the Yang–Mills (Minimal coupling) scenario, vector leptoquarks with a mass below 1.58 (1.35) TeV are excluded for a gauge coupling of 1.0 and below 2.05 (1.99) TeV for a gauge coupling of 2.5. In the case of single scalar leptoquark production, masses below 1.28 TeV (1.53 TeV) are excluded for a Yukawa coupling of 1.0 (2.5). Additionally, a search for pair production of leptoquarks with decays into third-generation leptons and quarks. In final states with hadronically decaying $\tau$ leptons, b-jets, and missing transverse momentum was performed in [54]: depending on the branching fraction into charged leptons, leptoquarks with masses up to around 1.25 TeV can be excluded at
the 95% confidence level for the case of scalar leptoquarks and up to 1.8 TeV (1.5 TeV) for vector leptoquarks in a Yang–Mills (minimal-coupling) scenario.

It is also possible to consider leptoquark states which couple only with the *i*-th generation quarks and the *j*-th generation leptons ($i \neq j$) without causing conflicts with severe indirect constraints. Such couplings have received renewed attention because they may provide an explanation to anomalies in rare B–meson decays and the anomalous magnetic moment of the muon. See Ref. [55, 56] and [57] and references therein for collider search strategies and limits on the pair production cross sections of this class of leptoquark states. In this framework, in [58] and [47] CMS presents a non-traditional search for pair production of LQs coupled to a top quark and a leptons. As no deviation from the Standard Model prediction was observed, scalar LQs decaying exclusively into top quark and lepton are excluded below 1.12–1.42 TeV depending on the lepton flavor. In [59] ATLAS conducted a search for pair production of scalar and vector leptoquarks, each decaying into first and second generation leptons and a third generation quarks. This is part of leptoquark search using ATLAS data to investigate cross- generation couplings that could provide explanations for recently observed anomalies in B meson decays. All possible decays of the pair-produced leptoquarks into quarks of the third generation and charged or neutral leptons of the first or second generation with exactly one electron or muon in the final state are investigated. No significant deviations from the Standard Model expectation are observed. Upper limits on the production cross-section are provided for different models as a function of the leptoquark mass and the branching ratio of the leptoquark into the charged or neutral lepton. Some of these models have the goal of providing an explanation for the recent B-anomalies. In such models, a vector leptoquark decays into charged and neutral leptons of the second generation with a similar branching fraction. Lower limits of 1.9 TeV and 1.7 TeV are set on the leptoquark mass for these two models.

The magnetic-dipole-type and the electric-quadrupole-type interactions of a vector leptoquark are not determined even if we fix its gauge quantum numbers as listed in the Table 94.1 [60]. The production of vector leptoquarks depends in general on additional assumptions, where the leptoquark couplings and their pair production cross sections are enhanced relative to the scalar leptoquark contributions. The most stringent limits on vector LQ production are now from CMS [61] where previous searches for squarks and gluinos have been reinterpreted to constrain models of leptoquark production. LQ masses below 1530 GeV are excluded assuming the Yang-Mills case with coupling $\kappa = 1$, or 1115 GeV in the minimal coupling case where $\kappa = 0$, placing the most stringent constraint to date from pair production of vector LQs. These results and the ones in [62] were updated in [49] where searches for phenomena beyond the standard model (BSM) were performed using events with hadronic jets and significant transverse momentum imbalance to constrain a range of BSM models including the pair production of scalar and vector leptoquarks each decaying to a neutrino and a top, bottom, or light-flavor quark.

The leptoquark pair-production cross sections in $e^{+}e^{-}$ collisions depend on the leptoquark $SU(2) \times U(1)$ quantum numbers and Yukawa coupling with electron [63].

Searches for first generation leptoquark singly produced were performed by the HERA experiments. Since the leptoquark single-production cross section depends on its Yukawa coupling, the leptoquark mass limits from HERA are usually displayed in the mass-coupling plane. For leptoquark Yukawa coupling $\lambda = 0.1$, early ZEUS Collaboration bounds on the first-generation leptoquarks range from 248 to 290 GeV, depending on the leptoquark species [64]. The ZEUS Collaboration has recently released a new paper [65] where data corresponding to a luminosity of around $1 \text{ fb}^{-1}$ have been used in the framework of $eeqq$ contact interactions (CI) to set limits on possible high-energy contributions beyond the Standard Model to electron-quark scattering. The analysis of the ep data has been based on simultaneous fits of parton distribution functions including contributions of Contact Interaction (CI) couplings to ep scattering. Several general

CI models and scenarios with heavy leptoquarks were considered. As unambiguous deviations from the SM cannot be established, limits for CI compositeness scales and LQ mass scales were set that are in the TeV range. The H1 Collaboration has a comprehensive summary of searches for first generation leptoquarks using the full data sample collected in ep collisions at HERA (446 $\text{pb}^{-1}$). No evidence of production of leptoquarks was observed in final states with a large transverse momentum electron or large missing transverse momentum. For a coupling strength $\lambda = 0.3$, first generation leptoquarks with masses up to 800 GeV are excluded at 95% C.L. [66].

At the LHC, the CMS collaboration performed searches for single production of first and second generation leptoquarks [67], which is complementary to the HERA searches in the high $\lambda$ region (for coupling strength $\lambda = 1.0$, first generation leptoquarks are excluded for masses up to 1.73 TeV and second generation leptoquark are excluded up to masses of 530 GeV). CMS also recently searched for third generation LQ decaying into $\tau$ and bottom in [68]. Assuming unit Yukawa coupling ($\lambda$), a third generation scalar leptoquark is excluded for masses below 740 GeV. Limits are also set on $\lambda$ of the hypothesized leptoquark as a function of its mass. Above $\lambda = 1.4$, the results provide the best upper limit on the mass of a third-generation scalar leptoquark decaying to a $\tau$ lepton and a bottom quark.

Searches for LQ will continue with more LHC data, particularly in light of the renewed interest in this type of particle to explain violation of lepton flavor universality and other anomalies, which point to explanations laying outside the Standard Model.

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# 95. Magnetic Monopoles

Revised March 2024 by D. Milstead (Stockholm U.) and E.J. Weinberg (Columbia U.).

## 95.1 Theory of magnetic monopoles

The symmetry between electric and magnetic fields in the source-free Maxwell's equations naturally suggests that electric charges might have magnetic counterparts, known as magnetic monopoles. Although the greatest interest has been in the super-massive monopoles that are a firm prediction of all grand unified theories, one cannot exclude the possibility of lighter monopoles.

In either case, the magnetic charge is constrained by a quantization condition first found by Dirac [1]. Consider a monopole with magnetic charge $Q_M$ and a Coulomb magnetic field

$$ \mathbf{B} = \frac{Q_M}{4\pi} \frac{\hat{\mathbf{r}}}{r^2}. \qquad (95.1) $$

Any vector potential A whose curl is equal to B must be singular along some line running from the origin to spatial infinity. This Dirac string singularity could potentially be detected through the extra phase that the wavefunction of a particle with electric charge $Q_E$ would acquire if it moved along a loop encircling the string. For the string to be unobservable, this phase must be a multiple of $2\pi$. Requiring that this be the case for any pair of electric and magnetic charges gives the condition that all charges be integer multiples of minimum charges $Q_E^{\min}$ and $Q_M^{\min}$ obeying

$$ Q_E^{\min} Q_M^{\min} = 2\pi. \qquad (95.2) $$

(For monopoles which also carry an electric charge, called dyons [2], the quantization conditions on their electric charges can be modified. However, the constraints on magnetic charges, as well as those on all purely electric particles, will be unchanged.)

Another way to understand this result is to note that the conserved orbital angular momentum of a point electric charge moving in the field of a magnetic monopole has an additional component, with

$$ \mathbf{L} = m\mathbf{r} \times \mathbf{v} - 4\pi Q_E Q_M \hat{\mathbf{r}}. \qquad (95.3) $$

Requiring the radial component of L to be quantized in half-integer units yields Eq. 95.2.

If there are unbroken gauge symmetries in addition to the U(1) of electromagnetism, the above analysis must be modified [3, 4]. For example, a monopole could have both a U(1) magnetic charge and a color magnetic charge. The latter could combine with the color charge of a quark to give an additional contribution to the phase factor associated with a loop around the Dirac string, so that the U(1) charge could be the Dirac charge $Q_M^D \equiv 2\pi/e$, the result that would be obtained by substituting the electron charge into Eq. (95.2). On the other hand, for monopoles without color-magnetic charge, one would simply insert the quark electric charges into Eq. 95.2 and conclude that $Q_M$ must be a multiple of $6\pi/e$.

The prediction of GUT monopoles arises from the work of 't Hooft [5] and Polyakov [6], who showed that certain spontaneously broken gauge theories have nonsingular classical solutions that lead to magnetic monopoles in the quantum theory. The simplest example occurs in a theory where the vacuum expectation value of a triplet Higgs field $\phi$ breaks an SU(2) gauge symmetry down to the U(1) of electromagnetism and gives a mass $M_V$ to two of the gauge bosons. In order to have finite energy, $\phi$ must approach a vacuum value at infinity. However, there is a continuous family of possible vacua, since the scalar field potential determines only the magnitude $v$ of $\langle \phi \rangle$, but not its orientation in the internal SU(2) space. In the monopole solution, the direction of $\phi$ in internal space is correlated with the position in physical space; i.e., $\phi^a \sim v\hat{\phi}^a$. The stability of the solution follows from the fact that this twisting Higgs field cannot be smoothly deformed to a spatially uniform vacuum configuration. Reducing the energetic cost of the spatial variation of $\phi$ requires a nonzero gauge potential, which turns out to yield the magnetic field corresponding to a charge $Q_M = 4\pi/e$. Numerical solution of the classical field equations shows that the mass of this monopole is

$$ M_{\text{mon}} \sim \frac{4\pi M_V}{e^2}. \qquad (95.4) $$

The essential ingredient here was the fact that the Higgs fields at spatial infinity could be arranged in a topologically nontrivial configuration. A discussion of the general conditions under which this is possible is beyond the scope of this review, so we restrict ourselves to the two phenomenologically most important cases.

The first is the standard electroweak theory, with SU(2) × U(1) broken to U(1). There are no topologically nontrivial configurations of the Higgs field, and hence no topologically stable monopole solutions. Although electroweak scale monopoles are thus not required, there have been claims that they might not be ruled out. For example, there have been a variety of proposals in this direction involving modifications of the Lagrangian.

The second case is when any simple Lie group is broken to a subgroup with a U(1) factor, a case that includes all grand unified theories. Here the spectrum of states must include a topologically stable monopole whose mass is determined by the mass scale of the symmetry breaking that allows nontrivial topology. For example, an SU(5) model with

$$ \mathrm{SU}(5) \xrightarrow{M_X} \mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1) \xrightarrow{M_W} \mathrm{SU}(3) \times \mathrm{U}(1) \qquad (95.5) $$

has a monopole [7] with $Q_M = 2\pi/e$ and mass

$$ M_{\text{mon}} \sim \frac{4\pi M_X}{g^2}, \qquad (95.6) $$

where g is the SU(5) gauge coupling. For a unification scale of $10^{16}$ GeV, these monopoles would have a mass $M_{\text{mon}} \sim 10^{17} - 10^{18}$ GeV.

In theories with several stages of symmetry breaking, monopoles of different mass scales can arise. In an SO(10) theory with

$$ \mathrm{SO}(10) \xrightarrow{M_1} \mathrm{SU}(4) \times \mathrm{SU}(2) \times \mathrm{SU}(2) \xrightarrow{M_2} \mathrm{SU}(3) \times \mathrm{SU}(2) \times \mathrm{U}(1) \qquad (95.7) $$

there is monopole with $Q_M = 2\pi/e$ and mass $\sim 4\pi M_1/g^2$ and a much lighter monopole with $Q_M = 4\pi/e$ and mass $\sim 4\pi M_2/g^2$ [8].

The central core of a GUT monopole contains the fields of the superheavy gauge bosons that mediate baryon number violation, so one might expect that baryon number conservation could be violated in baryon-monopole scattering. The surprising feature, pointed out by Callan [9] and Rubakov [10], is that these processes are not suppressed by powers of the gauge boson mass. Instead, the cross-sections for catalysis processes such as $p + \text{monopole} \rightarrow e^+ + \pi^0 + \text{monopole}$ are essentially geometric; i.e., $\sigma_{\Delta B} \beta \sim 10^{-27} \text{cm}^2$, where $\beta = v/c$. Note, however, that this catalysis is model-dependent and is not even a universal property of all GUT monopoles.

