# TF08 Snowmass Report: BSM Model Building

Convenors: Patrick J<EMAIL_ADDRESS>Graham D.
<EMAIL_ADDRESS>Hitoshi<EMAIL_ADDRESS>
Amin Aboubrahim  Institut für Theoretische Physik, Westfälische Wilhelms-
Universität Münster, Wilhelm-Klemm-Straße 9, 48149 Münster, Germany  Prateek
Agrawal  Rudolf Peierls Centre for Theoretical Physics, University of Oxford,
Parks Road, Oxford OX1 3PU, United Kingdom  Wolfgang Altmannshofer  Department
of Physics, University of California Santa Cruz, CA 95064, USA  Santa Cruz
Institute for Particle Physics, 1156 High St., Santa Cruz, CA 95064, USA
Howard Baer  Homer L. Dodge Department of Physics and Astronomy, University of
Oklahoma, Norman, OK 73019, USA  Avik Banerjee  Department of Physics,
Chalmers University of Technology, Fysikgården, 41296 Göteborg, Sweden  Vernon
Barger  Department of Physics, University of Wisconsin, Madison, WI 53706 USA
Brian Batell  Pittsburgh Particle Physics, Astrophysics, and Cosmology Center,
Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, USA
Kim V. Berghaus  C.N. Yang Institute for Theoretical Physics, Stony Brook
University, NY 11794, USA  Asher Berlin  Theory Division, Fermi National
Accelerator Laboratory, Batavia, IL 60510, USA  Nikita Blinov  Department of
Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada
Diogo Buarque Franzosi  Stockholm University, Department of Physics, 106 91
Stockholm, Sweden  Giacomo Cacciapaglia  Univ. Lyon, Université Claude Bernard
Lyon 1, CNRS/IN2P3,IP2I UMR5822, F-69622, Villeurbanne, France  Cari Cesarotti
Center for Theoretical Physics, Massachusetts Institute of Technology,
Cambridge, MA 02139, USA  Nathaniel Craig  Department of Physics, University
of California, Santa Barbara, CA 93106, USA  Csaba Csáki  Department of
Physics, LEPP, Cornell University, Ithaca, NY 14853, USA  Raffaele Tito
D’Agnolo  Université Paris-Saclay, CEA, Institut de Physique Théorique, 91191,
Gif-sur-Yvette, France  Jordy De Vries  Institute for Theoretical Physics
Amsterdam and Delta Institute for Theoretical Physics, University of
Amsterdam, Science Park 904, 1098 XH Amsterdam, The Netherlands  Nikhef,
Theory Group, Science Park 105, 1098 XG, Amsterdam, The Netherlands  Aldo
Deandrea  Univ. Lyon, Université Claude Bernard Lyon 1, CNRS/IN2P3,IP2I
UMR5822, F-69622, Villeurbanne, France  Matthew J. Dolan  ARC Centre of
Excellence for Dark Matter Particle Physics, School of Physics, University of
Melbourne, Victoria 3010, Australia  Patrick Draper  Department of Physics and
the Illinois Center for the Advanced Study of the Universe, University of
Illinois, Urbana, IL 61801  Gilly Elor  PRISMA+ Cluster of Excellence $\&$
Mainz Institute for Theoretical Physics Johannes Gutenberg University, 55099
Mainz, Germany  JiJi Fan  Department of Physics, Brown University, Providence,
RI, 02912, USA  Brown Theoretical Physics Center, Brown University,
Providence, RI, 02912, U.S.A.  Wan-Zhe Feng  Center for Joint Quantum Studies
and Department of Physics, School of Science, Tianjin University, Tianjin
300350, PR. China  Gabriele Ferretti  Department of Physics, Chalmers
