The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 3,200 new measurements from 903 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 118 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 96 review articles. Volume 2 consists of the Particle Listings and contains also 22 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group ( pdg.lbl.gov ) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app. The PDG API (Application Programming Interface) provides access to the data published in the Review in machine-readable format.

The stability of tree-level relations among the parameters of a quantum field theory with respect to renormalization group (RG) running is typically explained by the existence of a symmetry. We examine a toy model of a quantum field theory of two real scalars in which a tree-level relation among the squared-mass parameters of the scalar potential appears to be RG-stable without the presence of an appropriate underlying symmetry. The stability of this relation with respect to renormalization group running can be explained by complexifying the original scalar field theory. It is then possible to exhibit a symmetry that guarantees the relations of relevant beta functions of squared-mass parameters of the complexified theory. Among these relations, we can identify equations that are algebraically identical to the corresponding equations that guarantee the stability of the relations among the squared-mass parameters of the original real scalar field theory where the symmetry of the complexified theory is no longer present.

The observation of resonant di-Higgs production, which would strongly suggest the existence of a new heavy neutral scalar H , has been searched for extensively at the LHC. In the two-Higgs doublet model (2HDM) with m H ≫ m h , where h is the Higgs boson of mass 125 GeV observed at the LHC, we show that a direct correlation emerges between Br ( H → h h ) and Br ( H → V V ) , with V = Z , W , which depends only on m H (and m V ). In particular, for heavy scalar masses between 500 GeV and 1 TeV, we find that Br ( H → h h ) / Br ( H → Z Z ) ≈ 9.4 ± 0.25 . Moreover, H → h h is a dominant decay mode over a significant region of the parameter space and serves as the primary probe for a heavy scalar resonance at current and future hadron colliders. The origin of these predictions is most transparent in the Higgs basis, where the term in the scalar potential proportional to H 1 † H 1 H 1 † H 2 (and its Hermitian conjugate) generates the leading contributions to the H h h and H h h h couplings in the decoupling limit of the 2HDM. Additionally, the latter coupling governs the resonant prompt tri-Higgs production via H → h h h , which is also directly correlated to H → h h (and H → V V ), and can yield rates large enough to be measured at the High-Luminosity LHC.

The observation of resonant di-Higgs production, which would strongly suggest the existence of a new heavy neutral scalar H, has been searched for extensively at the LHC. In the two-Higgs doublet model (2HDM) with m_H≫ m_h, where h is the Higgs boson of mass 125 GeV observed at the LHC, we show that a direct correlation emerges between Br(H→ hh) and Br(H→ VV), with V=Z,W, which depends only on m_H (and m_V). In particular, for heavy scalar masses between 500 GeV and 1 TeV, we find that Br(H→ hh)/ Br(H→ ZZ)≈ 9.5. The origin of this prediction is most transparent in the Higgs basis, where the term in the scalar potential proportional to ℋ_1^†ℋ_1 ℋ_1^†ℋ_2 (and its hermitian conjugate) generates the leading contributions to the Hhh and Hhhh couplings in the decoupling limit of the 2HDM. Moreover, the latter coupling governs the resonant prompt tri-Higgs production via H→ hhh, which is also directly correlated to H→ hh (and H→ VV), and can yield rates large enough to be measured at the High-Luminosity LHC.

We examine the correlations between new scalar boson decays to photons and electric dipole moments (EDMs) in the CP-violating flavor-aligned two-Higgs-doublet model (2HDM). It is convenient to work in the Higgs basis {711; 712} where only the first Higgs doublet field 711 acquires a vacuum expectation value. In light of the LHC Higgs data, which agree well with Standard Model (SM) predictions, it follows that the parameters of the 2HDM are consistent with the Higgs alignment limit. In this parameter regime, the observed SM-like Higgs boson resides almost entirely in 711, and the other two physical neutral scalars, which reside almost entirely in 712, are approximate eigenstates of CP (denoted by the CP-even H and the CP-odd A). In the Higgs basis, the scalar potential term Z771 dagger 171271 dagger 2712 + H.c. governs the charged-Higgs loop contributions to the decay of H and A to photons. If ReZ7 Im Z7 not equal 0, then CP-violating effects are present and allow for an H+H-A coupling, which can yield a sizable branching ratio for A -> 77. These CP-violating effects also generate nonzero EDMs for the electron, the neutron and the proton. We examine these correlations for the cases of mA = 95 GeV and mA = 152 GeV where interesting excesses in the diphoton spectrum have been observed at the LHC. These excesses can be explained via the decay of A while being consistent with the experimental bound for the electron EDM in regions of parameter space that can be tested with future neutron and proton EDM measurements. This allows for the interesting possibility where the 95 GeV diphoton excess can be identified with A, while mH similar or equal to 98 GeV can account for the best fit to the LEP excess in e+e- -> ZH with H -> bb.