## 95.2 Production and Annihilation

GUT monopoles are far too massive to be produced in any foreseeable accelerator. However, they could have been produced in the early Universe as topological defects arising via the Kibble mechanism [11] in a symmetry-breaking phase transition. Estimates of the initial monopole abundance, and of the degree to which it can be reduced by monopole-antimonopole annihilation, predict a present-day monopole abundance that exceeds by many orders of magnitude the astrophysical and experimental bounds described below [12]. Cosmological inflation and other proposed solutions to this primordial monopole problem generically lead to present-day abundances exponentially smaller than could be plausibly detected, although potentially observable abundances can be obtained in scenarios with carefully tuned parameters.

If monopoles light enough to be produced at colliders exist, one would expect that these could be produced by analogs of the electromagnetic processes that produce pairs of electrically charged particles. Because of the large size of the magnetic charge, this is a strong coupling problem for which perturbation theory cannot be trusted. Indeed, the problem of obtaining reliable quantitative estimates of the production cross-sections remains an open one, on which there is no clear consensus.
## 95.3 Astrophysical and Cosmological Bounds

If there were no galactic magnetic field, one would expect monopoles in the galaxy to have typical velocities of the order of $10^{-3}$c, comparable to the virial velocity in the galaxy (relevant if the monopoles cluster with the galaxy) and the peculiar velocity of the galaxy with respect to the CMB rest frame (relevant if the monopoles are not bound to the galaxy). This situation is modified by the existence of a galactic magnetic field $B \sim 3\mu G$. A monopole with the Dirac charge and mass $M$ would be accelerated by this field to a velocity

$$v_{\text{mag}} \sim \begin{cases} c, & M \lesssim 10^{11} \text{GeV}, \\ 10^{-3} c \left( \frac{10^{17} \text{GeV}}{M} \right)^{1/2}, & M \gtrsim 10^{11} \text{GeV}. \end{cases} \quad (95.8)$$

Accelerating these monopoles drains energy from the magnetic field. Parker [13] obtained an upper bound on the flux of monopoles in the galaxy by requiring that the rate of this energy loss be small compared to the time scale on which the galactic field can be regenerated. With reasonable choices for the astrophysical parameters (see Ref. [14] for details), this Parker bound is

$$F < \begin{cases} 10^{-15} \text{cm}^{-2} \text{sr}^{-1} \text{sec}^{-1}, & M \lesssim 10^{17} \text{GeV}, \\ 10^{-15} \left( \frac{M}{10^{17} \text{GeV}} \right) \text{cm}^{-2} \text{sr}^{-1} \text{sec}^{-1}, & M \gtrsim 10^{17} \text{GeV}. \end{cases} \quad (95.9)$$

Applying similar arguments to an earlier seed field that was the progenitor of the current galactic field leads to a tighter bound [15],

$$F < \left[ \frac{M}{10^{17} \text{GeV}} + (3 \times 10^{-6}) \right] 10^{-16} \text{cm}^{-2} \text{sr}^{-1} \text{sec}^{-1}. \quad (95.10)$$

Considering magnetic fields in galactic clusters gives a bound [16] which, although less secure, is about three orders of magnitude lower than the Parker bound.

A flux bound can also be inferred from the total mass of monopoles in the Universe. If the monopole mass density is a fraction $\Omega_M$ of the critical density, and the monopoles were uniformly distributed throughout the Universe, there would be a monopole flux

$$F_{\text{uniform}} = 1.3 \times 10^{-16} \Omega_M \left( \frac{10^{17} \text{GeV}}{M} \right) \left( \frac{v}{10^{-3}c} \right) \text{cm}^{-2} \text{sr}^{-1} \text{sec}^{-1}. \quad (95.11)$$

If we assume that $\Omega_M \sim 0.1$, this gives a stronger constraint than the Parker bound for $M \sim 10^{15}$ GeV. However, monopoles with masses $\sim 10^{17}$ GeV are not ejected by the galactic field and can be gravitationally bound to the galaxy. In this case their flux within the galaxy is increased by about five orders of magnitude for a given value of $\Omega_M$, and the mass density bound only becomes stronger than the Parker bound for $M \sim 10^{18}$ GeV.

A much more stringent flux bound applies to GUT monopoles that catalyze baryon number violation. The essential idea is that compact astrophysical objects would capture monopoles at a rate proportional to the galactic flux. These monopoles would then catalyze proton decay, with the energy released in the decay leading to an observable increase in the luminosity of the object. A variety of bounds, based on neutron stars [17–21], white dwarfs [22], and Jovian planets [23] have been obtained. These depend in the obvious manner on the catalysis cross section, but also on the details of the astrophysical scenarios; e.g., on how much the accumulated density is reduced by monopole-antimonopole annihilation, and on whether monopoles accumulated in the progenitor star survive its collapse to a white dwarf or neutron star. The bounds obtained in this manner lie in the range

$$F \left( \frac{\sigma \Delta B \beta}{10^{-27} \text{cm}^2} \right) \sim (10^{-18} - 10^{-29}) \text{cm}^{-2} \text{sr}^{-1} \text{sec}^{-1}. \quad (95.12)$$

It is important to remember that not all GUT monopoles catalyze baryon number nonconservation. In particular, the intermediate mass monopoles that arise in some GUTs at later stages

of symmetry-breaking are examples of theoretically motivated monopoles that are exempt from the bound of the above equation.

## 95.4 Searches for Magnetic Monopoles

To date there have been no confirmed observations of exotic particles possessing magnetic charge. Precision measurements of the properties of known particles have led to tight limits on the values of magnetic charge they may possess. Using the induction method (see below), the electron's magnetic charge has been found to be $Q_m^e < 10^{-24} Q_M^D$ [24]. Furthermore, measurements of the anomalous magnetic moment of the muon have been used to place a model dependent lower limit of 120 GeV on the monopole mass [1] [25]. Nevertheless, guided mainly by Dirac's argument and the predicted existence of monopoles from spontaneous symmetry breaking mechanisms, searches have been routinely made for monopoles produced at accelerators, in cosmic rays, and bound in matter [26]. Although the resultant limits from such searches are usually made under the assumption of a particle possessing only magnetic charge, most of the searches are also sensitive to dyons.

## 95.5 Search Techniques

Search strategies are determined by the expected interactions of monopoles as they pass through matter. These would give rise to a number of striking characteristic signatures. Since a complete description of monopole search techniques falls outside of the scope of this minireview, only the most common methods are described below. More comprehensive descriptions of search techniques can be found in Refs. [27, 28].

The induction method exploits the long-range electromagnetic interaction of the monopole with the quantum state of a superconducting ring which would lead to a monopole which passes through such a ring inducing a permanent current. The induction technique typically uses Superconducting Quantum Interference Devices (SQUID) technology for detection and is employed for searches for monopoles in cosmic rays and matter. Another approach is to exploit the electromagnetic energy loss of monopoles. Monopoles with Dirac charge would typically lose energy at a rate which is several thousand times larger than that expected from particles possessing the elementary electric charge. Consequently, scintillators, gas chambers and nuclear track detectors (NTDs) have been used in cosmic ray and collider experiments. A further approach, which has been used at colliders, is to search for particles describing a non-helical path in a uniform magnetic field.

### 95.5.1 Searches for Monopoles Bound in Matter

Monopoles have been sought in a range of bulk materials which it is assumed would have absorbed incident cosmic ray monopoles over a long exposure time of order million years. Materials which have been studied include moon rock, meteorites, manganese modules, and sea water [29, 30]. A stringent upper limit on the monopoles per nucleon ratio of $\sim 10^{-29}$ has been obtained [30].

### 95.5.2 Searches in Cosmic Rays

Direct searches for monopoles in cosmic rays refer to those experiments in which the passage of the monopole is measured by an active detector. Searches made assuming a catalysis processes in which GUT monopoles could induce nucleon decay are discussed in the next section. To interpret the results of the non-catalysis searches, the cross section for the catalysis process is typically either set to zero [31] or assigned a modest value (1mb) [32].

Although early cosmic ray searches using the induction technique [33] and NTDs [34] observed monopole candidates, none of these apparent observations have been confirmed. Recent experiments have typically employed large scale detectors. The MACRO experiment at the Gran Sasso underground laboratory comprised three different types of detector: liquid scintillator, limited stream tubes, and NTDs, which provided a total acceptance of $\sim 10000\text{m}^2$ for an isotropic flux. As shown in Fig. 95.1, this experiment has so far provided the most extensive $\beta$-dependent flux limits for GUT monopoles with Dirac charge [32]. Also shown

<footnote n="1">¹Where no ambiguity is likely to arise, a reference to a monopole implies a particle possessing Dirac charge.</footnote>
<figure><img src="image_393.png" /><figcaption>**Figure 95.1:** Left: upper flux limits for GUT monopoles as a function of $\beta$. Right: upper flux limits for monopoles as a function of monopole mass for $\beta > 0.05$.</figcaption></figure>

are limits from an experiment at the OHYA mine in Japan [31], which used a 2000m² array of NTDs, and from the IceCube [35,36] and Antares [37] experiments which each employ the Cerenkov method.

In Fig. 95.1, upper flux limits are also shown as a function of monopole mass for monopole speed $\beta > 0.05$. In addition to MACRO and OYHA flux limits, results from the SLIM [38] high-altitude experiment are shown. The SLIM experiment provided a good sensitivity to intermediate mass monopoles ($10^5 \lesssim M \lesssim 10^{12}$ GeV).

In addition to the results shown in Fig. 95.1, the NoVA experiment [39] has recently set an upper limit on monopole flux of $2 \times 10^{-14} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$ for speeds $6 \times 10^{-4} < \beta < 10^{-3}$ for masses greater than 5 × 10⁸ GeV. Stringent constraints on the flux of ultra-relativistic monopoles have been obtained at the Pierre Auger Observatory [40] which was sensitive to monopoles with $\gamma$ values ranging from $10^9$ to $10^{12}$, leading to flux limits in the range $10^{-15} - 2.5 \times 10^{-21} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$. The RICE [41] and ANITA-II experiments [42] at the South Pole have also sought ultra-relativistic monopoles with $\gamma$ values of $10^7 \lesssim \gamma \lesssim 10^{12}$ and $10^9 \lesssim \gamma \lesssim 10^{13}$, respectively, and which produced flux limits as low as $2.5 \times 10^{-21} \text{ cm}^{-2}\text{s}^{-1}\text{sr}^{-1}$.

### 95.5.3 Searches via the Catalysis of Nucleon-Decay

Searches have been performed for evidence of the catalysed decay of a nucleon by a monopole, as predicted by the Callan-Rubakov mechanism. The searches are thus sensitive to the assumed value of the catalysis decay cross section. Searches have been made with the Soudan [43] and Macro [44] experiments, using tracking detectors. Searches at IMB [45], the underwater Lake Baikal experiment [46,47] and the IceCube experiment [48] which exploit the Cerenkov effect have also been made. The resulting $\beta$-dependent flux limits from these experiments typically vary between $\sim 10^{-18}$ and $\sim 10^{-14} \text{ cm}^{-2}\text{s}^{-1}\text{s}^{-1}$. A search for low energy neutrinos (assumed to be produced from induced proton decay in the sun) was made at Super-Kamiokande [49]. A model-and $\beta$-dependent limit of $6.3 \times 10^{-24} (\frac{\beta}{10^{-3}})^2 \text{ cm}^{-2}\text{s}^{-1}\text{s}^{-1}$ was obtained.

### 95.5.4 Searches at Colliders

Searches have been performed at hadron-hadron, electron-positron and lepton-hadron experiments. Collider searches can be broadly classed as being direct or indirect. In a direct search, evidence of the passage of a monopole through material, such as a charged particle track, is sought. In indirect searches, virtual monopole processes are assumed to influence the production rates of certain final states.

#### 95.5.4.1 Direct Searches at Colliders

Collider experiments typically express their results in terms of upper limits on a production cross section and/or monopole mass. To calculate these limits, ansatzes are used to model the kinematics of monopole-antimonopole pair production processes since perturbative field theory cannot be used to calculate the rate and kinematic properties of produced monopoles. Limits therefore suffer from a degree of model-dependence, implying that a comparison between the results of different experiments can be problematic, in particular when this concerns excluded mass regions. A conservative approach with as little model-dependence as possible is thus to present representative values of the upper cross-section limits as a function of the centre-of-mass energy of the collisions, as shown in Fig. 95.2 for recent results from high energy colliders.