University of Technology, Fysikgården, 41296 Göteborg, Sweden  Thomas Flacke
Center for AI and Natural Sciences, KIAS, Seoul 02455, Korea  Benjamin Fuks
Laboratoire de Physique Théorique et Hautes Energies (LPTHE), UMR 7589,
Sorbonne Université et CNRS, 4 place Jussieu, 75252 Paris Cedex 05, France
Keisuke Harigaya  CERN, Theoretical Physics Department, 1211 Geneva 23,
Switzerland  Julia Harz  PRISMA+ Cluster of Excellence $\&$ Mainz Institute
for Theoretical Physics Johannes Gutenberg University, 55099 Mainz, Germany
Anson Hook  Maryland Center for Fundamental Physics, University of Maryland,
College Park, MD 20742, USA  Seyda Ipek  Carleton University 1125 Colonel By
Drive, Ottawa, Ontario K1S 5B6, Canada  Andreas Karch  Theory Group,
Department of Physics, University of Texas, Austin, TX 78712, USA  Manuel
Kunkel  Institut für Theoretische Physik und Astrophysik, Uni Würzburg, Emil-
Hilb-Weg 22, D-97074 Würzburg, Germany  Benjamin Lillard  Department of
Physics and Illinois Center for the Advanced Study of the Universe, University
of Illinois, Urbana, IL 61801, USA  Matthew Low  Pittsburgh Particle Physics,
Astrophysics, and Cosmology Center, Department of Physics and Astronomy,
University of Pittsburgh, Pittsburgh, USA  Gustavo Marques-Tavares  Maryland
Center for Fundamental Physics, University of Maryland, College Park, MD
20742, USA  Rashmish K. Mishra  Harvard University, 17 Oxford Street,
Cambridge, MA, 02139, USA  Pran Nath  Department of Physics, Northeastern
University, Boston, MA 02115-5000, USA  Ethan T. Neil  Department of Physics,
University of Colorado, Boulder, Colorado 80309, USA  Luca Panizzi  Department
of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala,
Sweden  Werner Porod  Institut für Theoretische Physik und Astrophysik, Uni
Würzburg, Emil-Hilb-Weg 22, D-97074 Würzburg, Germany  Lisa Randall  Harvard
University, 17 Oxford Street, Cambridge, MA, 02139, USA  Matthew Reece
Harvard University, 17 Oxford Street, Cambridge, MA, 02139, USA  Tom Rudelius
Department of Physics, University of California, Berkeley, CA 94720, USA
Shadman Salam  Homer L. Dodge Department of Physics and Astronomy, University
of Oklahoma, Norman, OK 73019, USA  Leonard Schwarze  Institut für
Theoretische Physik und Astrophysik, Uni Würzburg, Emil-Hilb-Weg 22, D-97074
Würzburg, Germany  Dibyashree Sengupta  Department of Physics, National Taiwan
University, Taipei, Taiwan 10617, R.O.C.  Bibhushan Shakya  Deutsches
Elektronen-Synchrotron DESY, Notkestrasse 85, 22607 Hamburg, Germany  Jessie
Shelton  Department of Physics and Illinois Center for the Advanced Study of
the Universe, University of Illinois, Urbana, IL 61801, USA  Raman Sundrum
Maryland Center for Fundamental Physics, University of Maryland, College Park,
MD 20742, USA  Daniele Teresi  CERN, Theoretical Physics Department, 1211
Geneva 23, Switzerland  Christopher B. Verhaaren  Department of Physics and
Astronomy, Brigham Young University, Provo, UT, 84602 USA  Zhu-Yao Wang
Department of Physics, Northeastern University, Boston, MA 02115-5000, USA
Jure Zupan  Department of Physics, University of Cincinnati, Cincinnati, Ohio
45221, USA