There are only six independent types of symmetry-constrained (renormalizable) scalar potentials in the two Higgs doublet model (2HDM). For example, the scalar sector symmetry known as Z_2⊗Π_2, generated by the simultaneous application of two independent symmetries acting on the scalar fields, and the generalized CP symmetry known as GCP2 yield equivalent 2HDM scalar potentials. A similar situation arises for the scalar sector symmetries known as U(1)⊗Π_2 and GCP3, respectively. In this paper, we show that this "degeneracy" remains when the definitions of the corresponding symmetries are extended to the Yukawa sector with three quark generations. The proof involves the exploration of all possible extensions of the corresponding symmetries to the Yukawa sector, consistent with the phenomenological constraints of nonzero quark masses and a nontrivial quark mixing matrix. Moreover, we find that this result is a peculiarity of a Yukawa sector with three quark generations. In particular, with two quark generations, we find that models based on the extension of Z_2⊗Π_2 to the Yukawa sector are inequivalent with those based on GCP2.

This is a review of the theoretical aspects of the supersymmetric extension of the Standard Model of particle physics, extracted from Chapter 88 of the 2023 update of the Review of Particle Physics, which appears in R.L. Workman et al. (Particle Data Group), Prog. Theor. Exp. Phys. 2022, 083C01 (2022) and 2023 update. The companion review, "Supersymmetry, Part II (Experiment)", can be found in Chapter 89 of the Review of Particle Physics (op. cit.).

The Review summarizes much of particle physics and cosmology. Using data from previous editions, plus 2,717 new measurements from 869 papers, we list, evaluate, and average measured properties of gauge bosons and the recently discovered Higgs boson, leptons, quarks, mesons, and baryons. We summarize searches for hypothetical particles such as supersymmetric particles, heavy bosons, axions, dark photons, etc. Particle properties and search limits are listed in Summary Tables. We give numerous tables, figures, formulae, and reviews of topics such as Higgs Boson Physics, Supersymmetry, Grand Unified Theories, Neutrino Mixing, Dark Energy, Dark Matter, Cosmology, Particle Detectors, Colliders, Probability and Statistics. Most of the 120 reviews are updated, including many that are heavily revised. The Review is divided into two volumes. Volume 1 includes the Summary Tables and 97 review articles. Volume 2 consists of the Particle Listings and contains also 23 reviews that address specific aspects of the data presented in the Listings. The complete Review (both volumes) is published online on the website of the Particle Data Group (pdg.lbl.gov) and in a journal. Volume 1 is available in print as the PDG Book. A Particle Physics Booklet with the Summary Tables and essential tables, figures, and equations from selected review articles is available in print, as a web version optimized for use on phones, and as an Android app.

Explicit formulae for the 4×4 Lorentz transformation matrices corresponding to a pure boost and a pure three-dimensional rotation are very well known. Significantly less well known is the explicit formula for a general Lorentz transformation with arbitrary non-zero boost and rotation parameters. We revisit this more general formula by presenting two different derivations. The first derivation (which is somewhat simpler than previous ones appearing in the literature) evaluates the exponential of a 4×4 real matrix A, where A is a product of the diagonal matrix diag(+1,−1,−1,−1) and an arbitrary 4×4 real antisymmetric matrix. The formula for expA depends only on the eigenvalues of A and makes use of the Lagrange interpolating polynomial. The second derivation exploits the observation that the spinor product η†σ¯μχ transforms as a Lorentz four-vector, where χ and η are two-component spinors. The advantage of the latter derivation is that the corresponding formula for a general Lorentz transformation Λ reduces to the computation of the trace of a product of 2×2 matrices. Both computations are shown to yield equivalent expressions for Λ.

Dark Matter models that employ a vector portal to a dark sector are usually treated as an effective theory that incorporates kinetic mixing of the photon with a new U(1) gauge boson, with the Z boson integrated out. However, a more complete theory must employ the full SU(2)×L U(1)×Y U(1)Y′ gauge group, in which kinetic mixing of the Z boson with the new U(1) gauge boson is taken into account. The importance of the more complete analysis is demonstrated by an example where the parameter space of the effective theory that yields the observed dark matter relic density is in conflict with a suitably defined electroweak ρ parameter that is deduced from a global fit to Z physics data.

Eleven years ago, the Higgs boson was discovered at the LHC. I briefly survey the status of Higgs boson physics today and explore some of the implications for future Higgs studies. Although current experimental measurements are consistent with interpreting the observed Higgs boson as being consistent with the predictions of the Standard Model of particle physics, it is still possible that the Higgs boson is a member of an extended scalar sector that lies beyond the Standard Model. Nevertheless, an extended Higgs sector is already highly constrained. The Higgs sector can also serve as a portal to new physics beyond the Standard Model. Finally, two Higgs wishlists are assembled that merit future study and clarification at the LHC and future collider facilities now under development.

Abstract In models with a U(1) gauge extension beyond the Standard Model, one can derive sum rules for the couplings of the theory that are a consequence of tree-level unitarity. In this paper, we provide a comprehensive list of coupling sum rules for a general SU 2 L × U 1 Y × U 1 Y ′ $$ \textrm{SU}{(2)}_L\times \textrm{U}{(1)}_Y\times \textrm{U}{(1)}_{Y^{\prime }} $$ gauge theory coupled to an arbitrary set of fermion and scalar multiplets. These results are of particular interest for models of dark matter that employ an extended gauge sector mediated by a new (dark) Z ′ gauge boson. For the case of a minimal extension of the Standard Model with a U 1 Y ′ $$ \textrm{U}{(1)}_{Y^{\prime }} $$ gauge boson, we clarify the definitions of the weak mixing angle and the electroweak ρ parameter. We demonstrate the utility of a generalized ρ parameter (denoted by ρ ′ ) whose definition naturally follows from the unitarity sum rules developed in this paper.