<figure><img src="image_394.png" /><figcaption>**Figure 95.2:** Upper limits on the production cross sections of monopoles from various collider-based experiments. Results from lepton-hadron (triangle), electron-positron (filled circle), proton-antiproton (star) and proton-proton (filled square) experiments are shown.</figcaption></figure>

Searches for monopoles produced at the highest available energies in hadron-hadron collisions were made in pp collisions at the LHC by the ATLAS [50–53] and MoEDAL [54–57] experiments. ATLAS looked for highly ionising particles leaving a characteristic energy deposition profile in the tracker and calorimeter. MOEDAL used a NTD to tag highly ionising particles and the induction method to search for stopped monopoles. The charge-dependent mass limits extend up to around 4 TeV. The ATLAS experiment has considered hypotheses of monopoles with charges between $0.5 Q_M^D$ and $2Q_M^D$ while MoEDAL has quoted limits for monopoles in the charge range $Q_M^D$ to $5Q_M^D$. Models considered include monopole-pair production via photon fusion along with,
as is commonly used in hadron-hadron collisions, Drell-Yan processes [58]. MoEDAL has also looked for monopole produced via the Schwinger mechanism in the intense magnetic field created in PbPb collisions [57]. Tevatron searches have also been carried out by the CDF [59] and E882 [60] experiments. The CDF experiment used a dedicated time-of-flight system whereas the E882 experiment employed the induction technique to search for stopped monopoles in discarded detector material which had been part of the CDF and D0 detectors using periods of luminosity. Earlier searches at the Tevatron, such as [61], used NTDs and were based on comparatively modest amounts of integrated luminosity. Lower energy hadron-hadron experiments have employed a variety of search techniques including plastic track detectors [62] and searches for trapped monopoles [63].

The only LEP-2 search was made by OPAL [64] which quoted cross section limits for the production of monopoles possessing masses up to around 103 GeV. At LEP-1, searches were made with NTDs deployed around an interaction region. This allowed a range of charges to be sought for masses up to ~ 45 GeV. The L6-MODAL experiment [65] gave limits for monopoles with charges in the range $0.9Q_M^D$ and $3.6Q_M^D$, whilst an earlier search by the MODAL experiment was sensitive to monopoles with charges as low as $0.1Q_M^D$ [66]. The deployment of NTDs around the beam interaction point was also used at earlier $e^+e^-$ colliders such as KEK [67] and PETRA [68]. Searches at $e^+e^-$ facilities have also been made for particles following non-helical trajectories [69, 70].

There has so far been one search for monopole production in lepton-hadron scattering. Using the induction method, monopoles were sought which could have stopped in the aluminium beampipe which had been used by the H1 experiment at HERA [71]. Cross section limits were set for monopoles with charges in the range $Q_M^D - 6Q_M^D$ for masses up to around 140 GeV.

### 95.5.4.2 Indirect Searches at Colliders

It has been proposed that virtual monopoles can mediate processes which give rise to multi-photon final-states [72,73]. Photon-based searches were made by the D0 [74] and L3 [75] experiments. The D0 work led to spin-dependent lower mass limits of between 610 and 1580 GeV, while L3 reported a lower mass limit of 510 GeV. However, it should be stressed that uncertainties on the theoretical calculations which were used to derive these limits are difficult to estimate.

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INDEX
<figure><img src="image_395.png" /></figure>
Index