(())

###### Abstract

We summarize the state of Beyond the Standard Model (BSM) model building in
particle physics for Snowmass 2021, focusing mainly on several whitepaper
contributions to BSM model building (TF08) and closely related areas.

Submitted to the Proceedings of the US Community Study

on the Future of Particle Physics (Snowmass 2021)

##  1 Executive Summary

Despite its phenomenal successes, the Standard Model (SM) can only be
considered a low-energy, effective field theory (EFT) description of particle
physics which leaves many unanswered questions about the nature of reality at
distance scales shorter than $\sim\mathrm{TeV}^{-1}$. Among these so-far
unanswered questions are the origin of the neutrino masses, an explanation for
the quark and lepton flavor structures, the absence of measurable CP violation
in QCD, and why the scales associated with gravity and weak interactions are
so disparate. The SM also does not explain the observed asymmetry between
matter and antimatter in the Universe. It is known that the cosmological dark
matter cannot be composed of SM fields and the origin of the periods of
accelerated expansion of the Universe are a mystery. Any explanation for these
above mentioned puzzles must involve physics beyond the SM.

Using these clues, and others, the goal of beyond the Standard Model (BSM)
model building is to uncover the next set of principles which determine how
Nature behaves at the shortest distance scales and to build the “next”
Standard Model that addresses one or more of these puzzles. At some level BSM
model building can be thought of as turning “why?” questions into “how?”
questions. While all BSM models follow the principle of _primum non nocere_ ,
there are a plethora of creative, testable ideas that have been proposed that
use a broad range of theoretical approaches. Some use concepts familiar from
the SM while others introduce completely new ideas and techniques. Many lead
to unique experimentally testable predictions, across experiments/observations
that span a vast range of scales. Model building is an integral part of many
other aspects of HEP, both taking inspiration from, and providing inspiration
to, other areas [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. Through BSM model building,
theorists have also been instrumental in leading the case for new experimental
programs, as well as motivating new search strategies at existing experiments
[11]. The success of the theoretical efforts has been strongly advanced by the
semi-automated event generation pipeline of FeynRules, the UFO file format,
and event generators (for additional details see Sec. 2.8 of [12]).

Understanding the origin and stability of the electroweak scale has long been
pursued by BSM model builders. The so-far null results of searches for new
particles from LEP through to LHC have demonstrated that many elegant models
are constrained, requiring some to substantial fine-tuning, or are simply not
viable. This is not a failure – on the contrary, this demonstrates the
remarkable success of the synergy between theory and experiment where ideas
are proposed, models are built, particles are predicted, parameters are
constrained, and then ideas/models are ultimately ruled out. Most BSM theories
addressing the hierarchy problem are only midway through this shakeout process
with experiment. Model-building remains an extremely active area to address a
range of the puzzles of SM, and continues to push the envelope of new
experimental probes to find or exclude the BSM ideas.

Flavor probes are highly sensitive to new physics, and the existing flavor
constraints are very stringent, with a handful of hints of deviations beyond
the SM. Many solutions to the hierarchy problem, such as composite Higgs
models, models with extra dimensions, and models with low energy
supersymmetry, all require a non-trivial flavor structure in order to avoid
experimental bounds on BSM flavor-violation. The origin of such non-trivial
new physics flavor structure is an open question, as is the origin of the
hierarchies in the spectrum of the SM quarks and leptons, the so-called SM
flavor puzzle. An important aspect of flavor model building is to construct
mechanisms that address such open issues, implement them in new physics
models, and derive phenomenological consequences. The recent hint for BSM
physics associated with flavor, from the muon anomalous magnetic moment and
the $B$ anomalies, could point to an exciting future ahead.

Cosmology and astrophysics have deep implications for BSM model building
beyond providing evidence of dark matter and dark energy. The early universe
may be considered as a “laboratory” equipped with a high-temperature bath. Its
dynamics allows us to probe particle physics models in a way that is
impossible at the present time. For example, particles that are too heavy
and/or too feebly interacting to be abundantly produced today can be easily
produced at much earlier times, potentially leading to observable signatures
(e.g., dark radiation in many extensions to the SM) or constraints on new
particle physics models. In addition to understanding the origin of the baryon
asymmetry, the cosmos is also filled with exotic objects such as neutron stars
and supernovæ that provide unique constraints on BSM models. Developments
within observational cosmology play an increasingly important role in guiding
model-building efforts, e.g. [13, 8, 14, 15, 16, 17, 18, 19, 20]. With the
impressive constraints from dark matter direct detection experiments, along
with the apparent excess of photons from the Galactic center and the
discrepancy between early and late measurements of the Hubble constant, the
area of dark matter/dark sector model building has seen substantial growth in
the last decade.

There has also been an ever increasing need to study the structure of models
using methods beyond perturbative calculations. For example, a recurring theme
in dark sector model building, and many other areas of BSM model building, is
extended gauge sectors in which a new gauge group becomes strongly-coupled at
scales relevant to the model. While effective field theory techniques and
“scaled up QCD” can provide some insights, definitive results require
dedicated lattice gauge theory simulations to study the non-perturbative
dynamics. As detailed in [5], there is a strong synergy between effective
field theory and lattice gauge theory that continues to inform and strengthen
our understanding of gauge theory with applications to model-building beyond
the SM. The list of applications is extensive: determining the properties of a
QCD axion requires input from lattice QCD simulations; lattice simulations of
the non-perturbative hadronic corrections to $(g-2)_{\mu}$; lattice
simulations of theories of strongly-coupled dark matter to determine the
strength of the self-interactions as well as between dark matter and the SM.