Searches for new neutral Higgs bosons of an extended Higgs sector at the LHC can be interpreted in the framework of the two-Higgs doublet model. By employing generic flavor-aligned Higgs-fermion Yukawa couplings, we propose an analysis that uses experimental data to determine whether flavor alignment is a consequence of a symmetry that is either exact or at most softly broken. We illustrate our proposal in two different scenarios based on a few 3 sigma (local) excesses observed by the ATLAS and CMS Collaborations in their searches for heavy scalars. In Scenario 1, an excess of events is interpreted as $A\to ZH\to \ell^+\ell^- b\bar{b}$ (where $\ell=e$ or $\mu$), with the CP-odd and CP-even neutral scalar masses given by $m_A=610$ GeV and $m_H=290$ GeV, respectively. In Scenario 2, an excess of events in the production of $t\bar{t}$ and $\tau^+\tau^-$ final states is interpreted as decays of a CP-odd scalar of mass $m_A=400$ GeV. Scenario 1 is consistent with Type-I Yukawa interactions, which can arise in a 2HDM subject to a softly-broken $\mathbb{Z}_2$ discrete symmetry. Scenario 2 is inconsistent with a symmetry-based flavor alignment, but can be consistent with more general flavor-aligned Higgs-fermion Yukawa couplings.

A bstract In models with a U(1) gauge extension beyond the Standard Model, one can derive sum rules for the couplings of the theory that are a consequence of tree-level unitarity. In this paper, we provide a comprehensive list of coupling sum rules for a general $$ \textrm{SU}{(2)}_L\times \textrm{U}{(1)}_Y\times \textrm{U}{(1)}_{Y^{\prime }} $$ SU 2 L × U 1 Y × U 1 Y ′ gauge theory coupled to an arbitrary set of fermion and scalar multiplets. These results are of particular interest for models of dark matter that employ an extended gauge sector mediated by a new (dark) Z ′ gauge boson. For the case of a minimal extension of the Standard Model with a $$ \textrm{U}{(1)}_{Y^{\prime }} $$ U 1 Y ′ gauge boson, we clarify the definitions of the weak mixing angle and the electroweak ρ parameter. We demonstrate the utility of a generalized ρ parameter (denoted by ρ ′ ) whose definition naturally follows from the unitarity sum rules developed in this paper.

In models with a U(1) gauge extension beyond the Standard Model, one can derive sum rules for the couplings of the theory that are a consequence of tree-level unitarity. In this paper, we provide a comprehensive list of coupling sum rules for a general SU(2)_L×U(1)_Y×U(1)_Y^' gauge theory coupled to an arbitrary set of fermion and scalar multiplets. These results are of particular interest for models of dark matter that employ an extended gauge sector mediated by a new (dark) Z ′ gauge boson. For the case of a minimal extension of the Standard Model with a U(1)_Y^' gauge boson, we clarify the definitions of the weak mixing angle and the electroweak ρ parameter. We demonstrate the utility of a generalized ρ parameter (denoted by ρ ′ ) whose definition naturally follows from the unitarity sum rules developed in this paper.

Received 18 May 2022DOI:https://doi.org/10.1103/PhysRevD.105.119902Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Research AreasExtensions of Higgs sectorPhysical SystemsHiggs bosonsHypothetical scalarsPropertiesSymmetriesParticles & Fields

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community.

The properties of the Higgs boson discovered at the Large Hadron Collider are very well described by the Standard Model (SM). Thus, any theory that invokes an extended Higgs sector must explain why the neutral scalar observed at the LHC so closely resembles the SM Higgs boson. In this talk, I review the Higgs alignment limit, in which one neutral scalar state of the Higgs sector is SM-like. An approximate Higgs alignment can be achieved "naturally" either via decoupling or via an approximate symmetry. Using the two-Higgs doublet model as a prototype for an extended Higgs sector, I examine the symmetries of the scalar potential and their soft breakings that may be responsible for the SM-like properties of the observed Higgs boson, and I demonstrate how to extend such (softly-broken) symmetries to the Yukawa sector of the model.

A future Higgs Factory will provide improved precision on measurements of Higgs couplings beyond those obtained by the LHC, and will enable a broad range of investigations across the fields of fundamental physics, including the mechanism of electroweak symmetry breaking, the origin of the masses and mixing of fundamental particles, the predominance of matter over antimatter, and the nature of dark matter. Future colliders will measure Higgs couplings to a few per cent, giving a window to beyond the Standard Model (BSM) physics in the 1-10 TeV range. In addition, they will make precise measurements of the Higgs width, and characterize the Higgs self-coupling. This report details the work of the EF01 and EF02 working groups for the Snowmass 2021 study.