a meson resonances

<table>
  <tbody>
    <tr>
      <td>a<sub>0</sub>(980)</td>
      <td>34, 1444</td>
    </tr>
    <tr>
      <td>a<sub>0</sub>(1710)</td>
      <td>1509</td>
    </tr>
    <tr>
      <td>a<sub>0</sub>(1450)</td>
      <td>36, 1478</td>
    </tr>
    <tr>
      <td>a<sub>0</sub>(1950)</td>
      <td>1520</td>
    </tr>
    <tr>
      <td>a<sub>1</sub>(1260)</td>
      <td>35, 1455</td>
    </tr>
    <tr>
      <td>a<sub>1</sub>(1640)</td>
      <td>37, 1494</td>
    </tr>
    <tr>
      <td>a<sub>2</sub>(1320)</td>
      <td>35, 1465</td>
    </tr>
    <tr>
      <td>a<sub>2</sub>(1700)</td>
      <td>38, 1508</td>
    </tr>
    <tr>
      <td>a<sub>4</sub>(1970) [was a<sub>4</sub>(2040)]</td>
      <td>39, 1521</td>
    </tr>
    <tr>
      <td>A-parameter</td>
      <td>1041</td>
    </tr>
    <tr>
      <td>ABC, approximate Bayesian computation</td>
      <td>719</td>
    </tr>
    <tr>
      <td>Absolute monochromatic magnitude</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Accelerating Universe evidence</td>
      <td>486</td>
    </tr>
    <tr>
      <td>Accelerator parameters</td>
      <td>569</td>
    </tr>
    <tr>
      <td>Accelerator parameters for neutrino beam lines</td>
      <td>574</td>
    </tr>
    <tr>
      <td>Accelerator-based ν detectors</td>
      <td>635</td>
    </tr>
    <tr>
      <td>Accelerator-induced radioactivity</td>
      <td>681</td>
    </tr>
    <tr>
      <td>Acceptance-rejection method (Von Neumann)</td>
      <td>748</td>
    </tr>
    <tr>
      <td>Acoustic oscillations, baryon</td>
      <td>493</td>
    </tr>
    <tr>
      <td>Activation function</td>
      <td>724</td>
    </tr>
    <tr>
      <td>Active learning</td>
      <td>718, 719</td>
    </tr>
    <tr>
      <td>Activity, unit of</td>
      <td>679</td>
    </tr>
    <tr>
      <td>AD, automatic differentiation</td>
      <td>735</td>
    </tr>
    <tr>
      <td>AdaBoost, adaptive boost</td>
      <td>724</td>
    </tr>
    <tr>
      <td>ADAM, Adaptive Momentum Estimation</td>
      <td>735</td>
    </tr>
    <tr>
      <td>AdS, anti-de Sitter spacetime</td>
      <td>1021</td>
    </tr>
    <tr>
      <td>AdS/CFT</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">correspondence</td>
      <td>1021, 1105</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">dictionary</td>
      <td>1025, 1105</td>
    </tr>
    <tr>
      <td>Advanced acceleration schemes</td>
      <td>567</td>
    </tr>
    <tr>
      <td>Age of the Universe</td>
      <td>139, 446</td>
    </tr>
    <tr>
      <td>Air shower extensive, EAS</td>
      <td>649</td>
    </tr>
    <tr>
      <td>Aleatoric uncertainty</td>
      <td>739</td>
    </tr>
    <tr>
      <td>Algorithms for Monte Carlo</td>
      <td>749</td>
    </tr>
    <tr>
      <td>α<sub>s</sub>, QCD coupling constant</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Amplitudes, Lorentz invariant</td>
      <td>777</td>
    </tr>
    <tr>
      <td>AMS, approximate median significance</td>
      <td>739</td>
    </tr>
    <tr>
      <td>AMSB, anomaly-mediated SUSY breaking</td>
      <td>1040</td>
    </tr>
    <tr>
      <td>Angular-diameter distance, d<sub>A</sub></td>
      <td>446</td>
    </tr>
    <tr>
      <td>Anisotropy of CMB</td>
      <td>486, 524</td>
    </tr>
    <tr>
      <td>Annihilating dark matter</td>
      <td>532</td>
    </tr>
    <tr>
      <td>Anomalous dimension quark mass (MS)</td>
      <td>834</td>
    </tr>
    <tr>
      <td>Anomaly detection</td>
      <td>718, 741</td>
    </tr>
    <tr>
      <td>Anomaly-mediated SUSY breaking, AMSB</td>
      <td>1040</td>
    </tr>
    <tr>
      <td>Anthropic approach</td>
      <td>449</td>
    </tr>
    <tr>
      <td>Anthropic axion window</td>
      <td>1086</td>
    </tr>
    <tr>
      <td>Antineutrino flux from reactor</td>
      <td>308</td>
    </tr>
    <tr>
      <td>Antineutrinos, right-handed</td>
      <td>929</td>
    </tr>
    <tr>
      <td>Astronomical unit</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Astrophysics</td>
      <td>499</td>
    </tr>
    <tr>
      <td>Asymptotic freedom</td>
      <td>153</td>
    </tr>
    <tr>
      <td>Asymptotics, total hadronic cross sections behaviour</td>
      <td>423</td>
    </tr>
    <tr>
      <td>ATLAS – Toroidal LHC Apparatus, LHC</td>
      <td>218</td>
    </tr>
    <tr>
      <td>Atmospheric</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Cherenkov detectors</td>
      <td>651</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">fluorescence detector</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Fly's Eye</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">HiRes (high resolution) Fly's Eye</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Pierre Auger observatory</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Telescope Array</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">neutrino flux</td>
      <td>303</td>
    </tr>
    <tr>
      <td>Atmospheric pressure</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Atomic</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">and nuclear properties of materials, table</td>
      <td>144</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">mass unit</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Atomic weights of elements</td>
      <td>131</td>
    </tr>
    <tr>
      <td>Attention</td>
      <td>725, 729</td>
    </tr>
    <tr>
      <td>Attenuation length for photons</td>
      <td>583</td>
    </tr>
    <tr>
      <td>Auger observatory</td>
      <td>649, 1140</td>
    </tr>
    <tr>
      <td>Authors and consultants</td>
      <td>12</td>
    </tr>
    <tr>
      <td>Auto-encoder</td>
      <td>716, 718</td>
    </tr>
    <tr>
      <td>Averaging of data</td>
      <td>15</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>Averaging, unconstrained</td>
      <td>16</td>
    </tr>
    <tr>
      <td>Avogadro constant</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Axial vector mesons l = 1; 1<sup>++</sup> or 1<sup>+-</sup></td>
      <td>323</td>
    </tr>
    <tr>
      <td>Axial-vector mesons</td>
      <td></td>
    </tr>
    <tr>
      <td>K<sub>1A</sub>-K<sub>1B</sub> mixing</td>
      <td>874, 879</td>
    </tr>
    <tr>
      <td>f<sub>1</sub>(1285), f<sub>1</sub>(1420), f<sub>1</sub>(1510)</td>
      <td>879, 880</td>
    </tr>
    <tr>
      <td>Axion as dark matter</td>
      <td>502, 1079</td>
    </tr>
    <tr>
      <td>Axion searches</td>
      <td>1079</td>
    </tr>
    <tr>
      <td>Axion stars</td>
      <td>1087</td>
    </tr>
    <tr>
      <td>Axion-like particles (ALP)</td>
      <td>1079</td>
    </tr>
    <tr>
      <td>Axion-photon mixing</td>
      <td>532</td>
    </tr>
    <tr>
      <td>Axions (A<sup>0</sup>) and other very light bosons searches</td>
      <td>27, 1271</td>
    </tr>
    <tr>
      <td>B&#773;B mixing</td>
      <td>955</td>
    </tr>
    <tr>
      <td>b&#773;b mesons</td>
      <td>83, 2023</td>
    </tr>
    <tr>
      <td>B decay, CP violation in</td>
      <td>287, 952</td>
    </tr>
    <tr>
      <td>B decays polarization, note</td>
      <td>951</td>
    </tr>
    <tr>
      <td>B mesons</td>
      <td></td>
    </tr>
    <tr>
      <td>B<sub>sJ</sub>(6063)<sup>0</sup></td>
      <td>1892</td>
    </tr>
    <tr>
      <td>B<sub>sJ</sub>(6114)<sup>0</sup></td>
      <td>1892</td>
    </tr>
    <tr>
      <td>B<sup>*</sup></td>
      <td>69, 1860</td>
    </tr>
    <tr>
      <td>B<sup>0</sup></td>
      <td>61, 1751</td>
    </tr>
    <tr>
      <td>B<sup>&pm;</sup></td>
      <td>54, 1682</td>
    </tr>
    <tr>
      <td>B<sup>&pm;</sup>/B<sup>0</sup> admixture</td>
      <td>67, 1828</td>
    </tr>
    <tr>
      <td>B<sup>&pm;</sup>/B<sup>0</sup>/B<sup>s</sup>/B-baryon admixture</td>
      <td>68, 1851</td>
    </tr>
    <tr>
      <td>B<sub>1</sub>(5721)</td>
      <td>69, 1861</td>
    </tr>
    <tr>
      <td>B<sub>s</sub><sup>*</sup>(5747)</td>
      <td>69, 1862</td>
    </tr>
    <tr>
      <td>B<sub>J</sub><sup>*</sup>(5732) [was B<sup>**</sup>]</td>
      <td>1861</td>
    </tr>
    <tr>
      <td>B<sub>J</sub>(5840)</td>
      <td>1862</td>
    </tr>
    <tr>
      <td>B<sub>J</sub>(5970)</td>
      <td>69, 1863</td>
    </tr>
    <tr>
      <td>B<sub>c</sub><sup>+</sup></td>
      <td>72, 1893</td>
    </tr>
    <tr>
      <td>B<sub>c</sub>(2S)<sup>&pm;</sup></td>
      <td>72, 1897</td>
    </tr>
    <tr>
      <td>B<sub>s1</sub>(5830)<sup>0</sup></td>
      <td>71, 1890</td>
    </tr>
    <tr>
      <td>B<sub>s2</sub>(5840)<sup>0</sup></td>
      <td>71, 1891</td>
    </tr>
    <tr>
      <td>B<sub>sJ</sub>(5850)</td>
      <td>1891</td>
    </tr>
    <tr>
      <td>B<sub>sJ</sub>(6063)<sup>0</sup></td>
      <td>1892</td>
    </tr>
    <tr>
      <td>B<sub>sJ</sub>(6114)<sup>0</sup></td>
      <td>1892</td>
    </tr>
    <tr>
      <td>B<sub>s</sub><sup>*</sup></td>
      <td>71, 1890</td>
    </tr>
    <tr>
      <td>B<sub>s</sub><sup>0</sup></td>
      <td>70, 1865</td>
    </tr>
    <tr>
      <td>b' quark (4<sup>th</sup> generation), searches for</td>
      <td>32, 859, 1398</td>
    </tr>
    <tr>
      <td>b-baryon admixture</td>
      <td>111, 2283</td>
    </tr>
    <tr>
      <td>b-flavored Hadrons, production and decay</td>
      <td>940</td>
    </tr>
    <tr>
      <td>b-quark fragmentation</td>
      <td>397, 858</td>
    </tr>
    <tr>
      <td>b<sub>1</sub>(1235) meson</td>
      <td>35, 1454</td>
    </tr>
    <tr>
      <td>Background</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cosmic microwave, CMB</td>
      <td>524</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cosmic ray radiation</td>
      <td>680</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">relic cosmic neutrino</td>
      <td>491</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">relic light gravitons</td>
      <td>1022</td>
    </tr>
    <tr>
      <td>Background cosmology parameters</td>
      <td>526</td>
    </tr>
    <tr>
      <td>Backpropagation</td>
      <td>719, 735</td>
    </tr>
    <tr>
      <td>Bagging, bootstrap aggregating</td>
      <td>723</td>
    </tr>
    <tr>
      <td>Balitsky-Fadin-Kuraev-Lipatov (BFKL) limit</td>
      <td>156</td>
    </tr>
    <tr>
      <td>Barkas correction</td>
      <td>578</td>
    </tr>
    <tr>
      <td>Baryogenesis</td>
      <td>450</td>
    </tr>
    <tr>
      <td>Baryon</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">acoustic oscillations</td>
      <td>461, 486, 493</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">decay parameters, note on</td>
      <td>1001</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">density of the Universe</td>
      <td>138</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Hyperon nonleptonic decays</td>
      <td>1001</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">magnetic moments</td>
      <td>332, 337</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">number conservation</td>
      <td>120</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">oscillation spectroscopic survey</td>
      <td>486</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">resonances, naming scheme</td>
      <td>1002</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">resonances, SU(3) classification of</td>
      <td>327</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">semileptonic decays</td>
      <td>1001</td>
    </tr>
    <tr>
      <td>Baryon quick reference table</td>
      <td>89</td>
    </tr>
    <tr>
      <td>Baryon-to-photon ratio</td>
      <td>138, 476</td>
    </tr>
    <tr>
      <td>Baryonia</td>
      <td>874, 881</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">ρ(1900)</td>
      <td>879</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">f<sub>2</sub>(1565)</td>
      <td>881</td>
    </tr>
    <tr>
      <td>Baryons in quark model</td>
      <td>327</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>Batch</td>
      <td>735, 737</td>
    </tr>
    <tr>
      <td>Bayes' theorem</td>
      <td>466, 689</td>
    </tr>
    <tr>
      <td>Bayesian</td>
      <td></td>
    </tr>
    <tr>
      <td>approach</td>
      <td>698</td>
    </tr>
    <tr>
      <td>intervals</td>
      <td>704</td>
    </tr>
    <tr>
      <td>method</td>
      <td>694</td>
    </tr>
    <tr>
      <td>statistics</td>
      <td>704</td>
    </tr>
    <tr>
      <td>Bayesian machine learning</td>
      <td>740</td>
    </tr>
    <tr>
      <td>Bayesian optimization</td>
      <td>717, 722</td>
    </tr>
    <tr>
      <td>BBN, Big-Bang nucleosynthesis</td>
      <td>474</td>
    </tr>
    <tr>
      <td>Beam collimation</td>
      <td>561, 566</td>
    </tr>
    <tr>
      <td>Beam cooling</td>
      <td>561</td>
    </tr>
    <tr>
      <td>Beam dynamics</td>
      <td>559</td>
    </tr>
    <tr>
      <td>Beam momentum, c.m. energy and momentum vs</td>
      <td>777</td>
    </tr>
    <tr>
      <td>Beam-beam interaction</td>
      <td>562</td>
    </tr>
    <tr>
      <td>Beamstrahlung</td>
      <td>562, 564</td>
    </tr>
    <tr>
      <td>Becquerel, unit of radioactivity</td>
      <td>679</td>
    </tr>
    <tr>
      <td>BEPC</td>
      <td>569</td>
    </tr>
    <tr>
      <td>BEPC-II</td>
      <td>569</td>
    </tr>
    <tr>
      <td>β function of QCD</td>
      <td>153</td>
    </tr>
    <tr>
      <td>Beta distribution</td>
      <td>692, 750</td>
    </tr>
    <tr>
      <td>Beta function</td>
      <td>560</td>
    </tr>
    <tr>
      <td>β-rays, from radioactive sources</td>
      <td>685</td>
    </tr>
    <tr>
      <td>Betatron tune</td>
      <td>560</td>
    </tr>
    <tr>
      <td>Bethe equation</td>
      <td>576</td>
    </tr>
    <tr>
      <td>Beyond the general relativity physics</td>
      <td>532</td>
    </tr>
    <tr>
      <td>Beyond the SM physics, BSM</td>
      <td>270, 478, 502, 755</td>
    </tr>
    <tr>
      <td>Bhabha cross section</td>
      <td>581</td>
    </tr>
    <tr>
      <td>Bi-directional RNN</td>
      <td>729</td>
    </tr>
    <tr>
      <td>Bias of an estimator</td>
      <td>694</td>
    </tr>
    <tr>
      <td>Big-Bang cosmology</td>
      <td>444, 457</td>
    </tr>
    <tr>
      <td>Big-Bang nucleosynthesis (BBN)</td>
      <td>474</td>
    </tr>
    <tr>
      <td>Binary classification</td>
      <td>714, 715, 721</td>
    </tr>
    <tr>
      <td>Binary pulsars, strong-self-gravity</td>
      <td>438</td>
    </tr>
    <tr>
      <td>Bino</td>
      <td>1042</td>
    </tr>
    <tr>
      <td>Binomial distribution</td>
      <td>692, 749</td>
    </tr>
    <tr>
      <td>Biological damage from radiation</td>
      <td>679</td>
    </tr>
    <tr>
      <td>Birks' law</td>
      <td>595</td>
    </tr>
    <tr>
      <td>Black holes</td>
      <td></td>
    </tr>
    <tr>
      <td>binary</td>
      <td>438</td>
    </tr>
    <tr>
      <td>coalescing</td>
      <td>435</td>
    </tr>
    <tr>
      <td>horizon</td>
      <td>433</td>
    </tr>
    <tr>
      <td>microscopic, searches</td>
      <td>1023</td>
    </tr>
    <tr>
      <td>production</td>
      <td>1022</td>
    </tr>
    <tr>
      <td>strong gravitational fields</td>
      <td>432</td>
    </tr>
    <tr>
      <td>supermassive</td>
      <td>438</td>
    </tr>
    <tr>
      <td>Bloch correction</td>
      <td>578</td>
    </tr>
    <tr>
      <td>BMA, Bayesian model averaging</td>
      <td>740</td>
    </tr>
    <tr>
      <td>BN, batch normalization</td>
      <td>726, 736</td>
    </tr>
    <tr>
      <td>Bohr magneton</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Bohr radius</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Boiling points of cryogenic gases, table</td>
      <td>144</td>
    </tr>
    <tr>