Since the last Snowmass the landscape of experimental results has grown
substantially e.g. many of the Higgs boson’s properties have been measured and
confirmed to be SM like while there is no clear evidence for new particles at
the LHC after Run 2, $(g-2)_{\mu}$ appears to be discrepant from the SM
prediction, there are numerous flavor anomalies involving $b$-quarks, and the
search for direct detection of dark matter has tightly constrained dark
matter’s properties. Alongside this evolution, the theory landscape has also
substantially altered, which we outline in more details below, based upon
contributions to TF08 [21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34,
35, 36, 37].

Figure 1: Model Building’s connections to other facets of the Snowmass
process.

##  2 Naturalness

Naturalness has been one of the guiding principles in the development of
Beyond the Standard Model (BSM) physics over the last several decades. Many of
the naturalness puzzles of the Standard Model arise in trying to understand
why a dimensionless number is small rather than $O(1)$, which might be viewed
as the generic expectation. These include the famous electroweak hierarchy
problem ($m_{h}^{2}/M_{\mathrm{Pl}}^{2}\ll 1$); the cosmological constant
problem ($\rho_{\Lambda}/M_{\mathrm{Pl}}^{4}\ll 1$); the strong CP problem
(effective ${\theta}\ll 1$); and the flavor problem ($y_{f}\ll 1$, or more
broadly, the peculiar structure of fermion masses and mixings).

The scope of ideas to address the hiearchy puzzles has grown substantially.
This includes such well-known scenarios as low-scale supersymmetry, composite
Higgs, and extra dimensions as standard frameworks for BSM physics (for a
recent review [34]). However, the lack of evidence for new states at the LHC
has widened the playing field to new ideas, such as neutral naturalness, that
may be able to address part of the hierarchy problem while avoiding the
substantial constraints from experiment. These various proposals are discussed
in turn below. Moreover, models that solve the naturalness problems of the
Standard Model often have one or more dark matter candidates, having the
potential to solve multiple problems within one framework. In this section, we
focus on the naturalness, while in Sec. 3, we discuss dark matter models and
mechanisms.

###  2.1 Supersymmetry

Supersymmetry is perhaps the best known solution to the electroweak hierarchy
problem, and proceeds by making the mass of a scalar proportional to that of a
fermion, which is itself protected by chiral symmetry. This symmetry must be
softly broken in order to be consistent with the non-observation of degenerate
superpartners. For excellent reviews, see e.g. [38, 39]. One of the conceptual
virtues of supersymmetry, beyond the fact that supersymmetry is the most
general space-time symmetry allowed by Nature, is that it provides a very
concrete theory in which quadratic divergences are absent. In supersymmetric
extensions of the Standard Model, the quadratic divergences indeed vanish and
are replaced by the mass splittings between Standard Model particles and their
superpartners.

The status of weak scale supersymmetry, in light of LHC data, is still far
from settled. At this point it is fair to say that supersymmetry has not yet
appeared where the simplest implementations in a weak scale model would have
led us to expect it. In its original incarnation, the MSSM now has to exist in
moderately fine-tuned [40, 41] regions of its parameter space; searches for
Higgsinos are of particular importance as a way of gauging the level of
tuning. That is not to say that supersymmetry could not appear above the TeV
scale (e.g., see [22]), but this leaves a fair bit of daylight between Nature
and naturalness expectations. It is also possible that the superpartners most
easily accessible at the LHC are beyond reach, as can occur in variants of
supersymmetry such as split-SUSY[42, 43], or that the structure of weak scale
supersymmetry is qualitatively different from the MSSM [44, 45, 46, 47].