      <td>Boltzmann constant k</td>
      <td>137, 138</td>
    </tr>
    <tr>
      <td>Booklet, Particle Physics, how to get</td>
      <td>11</td>
    </tr>
    <tr>
      <td>Boosting</td>
      <td>723</td>
    </tr>
    <tr>
      <td>Bose-Einstein correlations</td>
      <td>418, 760, 815</td>
    </tr>
    <tr>
      <td>Bosons, Nambu-Goldstone composite</td>
      <td>1104</td>
    </tr>
    <tr>
      <td>BOSS, baryon oscillation spectroscopic survey</td>
      <td>486</td>
    </tr>
    <tr>
      <td>Bottleneck</td>
      <td>716, 732</td>
    </tr>
    <tr>
      <td>Bottom baryons</td>
      <td>108, 2263</td>
    </tr>
    <tr>
      <td>Bottom mesons</td>
      <td></td>
    </tr>
    <tr>
      <td>experimental rate measurements</td>
      <td>934</td>
    </tr>
    <tr>
      <td>production and decay</td>
      <td>940</td>
    </tr>
    <tr>
      <td>theoretical decay-constant calculations</td>
      <td>934</td>
    </tr>
    <tr>
      <td>Bottom mesons (B, B*)</td>
      <td>54, 1682</td>
    </tr>
    <tr>
      <td>Bottom, Charmed mesons (B<sub>c</sub>, B<sub>c</sub>(2S))</td>
      <td>72, 1893</td>
    </tr>
    <tr>
      <td>Bottom, Strange mesons (B<sub>s</sub>, B<sub>s</sub><sup>*</sup>, X)</td>
      <td>70, 1865</td>
    </tr>
    <tr>
      <td>Bottom-changing neutral currents, tests for</td>
      <td>121</td>
    </tr>
    <tr>
      <td>Bottomonium</td>
      <td>83, 2023</td>
    </tr>
    <tr>
      <td>Bragg additivity</td>
      <td>580</td>
    </tr>
    <tr>
      <td>Brane</td>
      <td>478, 1022, 1040, 1122</td>
    </tr>
    <tr>
      <td>Breit-Wigner distribution</td>
      <td>750</td>
    </tr>
    <tr>
      <td>Bremsstrahlung</td>
      <td></td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>at very high energies</td>
      <td>584</td>
    </tr>
    <tr>
      <td>by e<sup>±</sup></td>
      <td>582</td>
    </tr>
    <tr>
      <td>by muons</td>
      <td>586</td>
    </tr>
    <tr>
      <td>B<sub>s</sub><sup>0</sup> decay, CP violation in</td>
      <td>287</td>
    </tr>
    <tr>
      <td>BSM, beyond Standard Model</td>
      <td>502</td>
    </tr>
    <tr>
      <td>Bubble chambers</td>
      <td>635</td>
    </tr>
    <tr>
      <td>Bubble Universes</td>
      <td>449</td>
    </tr>
    <tr>
      <td>c<span style="text-decoration: overline;">c</span> mesons (including possibly non-q<span style="text-decoration: overline;">q</span> states)</td>
      <td>72, 1898</td>
    </tr>
    <tr>
      <td>C (charge conjugation), tests of conservation</td>
      <td>114</td>
    </tr>
    <tr>
      <td>c-quark fragmentation</td>
      <td>397</td>
    </tr>
    <tr>
      <td>Cabibbo angle</td>
      <td>904</td>
    </tr>
    <tr>
      <td>Calorimeter</td>
      <td></td>
    </tr>
    <tr>
      <td>electromagnetic (ECAL)</td>
      <td>627</td>
    </tr>
    <tr>
      <td>hadronic (HCAL)</td>
      <td>627</td>
    </tr>
    <tr>
      <td>homogeneous</td>
      <td>627</td>
    </tr>
    <tr>
      <td>sampling</td>
      <td>627</td>
    </tr>
    <tr>
      <td>CBR - Cosmic background radiation (see CMB)</td>
      <td>524</td>
    </tr>
    <tr>
      <td>CDM, cold dark matter</td>
      <td>499</td>
    </tr>
    <tr>
      <td>Central limit theorem</td>
      <td>691</td>
    </tr>
    <tr>
      <td>CEPC</td>
      <td>564</td>
    </tr>
    <tr>
      <td>Cepheid variable stars</td>
      <td>485</td>
    </tr>
    <tr>
      <td>CESR (Cornell)</td>
      <td>570</td>
    </tr>
    <tr>
      <td>CESR-C (Cornell)</td>
      <td>570</td>
    </tr>
    <tr>
      <td>CFT, 4d conformal field theory</td>
      <td>1025</td>
    </tr>
    <tr>
      <td>Chandrasekhar mass</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Change of random variables</td>
      <td>690</td>
    </tr>
    <tr>
      <td>Channels</td>
      <td>720, 725, 737</td>
    </tr>
    <tr>
      <td>Characteristic functions</td>
      <td>690</td>
    </tr>
    <tr>
      <td>Charge conjugation (C) conservation</td>
      <td>114</td>
    </tr>
    <tr>
      <td>Charge conjugation of q<span style="text-decoration: overline;">q</span> states</td>
      <td>323</td>
    </tr>
    <tr>
      <td>Charge conservation</td>
      <td>117</td>
    </tr>
    <tr>
      <td>Charged Higgs bosons (H<sup>±</sup> and H<sup>±±</sup>) searches</td>
      <td>27, 1248</td>
    </tr>
    <tr>
      <td>Chargino mass limits</td>
      <td>1065</td>
    </tr>
    <tr>
      <td>Charginos</td>
      <td>1042</td>
    </tr>
    <tr>
      <td>Charm decays, CP violation in</td>
      <td>285</td>
    </tr>
    <tr>
      <td>Charm mixing and CP violation</td>
      <td>913</td>
    </tr>
    <tr>
      <td>Charm-changing neutral currents, tests for</td>
      <td>121</td>
    </tr>
    <tr>
      <td>Charmed baryons (Λ<sub>c</sub>, Σ<sub>c</sub>, Ξ<sub>c</sub>, Ω<sub>c</sub><sup>0</sup>)</td>
      <td>103, 2234</td>
    </tr>
    <tr>
      <td>Charmed baryons, note on</td>
      <td>103, 2234</td>
    </tr>
    <tr>
      <td>Charmed mesons</td>
      <td></td>
    </tr>
    <tr>
      <td>experimental rate measurements</td>
      <td>932</td>
    </tr>
    <tr>
      <td>theoretical decay-constant calculations</td>
      <td>933</td>
    </tr>
    <tr>
      <td>Charmed mesons (D, D<sup>*</sup>, D<sub>J</sub>)</td>
      <td>43, 1592</td>
    </tr>
    <tr>
      <td>Charmed, Strange mesons (D<sub>s</sub>, D<sub>s</sub><sup>*</sup>, D<sub>sJ</sub>, X)</td>
      <td>50, 1657</td>
    </tr>
    <tr>
      <td>Chemical potential</td>
      <td>360, 447</td>
    </tr>
    <tr>
      <td>Chemical potential, neutrino</td>
      <td>532</td>
    </tr>
    <tr>
      <td>Cherenkov detectors</td>
      <td>599</td>
    </tr>
    <tr>
      <td>at accelerators</td>
      <td></td>
    </tr>
    <tr>
      <td>differential</td>
      <td>599</td>
    </tr>
    <tr>
      <td>ring imaging</td>
      <td>599</td>
    </tr>
    <tr>
      <td>threshold</td>
      <td>599</td>
    </tr>
    <tr>
      <td>tracking</td>
      <td>598</td>
    </tr>
    <tr>
      <td>electromagnetic calorimeters</td>
      <td>598</td>
    </tr>
    <tr>
      <td>fast paticle counter</td>
      <td>598</td>
    </tr>
    <tr>
      <td>nonaccelerator</td>
      <td></td>
    </tr>
    <tr>
      <td>atmospheric</td>
      <td>651</td>
    </tr>
    <tr>
      <td>deep underground</td>
      <td>652</td>
    </tr>
    <tr>
      <td>particle identification PID</td>
      <td>598</td>
    </tr>
    <tr>
      <td>Cherenkov radiation</td>
      <td>587</td>
    </tr>
    <tr>
      <td>χ<sup>2</sup> distribution</td>
      <td>691, 749</td>
    </tr>
    <tr>
      <td>χ<sub>b</sub> and χ<sub>c</sub> mesons</td>
      <td></td>
    </tr>
    <tr>
      <td>χ<sub>b0</sub>(1P)</td>
      <td>85, 2031</td>
    </tr>
    <tr>
      <td>χ<sub>b0</sub>(2P)</td>
      <td>86, 2043</td>
    </tr>
    <tr>
      <td>χ<sub>b1</sub>(1P)</td>
      <td>85, 2033</td>
    </tr>
    <tr>
      <td>χ<sub>b1</sub>(2P)</td>
      <td>86, 2045</td>
    </tr>
    <tr>
      <td>χ<sub>b1</sub>(3P)</td>
      <td>87, 2053</td>
    </tr>
    <tr>
      <td>χ<sub>b2</sub>(1P)</td>
      <td>85, 2035</td>
    </tr>
    <tr>
      <td>χ<sub>b2</sub>(2P)</td>
      <td>87, 2047</td>
    </tr>
    <tr>
      <td>χ<sub>b2</sub>(3P)</td>
      <td>87, 2053</td>
    </tr>
    <tr>
      <td>χ<sub>c0</sub>(1P)</td>
      <td>75, 1935</td>
    </tr>
    <tr>
      <td>χ<sub>c0</sub>(3860)</td>
      <td>1996</td>
    </tr>
    <tr>
      <td>χ<sub>c0</sub>(3915) [was X(3915)]</td>
      <td>81, 2000</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>χ<sub>c0</sub>(4500) [was X(4500)]</td>
      <td>2019</td>
    </tr>
    <tr>
      <td>χ<sub>c0</sub>(4700) [was X(4700)]</td>
      <td>2022</td>
    </tr>
    <tr>
      <td>χ<sub>c1</sub>(1P)</td>
      <td>76, 1945</td>
    </tr>
    <tr>
      <td>χ<sub>c1</sub>(3872) [aka X(3872)]</td>
      <td>81, 1996</td>
    </tr>
    <tr>
      <td>χ<sub>c1</sub>(4140) [was X(4140)]</td>
      <td>82, 2005</td>
    </tr>
    <tr>
      <td>χ<sub>c1</sub>(4274) [was X(4274)]</td>
      <td>83, 2014</td>
    </tr>
    <tr>
      <td>χ<sub>c1</sub>(4685)</td>
      <td>2022</td>
    </tr>
    <tr>
      <td>χ<sub>c2</sub>(1P)</td>
      <td>77, 1956</td>
    </tr>
    <tr>
      <td>χ<sub>c2</sub>(3930)</td>
      <td>81, 2001</td>
    </tr>
    <tr>
      <td>Chiral perturbation theory</td>
      <td>354, 837, 889, 896</td>
    </tr>
    <tr>
      <td>Chiral superfields</td>
      <td>1038</td>
    </tr>
    <tr>
      <td>Chromaticity</td>
      <td>561</td>
    </tr>
    <tr>
      <td>Chromomagnetic dipole moment</td>
      <td>850</td>
    </tr>
    <tr>
      <td>Circular Colliders</td>
      <td>559</td>
    </tr>
    <tr>
      <td>Circular Higgs factories</td>
      <td>564</td>
    </tr>
    <tr>
      <td>CKM (Cabibbo-Kobayashi-Maskawa) quark mixing matrix</td>
      <td>980</td>
    </tr>
    <tr>
      <td>CKM angles</td>
      <td></td>
    </tr>
    <tr>
      <td>α</td>
      <td>980</td>
    </tr>
    <tr>
      <td>β</td>
      <td>980</td>
    </tr>
    <tr>
      <td>γ</td>
      <td>982</td>
    </tr>
    <tr>
      <td>from B hadrons determination, note</td>
      <td>980</td>
    </tr>
    <tr>
      <td>CKM matrix elements</td>
      <td>980</td>
    </tr>
    <tr>
      <td>CKM quark-mixing matrix, note on</td>
      <td>270</td>
    </tr>
    <tr>
      <td>CKM unitarity constraints</td>
      <td>905</td>
    </tr>
    <tr>
      <td>Classical electron radius</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Classification</td>
      <td>711, 714, 718, 721, 722, 726, 732, 740</td>
    </tr>
    <tr>
      <td>Clebsch-Gordan coefficients</td>
      <td>772, 773</td>
    </tr>
    <tr>
      <td>CLIC (CERN) future collider</td>
      <td>570</td>
    </tr>
    <tr>
      <td>Clustering</td>
      <td>716, 732</td>
    </tr>
    <tr>
      <td>CMB</td>
      <td></td>
    </tr>
    <tr>
      <td>Planck satellite</td>
      <td>461, 519, 527</td>
    </tr>
    <tr>
      <td>anisotropy</td>
      <td>453, 486</td>
    </tr>
    <tr>
      <td>anisotropy power spectrum</td>
      <td>524</td>
    </tr>
    <tr>
      <td>COBE satellite</td>
      <td>483, 524</td>
    </tr>
    <tr>
      <td>Compton distortion</td>
      <td>530</td>
    </tr>
    <tr>
      <td>concordance with baryon density</td>
      <td>477</td>
    </tr>
    <tr>
      <td>cosmic microwave background</td>
      <td>524</td>
    </tr>
    <tr>
      <td>cosmic variance</td>
      <td>525</td>
    </tr>
    <tr>
      <td>detectors</td>
      <td>666</td>
    </tr>
    <tr>
      <td>dipole</td>
      <td>524</td>
    </tr>
    <tr>
      <td>future Simons observatory</td>
      <td>488</td>
    </tr>
    <tr>
      <td>lensing</td>
      <td>494</td>
    </tr>
    <tr>
      <td>LiteBIRD satellite</td>
      <td>529</td>
    </tr>
    <tr>
      <td>Lorentz-boosted temperature pattern</td>
      <td>524</td>
    </tr>
    <tr>
      <td>mean temperature, monopole</td>
      <td>524</td>
    </tr>
    <tr>
      <td>monopole</td>
      <td>524</td>
    </tr>
    <tr>
      <td>multipoles</td>
      <td>524</td>
    </tr>
    <tr>
      <td>non-Gaussianity</td>
      <td>451, 467, 525</td>
    </tr>
    <tr>
      <td>polarization</td>
      <td>528</td>
    </tr>
    <tr>
      <td>primordial perturbation</td>
      <td>526</td>
    </tr>
    <tr>
      <td>radiation density of Universe</td>
      <td>138</td>
    </tr>
    <tr>
      <td>scalar perturbations</td>
      <td>526</td>
    </tr>
    <tr>
      <td>sky map</td>
      <td>524</td>
    </tr>
    <tr>
      <td>Solar System motion</td>
      <td>524</td>
    </tr>
    <tr>
      <td>spectrum</td>
      <td>524</td>
    </tr>
    <tr>
      <td>tensor perturbations</td>
      <td>526</td>
    </tr>
    <tr>
      <td>Wilkinson Microwave Anisotropy Probe, WMAP</td>
      <td>524</td>
    </tr>
    <tr>
      <td>WMAP satellite</td>
      <td>519</td>
    </tr>
    <tr>
      <td>CMB-Cosmic microwave background</td>
      <td>450, 486</td>
    </tr>
    <tr>
      <td>CMS - Compact Muon Solenoid, LHC</td>
      <td>218</td>
    </tr>
    <tr>
      <td>CMSSM, Constrained MSSM</td>
      <td>1046, 1059</td>
    </tr>
    <tr>
      <td>CNN, convolutional neural network</td>
      <td>714, 720, 725, 737</td>
    </tr>
    <tr>
      <td>CNO cycle, solar neutrino</td>
      <td>302</td>
    </tr>
    <tr>
      <td>COBE - COsmic Background Explorer</td>
      <td>524</td>
    </tr>
    <tr>
      <td>Coherent radio Cherenkov radiation detectors</td>
      <td>657</td>
    </tr>
    <tr>
      <td>Cold dark matter (CDM)</td>
      <td>452</td>
    </tr>
    <tr>
      <td>Cold dark matter density</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Collaboration databases</td>
      <td>22</td>
    </tr>
    <tr>
      <td>Collaborations</td>
      <td></td>
    </tr>
    <tr>
      <td>Planck</td>
      <td>485</td>
    </tr>
    <tr>
      <td>ALEPH</td>
      <td>815, 956</td>
    </tr>
    <tr>
      <td>ALICE</td>
      <td>412</td>
    </tr>
    <tr>
      <td>ALPHA</td>
      <td>359</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>ANITA</td>
      <td>659</td>
    </tr>
    <tr>
      <td>ARIANNA</td>
      <td>660</td>
    </tr>
    <tr>
      <td>ATLAS</td>
      <td>412, 503, 815, 985, 1029</td>
    </tr>
    <tr>
      <td>B-factories</td>
      <td>985</td>
    </tr>
    <tr>
      <td>BaBar</td>
      <td>830, 934, 940, 956, 985, 1049</td>
    </tr>
    <tr>
      <td>Belle</td>
      <td>830, 934, 940, 956, 985, 1049</td>
    </tr>
    <tr>
      <td>BelleII</td>
      <td>956</td>
    </tr>
    <tr>
      <td>BERT</td>
      <td>1081</td>
    </tr>
    <tr>
      <td>BESIII</td>
      <td>985</td>
    </tr>
    <tr>
      <td>CALICE</td>
      <td>631</td>
    </tr>
    <tr>
      <td>CCFR</td>
      <td>638</td>
    </tr>
    <tr>
      <td>CDF</td>
      <td>815, 940, 956</td>
    </tr>
    <tr>
      <td>CJ</td>
      <td>380</td>
    </tr>
    <tr>
      <td>CLEO</td>
      <td>940</td>
    </tr>
    <tr>
      <td>CLEO-c</td>
      <td>985</td>
    </tr>
    <tr>
      <td>CMS</td>
      <td>503, 815, 985, 1029, 1035, 1070, 1136</td>
    </tr>
    <tr>
      <td>COMPASS</td>
      <td>872</td>
    </tr>
    <tr>
      <td>COMPETE</td>
      <td>413, 423</td>
    </tr>
    <tr>
      <td>CTA</td>
      <td>651</td>
    </tr>
    <tr>
      <td>D0</td>
      <td>421, 815, 941, 956, 1036</td>
    </tr>
    <tr>
      <td>DAMIC-M</td>
      <td>507</td>
    </tr>
    <tr>
      <td>DELPHI</td>
      <td>815, 956</td>
    </tr>
    <tr>
      <td>DREAM/RD52</td>
      <td>633</td>
    </tr>
    <tr>
      <td>DSSV</td>
      <td>372</td>
    </tr>
    <tr>
      <td>eBOSS</td>
      <td>518</td>
    </tr>
    <tr>
      <td>ETM</td>
      <td>936</td>
    </tr>
    <tr>
      <td>Event Horizon Telescope</td>
      <td>439</td>
    </tr>
    <tr>
      <td>Fermi-LAT</td>
      <td>1084</td>
    </tr>
    <tr>
      <td>Fermilab-MILC</td>
      <td>936</td>
    </tr>
    <tr>
      <td>FLAG</td>
      <td>936</td>
    </tr>
    <tr>
      <td>GlueX</td>
      <td>1014</td>
    </tr>
    <tr>
      <td>GRAND</td>
      <td>661</td>
    </tr>
    <tr>
      <td>H.E.S.S.</td>
      <td>651, 1084</td>
    </tr>
    <tr>
      <td>H1</td>
      <td>398, 1136</td>
    </tr>
    <tr>
      <td>HERA</td>
      <td>398, 1069</td>
    </tr>
    <tr>
      <td>HFLAV</td>
      <td>936</td>
    </tr>
    <tr>
      <td>HPQCD</td>
      <td>359, 936</td>
    </tr>
    <tr>
      <td>HWPF</td>
      <td>637</td>
    </tr>
    <tr>
      <td>L3</td>
      <td>815, 956</td>
    </tr>
    <tr>
      <td>Lattice QCD</td>
      <td>838</td>
    </tr>
    <tr>
      <td>LEP</td>
      <td>815, 817, 1034, 1069</td>
    </tr>
    <tr>
      <td>LHC</td>
      <td>815, 1035</td>
    </tr>
    <tr>
      <td>LHCb</td>
      <td>815, 940, 952, 956, 985, 994, 1035, 1049</td>
    </tr>
    <tr>
      <td>LIGO-Virgo</td>
      <td>435</td>
    </tr>
    <tr>
      <td>LVC</td>
      <td>435</td>
    </tr>
    <tr>
      <td>LVK</td>
      <td>435</td>
    </tr>
    <tr>
      <td>MAGIC</td>
      <td>651</td>
    </tr>
    <tr>
      <td>MAMI</td>
      <td>872</td>
    </tr>
    <tr>
      <td>MILC</td>
      <td>934</td>
    </tr>
    <tr>
      <td>MOSCAB</td>
      <td>507</td>
    </tr>
    <tr>
      <td>NEWS-G</td>
      <td>507</td>
    </tr>
    <tr>
      <td>NEWSdm</td>
      <td>508</td>
    </tr>
    <tr>
      <td>NINJA</td>
      <td>638</td>
    </tr>
    <tr>
      <td>NuTeV</td>
      <td>638</td>
    </tr>
    <tr>
      <td>OPAL</td>
      <td>815, 956</td>
    </tr>
    <tr>
      <td>PDG, Particle Data Group</td>
      <td>2</td>
    </tr>
    <tr>
      <td>PIBETA</td>
      <td>871</td>
    </tr>
    <tr>
      <td>RBC/UKQCD</td>
      <td>969</td>
    </tr>
    <tr>
      <td>RD51</td>
      <td>607</td>
    </tr>
    <tr>
      <td>RM123-Soton</td>
      <td>930</td>
    </tr>
    <tr>
      <td>RNO-G</td>
      <td>660</td>
    </tr>
    <tr>
      <td>SLD</td>
      <td>819</td>
    </tr>
    <tr>
      <td>Sp̄</td>
      <td>1098</td>
    </tr>
    <tr>
      <td>Tevatron</td>
      <td>815, 1036, 1069</td>
    </tr>
    <tr>
      <td>TOTEM</td>
      <td>410</td>
    </tr>
    <tr>
      <td>Tunka-Rex</td>
      <td>660</td>
    </tr>
    <tr>
      <td>UA4</td>
      <td>421</td>
    </tr>
    <tr>
      <td>VERITAS</td>
      <td>651</td>
    </tr>
    <tr>
      <td>WMAP</td>
      <td>487</td>
    </tr>
    <tr>
      <td>ZEUS</td>
      <td>398, 1069, 1136</td>
    </tr>
    <tr>
      <td>Collider parameters</td>
      <td>569</td>
    </tr>
    <tr>
      <td>Colliders</td>
      <td>559</td>
    </tr>
    <tr>
      <td>future</td>
      <td>564</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>present</td>
      <td>563</td>
    </tr>
    <tr>
      <td>recent</td>
      <td>562</td>
    </tr>
    <tr>
      <td>Colliders based on Energy Recovery Linacs</td>
      <td>566</td>
    </tr>
    <tr>
      <td>Collinear and infrared safety</td>
      <td>158, 161</td>
    </tr>
    <tr>
      <td>Collinear factorization</td>
      <td>156</td>
    </tr>
    <tr>
      <td>Color confinement</td>
      <td>1086</td>
    </tr>
    <tr>
      <td>Color factor</td>
      <td>153, 163</td>
    </tr>
    <tr>
      <td>Color reconnection</td>
      <td>815</td>
    </tr>
    <tr>
      <td>Color reconnection phenomenon</td>
      <td>418, 761</td>
    </tr>
    <tr>
      <td>Colorons (axigluons) search</td>
      <td>1114</td>
    </tr>
    <tr>
      <td>Comments, e-mail address to contact</td>
      <td>11</td>
    </tr>
    <tr>
      <td>Compact Linear Collider (CLIC)</td>
      <td>566</td>
    </tr>
    <tr>
      <td>Compaction</td>
      <td>1087</td>
    </tr>
    <tr>
      <td>Compensation</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">intrinsic</td>
      <td>632</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">software</td>
      <td>632</td>
    </tr>
    <tr>
      <td>Composite Higgs boson</td>
      <td>243</td>
    </tr>
    <tr>
      <td>Compton wavelength, electron</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Concordance cosmology</td>
      <td>483</td>
    </tr>
    <tr>
      <td>Conditional probability density function</td>
      <td>690</td>
    </tr>
    <tr>
      <td>Confidence intervals</td>
      <td>703</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">frequentist</td>
      <td>704</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Gaussian</td>
      <td>15</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Poisson</td>
      <td>706</td>
    </tr>
    <tr>
      <td>Confinement</td>
      <td>360</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">-deconfinement quarks-hadrons transition</td>
      <td>448</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">color</td>
      <td>1086</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">harmonic</td>
      <td>328</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">linear</td>
      <td>328, 757</td>
    </tr>
    <tr>
      <td>Conformal field theory, CFT</td>
      <td>1025</td>
    </tr>
    <tr>
      <td>Conservation laws</td>
      <td>114</td>
    </tr>
    <tr>
      <td>Consistency of an estimator</td>
      <td>694</td>
    </tr>
    <tr>
      <td>Constancy of constants tests</td>
      <td>437</td>
    </tr>
    <tr>
      <td>Constrained fit</td>
      <td>829</td>
    </tr>
    <tr>
      <td>Constrained fits, procedures for</td>
      <td>16</td>
    </tr>
    <tr>
      <td>Constrained MSSM, CMSSM</td>
      <td>1046, 1059</td>
    </tr>
    <tr>
      <td>Constraints, parameter estimation with</td>
      <td>697</td>
    </tr>
    <tr>
      <td>Consultants</td>
      <td>12</td>
    </tr>
    <tr>
      <td>Contour-improved perturbation theory (CIPT)</td>
      <td>168</td>
    </tr>
    <tr>
      <td>Conversion constant</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Conversion probability for photons to e<sup>+</sup>e<sup>-</sup></td>
      <td>583</td>
    </tr>
    <tr>
      <td>Convolution kernel</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Convolution, 1&times;1</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Convolution, kernel size</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Convolution, padding</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Convolution, stride</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Convolution-transpose</td>
      <td>726</td>
    </tr>
    <tr>
      <td>Copernican Principle</td>
      <td>444</td>
    </tr>
    <tr>
      <td>Correlation coefficient, definition</td>
      <td>690</td>
    </tr>
    <tr>
      <td>Correlation matrices</td>
      <td>829</td>
    </tr>
    <tr>
      <td>Cosmic acceleration, dark energy</td>
      <td>515</td>
    </tr>
    <tr>
      <td>Cosmic background radiation temperature</td>
      <td>524</td>
    </tr>
    <tr>
      <td>Cosmic microwave background, CMB</td>
      <td>450, 486, 524</td>
    </tr>
    <tr>
      <td>Cosmic neutrino background, CνB</td>
      <td>491</td>
    </tr>
    <tr>
      <td>Cosmic ray(s)</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">background in counters</td>
      <td>680</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">fluorescence detectors FDs</td>
      <td>649</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">radio detection of air showers</td>
      <td>660</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">ultra-high energy, UHE</td>
      <td>658</td>
    </tr>
    <tr>
      <td>Cosmic topology</td>
      <td>485</td>
    </tr>
    <tr>
      <td>Cosmological</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">constant Λ</td>
      <td>138, 444, 457, 515, 526</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">density parameter, Ω</td>
      <td>445</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">equation of state</td>
      <td>445</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">mass density parameter</td>
      <td>444</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">parameters, note on</td>
      <td>482</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">standard model</td>
      <td>532</td>
    </tr>
    <tr>
      <td>Cosmological probes</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">CMB</td>
      <td>530</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">galaxy peculiar velocities</td>
      <td>487</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">integrated Sachs-Wolfe effect</td>
      <td>487</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">redshift</td>
      <td>444</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">supernovae</td>
      <td>485</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>Cosmology</td>
      <td>482, 499</td>
    </tr>
    <tr>
      <td>ΛCDM</td>
      <td>499</td>
    </tr>
    <tr>
      <td>Big-Bang</td>
      <td>444, 457, 499</td>
    </tr>
    <tr>
      <td>modern</td>
      <td>499</td>
    </tr>
    <tr>
      <td>outlook for the future</td>
      <td>488</td>
    </tr>
    <tr>
      <td>Robertson-Walker metric</td>
      <td>457</td>
    </tr>
    <tr>
      <td>scalar field</td>
      <td>458</td>
    </tr>
    <tr>
      <td>standard</td>
      <td>502</td>
    </tr>
    <tr>
      <td>standard early Universe</td>
      <td>457</td>
    </tr>
    <tr>
      <td>standard neutrino</td>
      <td>491</td>
    </tr>
    <tr>
      <td>Coupling between matter and gravity</td>
      <td>437</td>
    </tr>
    <tr>
      <td>Coupling constant in QCD</td>
      <td>137, 153</td>
    </tr>
    <tr>
      <td>Coupling unification</td>
      <td>1122</td>
    </tr>
    <tr>
      <td>Covariance matrix</td>
      <td>696</td>
    </tr>
    <tr>
      <td>Covariance, definition</td>
      <td>690</td>
    </tr>
    <tr>
      <td>Coverage</td>
      <td>704</td>
    </tr>
    <tr>
      <td>CP, tests of conservation</td>
      <td>114</td>
    </tr>
    <tr>
      <td>CP violation</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">and D<sup>0</sup> - D<sup>0</sup> mixing</td>
      <td>917</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">charm mixing</td>
      <td>913</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">classification of effects</td>
      <td>282</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in BB mixing</td>
      <td>958</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in B and B<sub>s</sub><sup>0</sup> mixing and decay</td>
      <td>287</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in B decay</td>
      <td>940</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in K<sub>L</sub><sup>0</sup> decay</td>
      <td>284</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in K<sub>L</sub><sup>0</sup> decay, note on</td>
      <td>908</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in charm</td>
      <td>285</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in decays of Beauty to Charm</td>
      <td>912</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">in the quark sector, note</td>
      <td>280</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">interference between tree and penguin amplitudes</td>
      <td>287</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">overview</td>
      <td>114, 280</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">the CKM matrix</td>
      <td>283</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">the Kobayashi-Maskawa mechanism</td>
      <td>283</td>
    </tr>
    <tr>
      <td>CPT invariance tests in neutral kaon decay</td>
      <td>902</td>
    </tr>
    <tr>
      <td>CPT tests of conservation</td>
      <td>117</td>
    </tr>
    <tr>
      <td>Critical density in cosmology</td>
      <td>444</td>
    </tr>
    <tr>
      <td>Critical density of the Universe</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Critical energy</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">for electrons</td>
      <td>583</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">for muons</td>
      <td>586</td>
    </tr>
    <tr>
      <td>Cross sections and related quantities, plots of</td>
      <td>807</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">e<sup>+</sup>e<sup>-</sup> annihilation cross section near M<sub>Z</sub></td>
      <td>810</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Pseudorapidity distribution in pp and p<span style="text-decoration: overline">p</span> interactions</td>
      <td>807</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Average hadron multiplicities in e<sup>+</sup>e<sup>-</sup> annihilation events</td>
      <td>808</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">nucleon structure functions</td>
      <td>367</td>
    </tr>
    <tr>
      <td>Cross sections, relations for</td>
      <td>779, 792</td>
    </tr>
    <tr>
      <td>Cross-entropy loss</td>
      <td>715</td>
    </tr>
    <tr>
      <td>Cross-validation</td>
      <td>713</td>
    </tr>
    <tr>
      <td>Cryogenic beam vacuum system</td>
      <td>566</td>
    </tr>
    <tr>
      <td>Cryogenic gases, boiling points, table</td>
      <td>144</td>
    </tr>
    <tr>
      <td>Crystal accelerator</td>
      <td>567</td>
    </tr>
    <tr>
      <td>Cumulative distribution function, definition</td>
      <td>689</td>
    </tr>
    <tr>
      <td>Curie, unit of radioactivity</td>
      <td>679</td>
    </tr>
    <tr>
      <td>Curvature</td>
      <td>139</td>
    </tr>
    <tr>
      <td>d functions</td>
      <td>772</td>
    </tr>
    <tr>
      <td>D mesons</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sup>0</sup>, D<sup>0</sup></td>
      <td>46, 1610</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sup>±</sup></td>
      <td>43, 1592</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D(3000)<sup>0</sup></td>
      <td>1655</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sup>*</sup>(2007)<sup>0</sup></td>
      <td>50, 1646</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sup>*</sup>(2010)<sup>±</sup></td>
      <td>50, 1647</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sup>*</sup>(2640)<sup>±</sup></td>
      <td>1654</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>0</sub><sup>*</sup>(2300) [was D<sub>0</sub><sup>*</sup>(2400)]</td>
      <td>50, 1648</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>0</sub><sup>0</sup>(2550)<sup>0</sup> [was D<sub>J</sub><sup>*</sup>(2600)]</td>
      <td>1653</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>1</sub><sup>*</sup>(2600)<sup>0</sup> [was D<sub>J</sub><sup>*</sup>(2600)]</td>
      <td>1653</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>1</sub><sup>0</sup>(2760)<sup>0</sup></td>
      <td>1655</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>1</sub>(2420)</td>
      <td>50, 1649</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>1</sub>(2430)<sup>0</sup></td>
      <td>50, 1650</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>2</sub><sup>*</sup>(2460)</td>
      <td>50, 1651</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>2</sub>(2740)<sup>0</sup> [was D(2740)<sup>0</sup>]</td>
      <td>1654</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">D<sub>3</sub><sup>*</sup>(2750)</td>
      <td>50, 1654</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>D<sub>s0</sub>(2317)<sup>±</sup></td>
      <td>53, 1674</td>
    </tr>
    <tr>
      <td>D<sub>s0</sub>(2590)<sup>+</sup></td>
      <td>1678</td>
    </tr>
    <tr>
      <td>D<sub>s1</sub>(2700)<sup>±</sup></td>
      <td>53, 1678</td>
    </tr>
    <tr>
      <td>D<sub>s1</sub>(2860)<sup>±</sup></td>
      <td>1679</td>
    </tr>
    <tr>
      <td>D<sub>s1</sub>(2460)<sup>±</sup></td>
      <td>53, 1675</td>
    </tr>
    <tr>
      <td>D<sub>s1</sub>(2536)<sup>±</sup></td>
      <td>53, 1676</td>
    </tr>
    <tr>
      <td>D<sub>s2</sub>(2573)<sup>±</sup></td>
      <td>53, 1677</td>
    </tr>
    <tr>
      <td>D<sub>s3</sub>(2860)<sup>±</sup></td>
      <td>53, 1679</td>
    </tr>
    <tr>
      <td>D<sub>sJ</sub>(3040)<sup>±</sup></td>
      <td>1680</td>
    </tr>
    <tr>
      <td>D<sub>s</sub><sup>*±</sup></td>
      <td>53, 1673</td>
    </tr>
    <tr>
      <td>D<sub>s</sub><sup>±</sup></td>
      <td>50, 1657</td>
    </tr>
    <tr>
      <td>D<sup>0</sup>-D<sup>0</sup> mixing, note on</td>