###  2.2 Warped Extra Dimensions and Composite Higgs Theories

Warped extra dimensions (reviewed in [35]) have provided a major driving force
for many model building and phenomenological activities in high energy physics
in the last few decades. The initial work in the late 90’s on Randall-Sundrum
(RS) models, based on warped extra-dimensional geometry, was a new Beyond
Standard Model (BSM) framework to maintain the EW hierarchy and as an added
feature could naturally account for fermion hierarchies, making it one of the
few of the electroweak theories to naturally account for both hierarchies with
a single underlying mechanism. The experimental efforts to look for new
physics in this framework, both by direct production, or by precision
measurements, has been one of the drivers of our experimental programs–often
in ways applicable to other BSM scenarios. In another work with the same broad
motivation, ref. [48] constructed a 5D model where the KK states form a
continuum beyond a certain scale–a qualitatively different spectrum of new
physics states.

Models of electroweak symmetry breaking by a composite Higgs [49] with partial
compositeness [50] in the top-quark sector give promising solutions to the
hierarchy problem [51, 52, 53, 54, 55] of the Standard Model, extensively
reviewed in [36]. At the effective field theory level, they can be described
by specifying the pattern of symmetry breaking involved. Generically these
models predict the existence of light scalars in addition to the Higgs boson,
all emerging as pseudo Nambu-Goldstone bosons. Partial compositeness also
implies the presence of vector-like quarks. This proliferation of new
particles requires a systematic approach to study this class of models and to
facilitate a seamless transition between theory, data, and simulation codes.

There are many approaches to strongly-coupled electroweak symmetry breaking
scenarios [52, 53, 54, 55]. The most investigated ones include, e.g., 5D
holographic theories [56] and multi-site deconstructed models like Little
Higgs models [57]. There are also a class of composite Higgs models based on
4D asymptotically free (hypercolor) gauge theories. The assumption is that the
hypercolor theory, after going through a near conformal running [58, 59],
confines at the multi-TeV scale. To include top partial compositeness, its
fundamental degrees of freedom contain fermionic matter in two inequivalent
irreducible representations of hypercolor [60, 61], chosen in order to
sequester the EW coset from the composite states carrying QCD color. There are
two major types of experimental signatures in the low energy range. First, the
pNGB nature of the Higgs boson implies modifications of its couplings with the
other SM particles [62, 63, 64, 65, 66]. The other kind of signature involves
additional particles beyond the SM, predicted by these models, for example,
exotic electroweak pNGBs [67, 68, 69, 70], colored pNGBs [71, 69], vector-like
quarks [72, 73, 74, 75, 76, 77, 78] and other colored fermionic states in non-
triplet irreps [79], vector resonances [80, 81, 82, 83, 84], and axion-like
particles [85, 86].

These theories can also address the flavor structure of the SM, naturally
explaining neutrino masses and large mixing angles in the lepton sector
alongside small mixing angles in the quark sector. The scale of new physics
need not be exceptionally high, for example in RS models this arises due a RS
GIM mechanism [87, 88, 89, 90]. Nevertheless, a multi-TeV (or higher) scale
can pose challenges, but also in principle makes the framework more readily
testable than many flavor models–although signals can still be challenging.
More details on the flavor structure of the models is discussed in Sec. 5.

###  2.3 Neutral Naturalness

Higgs naturalness could arise by positing a new symmetry which relates the SM
quarks to colorless partners, which has become known as neutral naturalness
(reviewed in [23]). These are primarily bottom-up constructions that
characterize the new partner particles and interactions only up to the few TeV
scale and require completion at high energies, solving the so-called “little”
hierarchy problem. Typically, these completions include new colored states
with masses of order a few TeV, motivating future high-energy colliders to
thoroughly test Higgs naturalness due to new symmetries.

Realizations of neutral naturalness typically include a hidden, dark, or
secluded sector of particles that are related to at least some of the SM
fields by a discrete symmetry. Because at least some of the hidden-sector
particles are essential to explaining the mass of the Higgs boson, the Higgs
is a robust link between the sectors. Signals of these connections can appear
in deviations from the SM Higgs couplings and exotic Higgs decay modes that
can be probed at future Higgs factories. Examining the Higgs for indications
of these structures is highly motivated. The Higgs often acquires new, or
exotic, decay modes. The strengths of these couplings and the mass of the twin
fermions are both controlled by the ratio of the SM Higgs VEV to the twin
Higgs VEV, $v/f$. This quantity is also directly proportional to the tuning of
the model, making both Higgs coupling deviations and the invisible Higgs width
direct probes of naturalness.