      <td>917</td>
    </tr>
    <tr>
      <td>DAΦNE</td>
      <td>569</td>
    </tr>
    <tr>
      <td>d<sub>A</sub>, angular-diameter distance</td>
      <td>486, 531</td>
    </tr>
    <tr>
      <td>Dalitz plot, relations for</td>
      <td>778</td>
    </tr>
    <tr>
      <td>Damage, biological, from radiation</td>
      <td>679</td>
    </tr>
    <tr>
      <td>Dark energy</td>
      <td>445, 484, 515</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cosmic acceleration</td>
      <td>515</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">density parameter</td>
      <td>138</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">equation of state parameter</td>
      <td>139</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">equation of state parameter w</td>
      <td>486, 515</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Euclid satellite</td>
      <td>470</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">experiments</td>
      <td>518</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">observational probes</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">baryon acoustic oscillations, BAO</td>
      <td>517</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">CMB anisotropies</td>
      <td>517</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Type Ia supernovae</td>
      <td>517</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">weak gravitational lensing</td>
      <td>517</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">parameter, Ω<sub>N</sub></td>
      <td>445</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">quintessence</td>
      <td>454</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">repulsive gravity</td>
      <td>516</td>
    </tr>
    <tr>
      <td>Dark energy spectroscopic instrument (DESI)</td>
      <td>487, 518</td>
    </tr>
    <tr>
      <td>Dark matter</td>
      <td>452, 484</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">annihilating</td>
      <td>532</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">CDM cosmology</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cusp-core problem</td>
      <td>501</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">density distribution</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">detectors</td>
      <td>666</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Gaia satellite</td>
      <td>501</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Galactic halo shape</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, cannibalization</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, DM anti-DM asymmetry</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, freeze-in</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, freeze-out</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, non-thermal production</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">genesis, primordial black holes</td>
      <td>500</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">laboratory detection</td>
      <td>503</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">missing satellites problem</td>
      <td>501</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">non-baryonic</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Too-big-to-fail problem</td>
      <td>501</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">velocity distribution</td>
      <td>501</td>
    </tr>
    <tr>
      <td>Dark matter astrophysical detection</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cosmic-ray antimatter</td>
      <td>510</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">cosmology</td>
      <td>510</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">gamma rays</td>
      <td>508</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">multi-wavelength</td>
      <td>510</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">neutrinos</td>
      <td>509</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">PBH detection</td>
      <td>510</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">staller physics</td>
      <td>510</td>
    </tr>
    <tr>
      <td>Dark matter candidates</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">axions</td>
      <td>502</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">dark photon</td>
      <td>502</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">gaugino</td>
      <td>1041</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">gravitino</td>
      <td>1040</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">higgsino</td>
      <td>1041</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">sterile neutrinos</td>
      <td>502</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">WIMPs</td>
      <td>502</td>
    </tr>
    <tr>
      <td>Dark matter properties</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">darkness</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">mass lower and upper limits</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">self-interactions</td>
      <td>499</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">stability</td>
      <td>499</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>Data</td>
      <td>22</td>
    </tr>
    <tr>
      <td>Data augmentation</td>
      <td>721, 738, 739</td>
    </tr>
    <tr>
      <td>Data manifold</td>
      <td>721</td>
    </tr>
    <tr>
      <td>Data, averaging and fitting procedures</td>
      <td>15</td>
    </tr>
    <tr>
      <td>Data, selecting and treatment</td>
      <td>15</td>
    </tr>
    <tr>
      <td>Databases</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">availability online</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">conferences</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">experiments</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">high-energy physics</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Institutions</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">INSPIRE</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Authors</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Conferences</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Experiments</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Institutions</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Jobs</td>
      <td>22</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Journals</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Literature</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">Seminars</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">institutions</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">journals</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 4em;">literature</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">ADS</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">arXiv.org</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">INSPIRE</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">MathSciNet</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">OSTI</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">ORCID</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">particle physics</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">PDG API</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">PDGLive, PDG web browser</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">Review of Particle Physics (RPP)</td>
      <td>20</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">ROR</td>
      <td>21</td>
    </tr>
    <tr>
      <td style="padding-left: 6em;">RPP computer-readable files</td>
      <td>20</td>
    </tr>
    <tr>
      <td>Day, sidereal</td>
      <td>138</td>
    </tr>
    <tr>
      <td>dE/dx</td>
      <td>575</td>
    </tr>
    <tr>
      <td>Decay parameters, Michel</td>
      <td>832</td>
    </tr>
    <tr>
      <td>Decays, kinematics and phase space for</td>
      <td>777</td>
    </tr>
    <tr>
      <td>Deceleration parameter, q<sub>0</sub></td>
      <td>445</td>
    </tr>
    <tr>
      <td>Decision trees</td>
      <td>712</td>
    </tr>
    <tr>
      <td>Decoder</td>
      <td>716, 726, 731, 733</td>
    </tr>
    <tr>
      <td>Deep inelastic scattering, DIS</td>
      <td>155, 367, 412, 635</td>
    </tr>
    <tr>
      <td>Deep learning</td>
      <td>725</td>
    </tr>
    <tr>
      <td>Deep Sets</td>
      <td>720, 731</td>
    </tr>
    <tr>
      <td>Degree of freedom, number of</td>
      <td>696</td>
    </tr>
    <tr>
      <td>ΔB = 1, weak-neutral currents, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>ΔB = 2, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>ΔC = 1, weak-neutral currents, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>ΔC = 2, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>Δ resonances</td>
      <td></td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1232)</td>
      <td>97, 2137</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1600)</td>
      <td>97, 2139</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1620)</td>
      <td>97, 2141</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1700)</td>
      <td>97, 2142</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1750)</td>
      <td>2144</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1900)</td>
      <td>97, 2145</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1905)</td>
      <td>98, 2146</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1910)</td>
      <td>98, 2148</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1920)</td>
      <td>98, 2149</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1930)</td>
      <td>98, 2151</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1940)</td>
      <td>2152</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(1950)</td>
      <td>98, 2153</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2000)</td>
      <td>2155</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2150)</td>
      <td>2156</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2200)</td>
      <td>98, 2156</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2300)</td>
      <td>2157</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2350)</td>
      <td>2157</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2390)</td>
      <td>2158</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2400)</td>
      <td>2158</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2420)</td>
      <td>98, 2159</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2750)</td>
      <td>2159</td>
    </tr>
    <tr>
      <td style="padding-left: 2em;">Δ(2950)</td>
      <td>2160</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>ΔS = 1, weak-neutral currents, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>ΔS = ΔQ tests of</td>
      <td>114</td>
    </tr>
    <tr>
      <td>ΔT = 1, weak-neutral currents, tests for</td>
      <td>114</td>
    </tr>
    <tr>
      <td>Δ(~ 3000 Region) Partial-Wave Analyses</td>
      <td>2160</td>
    </tr>
    <tr>
      <td>δ-rays</td>
      <td>579</td>
    </tr>
    <tr>
      <td>DenseNet</td>
      <td>727</td>
    </tr>
    <tr>
      <td>Density of CMB photons</td>
      <td>138</td>
    </tr>
    <tr>
      <td>of materials, table</td>
      <td>144</td>
    </tr>
    <tr>
      <td>of Universe, critical</td>
      <td>138</td>
    </tr>
    <tr>
      <td>parameter of the Universe Ω<sub>0</sub></td>
      <td>138</td>
    </tr>
    <tr>
      <td>Density effect in energy loss rate</td>
      <td>576</td>
    </tr>
    <tr>
      <td>Density estimation</td>
      <td>715, 719, 732, 739, 740</td>
    </tr>
    <tr>
      <td>DESI – dark energy spectroscopic instrument</td>
      <td>470, 487, 518</td>
    </tr>
    <tr>
      <td>Detectors bubble chambers</td>
      <td>635</td>
    </tr>
    <tr>
      <td>calorimeters electromagnetic</td>
      <td>629</td>
    </tr>
    <tr>
      <td>Cherenkov</td>
      <td>598, 651</td>
    </tr>
    <tr>
      <td>CMB detectors</td>
      <td>666</td>
    </tr>
    <tr>
      <td>coherent radio Cherenkov radiation</td>
      <td>657</td>
    </tr>
    <tr>
      <td>Dark matter</td>
      <td>666</td>
    </tr>
    <tr>
      <td>fluorescence, atmospheric</td>
      <td>649</td>
    </tr>
    <tr>
      <td>for rare events</td>
      <td>661</td>
    </tr>
    <tr>
      <td>gas-filled drift chamber</td>
      <td>603, 634</td>
    </tr>
    <tr>
      <td>high rate effects</td>
      <td>604</td>
    </tr>
    <tr>
      <td>micro-pattern</td>
      <td>605</td>
    </tr>
    <tr>
      <td>micro-strip chamber</td>
      <td>607</td>
    </tr>
    <tr>
      <td>multi-wire proportional chambers, MWPC</td>
      <td>603</td>
    </tr>
    <tr>
      <td>resitive plate chambers, RPC</td>
      <td>611</td>
    </tr>
    <tr>
      <td>time-projection chambers, TPC</td>
      <td>607</td>
    </tr>
    <tr>
      <td>transition radiation, TRD</td>
      <td>609</td>
    </tr>
    <tr>
      <td>gravitation wave observatory, Virgo</td>
      <td>435</td>
    </tr>
    <tr>
      <td>hadronic shower</td>
      <td>591</td>
    </tr>
    <tr>
      <td>ice-based</td>
      <td>659</td>
    </tr>
    <tr>
      <td>inorganic scintillator</td>
      <td>596</td>
    </tr>
    <tr>
      <td>Kinetic Inductance Detectors (KIDs)</td>
      <td>666</td>
    </tr>
    <tr>
      <td>LAr Time projection chambers</td>
      <td>613</td>
    </tr>
    <tr>
      <td>laser interferometer gravitation observatory, LIGO</td>
      <td>435</td>
    </tr>
    <tr>
      <td>liquid ionization chamber</td>
      <td>634</td>
    </tr>
    <tr>
      <td>liquid scintillator</td>
      <td>652</td>
    </tr>
    <tr>
      <td>Low Temperature Detectors (LTDs)</td>
      <td>665</td>
    </tr>
    <tr>
      <td>low-noise readout</td>
      <td>623</td>
    </tr>
    <tr>
      <td>low-radioactivity background techniques</td>
      <td>670</td>
    </tr>
    <tr>
      <td>Magnetic Metallic Calorimeters (MMCs)</td>
      <td>668</td>
    </tr>
    <tr>
      <td>Neutrino cryogenic detectors</td>
      <td>666</td>
    </tr>
    <tr>
      <td>neutrino telescopes</td>
      <td>654</td>
    </tr>
    <tr>
      <td>neutrino, calibration of</td>
      <td>685</td>
    </tr>
    <tr>
      <td>neutrinos accelerator-based</td>
      <td>635</td>
    </tr>
    <tr>
      <td>bubble chambers</td>
      <td>635</td>
    </tr>
    <tr>
      <td>Cherenkov</td>
      <td>637</td>
    </tr>
    <tr>
      <td>emulsion</td>
      <td>638</td>
    </tr>
    <tr>
      <td>iron tracking calorimeters</td>
      <td>636</td>
    </tr>
    <tr>
      <td>liquid argon TPC</td>
      <td>637</td>
    </tr>
    <tr>
      <td>plastic scintillators</td>
      <td>637</td>
    </tr>
    <tr>
      <td>noble liquid</td>
      <td>654</td>
    </tr>
    <tr>
      <td>organic scintillator</td>
      <td>594</td>
    </tr>
    <tr>
      <td>proton decay</td>
      <td>652</td>
    </tr>
    <tr>
      <td>radio-detection of cosmic ray air showers</td>
      <td>660</td>
    </tr>
    <tr>
      <td>rare event search 0νβ decay</td>
      <td>664</td>
    </tr>
    <tr>
      <td>WIMPs</td>
      <td>663</td>
    </tr>
    <tr>
      <td>semiconductor (D)MAPS</td>
      <td>619</td>
    </tr>
    <tr>
      <td>3D-Si</td>
      <td>619</td>
    </tr>
    <tr>
      <td>DEPFET</td>
      <td>619</td>
    </tr>
    <tr>
      <td>hybrid pixels</td>
      <td>619</td>
    </tr>
    <tr>
      <td>LGAD</td>
      <td>620</td>
    </tr>
    <tr>
      <td>microstrip</td>
      <td>619</td>
    </tr>
    <tr>
      <td>monolithic pixels</td>
      <td>619</td>
    </tr>
    <tr>
      <td>radiation damage</td>
      <td>621</td>
    </tr>
  </tbody>
</table>

<table>
  <tbody>
    <tr>
      <td>silicon driftchamber</td>
      <td>619</td>
    </tr>
    <tr>
      <td>Semiconductor Thermistors</td>
      <td>667</td>
    </tr>
    <tr>
      <td>showers</td>
      <td>629</td>
    </tr>
    <tr>
      <td>superconducting solenoid magnets for</td>
      <td>639</td>
    </tr>
    <tr>
      <td>superconducting toroidal magnets for</td>
      <td>640</td>
    </tr>
    <tr>
      <td>Superconducting Tunnel Junctions (STJs)</td>
      <td>666</td>
    </tr>
    <tr>
      <td>Transition Edge Sensors (TESs)</td>
      <td>667</td>
    </tr>
    <tr>
      <td>water Cherenkov</td>
      <td>653</td>
    </tr>
    <tr>
      <td>wire chambers</td>
      <td>613</td>
    </tr>
    <tr>
      <td>Deuterium abundance</td>
      <td>474</td>
    </tr>
    <tr>
      <td>Deuteron mass</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Deuteron structure function</td>
      <td>379</td>
    </tr>
    <tr>
      <td>DIEHARD</td>
      <td>748</td>
    </tr>
    <tr>
      <td>Dielectric constant of gaseous elements, table</td>
      <td>145</td>
    </tr>
    <tr>
      <td>Dielectric laser accelerator</td>
      <td>567</td>
    </tr>
    <tr>
      <td>Dielectric suppression of bremsstrahlung</td>
      <td>582</td>
    </tr>
    <tr>
      <td>Dielectric wakefield accelerators</td>
      <td>567</td>
    </tr>
    <tr>
      <td>Differentiable simulator</td>
      <td>719</td>
    </tr>
    <tr>
      <td>Differential Cherenkov detectors</td>
      <td>599</td>
    </tr>
    <tr>
      <td>Diffraction and high energy soft QCD</td>
      <td>406</td>
    </tr>
    <tr>
      <td>Diffractive parton distribution</td>
      <td>412</td>
    </tr>
    <tr>
      <td>Diffractive processes</td>
      <td>406</td>
    </tr>
    <tr>
      <td>Dirac gauginos</td>
      <td>1051</td>
    </tr>
    <tr>
      <td>Dirac neutrinos</td>
      <td>296</td>
    </tr>
    <tr>
      <td>Direct CP asymmetry in B decays</td>
      <td>952</td>
    </tr>
    <tr>
      <td>Directories, online, people, and organizations</td>
      <td>20</td>
    </tr>
    <tr>
      <td>DIS, deep inelastic scattering</td>
      <td>367, 412</td>
    </tr>
    <tr>
      <td>Discriminative model</td>
      <td>711, 713, 732</td>
    </tr>
    <tr>
      <td>Disk density</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Dispersion relation</td>
      <td>422, 888, 904</td>
    </tr>
    <tr>
      <td>Distance ladders</td>
      <td>485</td>
    </tr>
    <tr>
      <td>Distance-redshift relation</td>
      <td>444, 446, 482, 485, 516</td>
    </tr>
    <tr>
      <td>Distribution shift</td>
      <td>712</td>
    </tr>
    <tr>
      <td>Dokshitzer-Gribov-Lipatov-Altarelli-Parisie (DGLAP) equations</td>
      <td>156</td>
    </tr>
    <tr>
      <td>Domain adaptation</td>
      <td>738</td>
    </tr>
    <tr>
      <td>Domain shift</td>
      <td>712, 738</td>
    </tr>
    <tr>
      <td>Donnachie-Landshoff pp-scattering amplitude</td>
      <td>407</td>
    </tr>
    <tr>
      <td>Dose rate from γ ray sources</td>
      <td>681</td>
    </tr>
    <tr>
      <td>Dose, radioactivity, unit of absorbed</td>
      <td>680</td>
    </tr>
    <tr>
      <td>Double PDFs</td>
      <td>372</td>
    </tr>
    <tr>
      <td>Double-β decay</td>
      <td>1343</td>
    </tr>
    <tr>
      <td>Doubly charmed baryons</td>
      <td>2262</td>
    </tr>
    <tr>
      <td>Drell-Yan process</td>
      <td>220, 346, 375, 1026</td>
    </tr>
    <tr>
      <td>Drift chambers</td>
      <td>603</td>
    </tr>
    <tr>
      <td>Drift velocities of electrons</td>
      <td>634</td>
    </tr>
    <tr>
      <td>Dropout</td>
      <td>714, 725</td>
    </tr>
    <tr>
      <td>D<sub>s</sub><sup>+</sup> branching fractions, note on</td>
      <td>927</td>
    </tr>
    <tr>
      <td>Dual problem</td>
      <td>721</td>
    </tr>
    <tr>
      <td>Dual readout</td>
      <td>632</td>
    </tr>
    <tr>
      <td>Dynamic Graph CNN</td>
      <td>731</td>
    </tr>
    <tr>
      <td>Dynamical electroweak symmetry breaking</td>
      <td>1104</td>
    </tr>
    <tr>
      <td>e (electron)</td>
      <td>28, 1297</td>
    </tr>
    <tr>
      <td>e (natural log base)</td>
      <td>137</td>
    </tr>
    <tr>
      <td>e<sup>-</sup> Compton wavelength</td>
      <td>137</td>
    </tr>
    <tr>
      <td>Early stopping</td>
      <td>712, 714, 724, 735, 736</td>
    </tr>
    <tr>
      <td>Early Universe</td>
      <td>457, 474</td>
    </tr>
    <tr>
      <td>Earth equatorial radius</td>
      <td>138</td>
    </tr>
    <tr>
      <td>mass</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Eddington luminosity</td>
      <td>138</td>
    </tr>
    <tr>
      <td>Edge</td>
      <td>731</td>
    </tr>
    <tr>
      <td>Education databases</td>
      <td>22</td>
    </tr>
    <tr>
      <td>Effective number of neutrinos</td>
      <td>139</td>
    </tr>
    <tr>
      <td>Effective dose of radioactivity</td>
      <td>679</td>
    </tr>
    <tr>
      <td>Effective field theories (EFTs)</td>
      <td>341</td>
    </tr>
    <tr>
      <td>Effective skin depth δ</td>
      <td>146</td>
    </tr>
    <tr>
      <td>Efficiency of an estimator</td>
      <td>694</td>
    </tr>
    <tr>
      <td>EFT – effective field theories</td>
      <td>341</td>
    </tr>
    <tr>
      <td>Elastic cross sections</td>
      <td>412</td>
    </tr>
    <tr>
      <td>Elastic scattering</td>
      <td>406</td>
    </tr>
  </tbody>
</table>