While there are a variety of realizations of the idea of neutral naturalness,
the twin Higgs framework has received extensive analysis. This pertains to
higher-energy (UV) completions, collider phenomenology, dark matter
candidates, cosmological and astrophysical signals, and intersections with
neutrino and flavor physics. That this narrower focus has led to such a rich
variety of signals and overlaps with other aspects of beyond the SM physics is
impressive, but also points the way to further exploration through other
neutral naturalness models. For example, the so-called fraternal model [91]
makes $\mathbb{Z}_{2}$ breaking a main feature, only twinning the SM’s third
generation and allowing for modest deviations from the twin equality in some
couplings. In effect, the model keeps only the minimal ingredients required
for a twin-Higgs-like protection of the Higgs mass. In a similar vein, if the
twin top quark is taken to be vector-like then even the third generation
leptons can be removed without generating anomalies [92]. Rather than removing
entire generations from the mirror twin model, simply allowing significant
$\mathbb{Z}_{2}$ breaking between the fermion Yukawa couplings (other than the
top quark) is enough to eliminate some cosmological concerns [93]. In weakly-
coupled UV completions, a hard breaking of the $\mathbb{Z}_{2}$ in the quartic
terms of the scalar potential can further reduce the need for fine-tuning
[94].

Neutral naturalness models typically include a confining gauge group in the
hidden sector. In the case of a mirror twin Higgs model, this includes states
at or below the hidden confining scale, but this appears to be more the
exception than the rule. Without light quarks, which can be pair produced to
fragment tubes of confining color flux, states much heavier than the
confinement scale evolve as though connected by a string of constant tension.
These quirky bound states must shed energy until they reach low angular
momentum configurations, after which they can decay efficiently. In addition
to decays into SM vectors, the quirks or squirks have a significant branching
fraction into hidden gluons. Thus, heavy quirks can produce showers of
glueballs [95, 96]. Some fraction of these glueballs, the $0^{++}$ states,
have displaced decays back into the SM, leading to striking signatures at
current and upcoming colliders [97].

###  2.4 Cosmological Selection

The past decade has seen the emergence of several entirely new approaches, in
some cases inspired by proposals for the strong CP and cosmological constant
problems. Chief among these is relaxation of the weak scale. Aspects of these
approaches can be found in several whitepapers, including [37, 33, 34].

The original incarnation is the relaxion [98], with a QCD axion-like particle
$\phi$ coupled to the Standard Model with an additional inflationary sector
whose properties are necessarily somewhat special. The scalar field $\phi$
must transit very large field values so it is a non-compact field. Below the
QCD confinement scale, the coupling between $\phi$ and the gluon field
strength gives rise to the familiar periodic axion potential with the height
of the cosine potential typically $\Lambda^{4}\sim f_{\pi}^{2}m_{\pi}^{2}\sim
yvf_{\pi}^{3}$. The barrier height is linearly proportional to the Higgs VEV
since $m_{\pi}^{2}$ changes linearly with the quark masses.

The idea is thus: starting at values of $\phi$ such that the total Higgs mass
is large and positive, and assuming the slope of the $\phi$ potential causes
it to evolve in a direction that lowers the Higgs mass, the $\phi$ potential
will initially be completely dominated by the potential terms, until the point
at which the total Higgs mass-squared goes from positive to negative and the
Higgs acquires a vacuum expectation value. At this point the wiggles due to
the quark masses grow linearly in the Higgs VEV, and generically $\phi$ will
stop when the slope of the QCD-induced wiggles matches the slope of the
potential of $\phi$. This classical stopping point leads to a small
electroweak scale relative to moderately large cutoff scale (perhaps $10^{7}$
GeV or more).

There are challenges to protecting the shift symmetry of the relaxion over the
vastly trans-Planckian excursions in field space required to explain the value
of the weak scale, as enumerated by the Swampland program (see e.g. [99, 28]).

An alternative cosmological selection approach is to put many copies of the
Standard Model in the same universe, but explain why one copy acquires the
dominant energy density, called $N$-Naturalness [100]. $N$ sectors, e.g., $N$
copies of the Standard Model, are taken where from copy to copy, the Higgs
mass parameters are distributed in some range from $-\Lambda_{H}^{2}$ to
$\Lambda_{H}^{2}$ according to some probability distribution. For a wide range
of distributions, the generic expectation is that some sectors have
accidentally small Higgs masses, $m_{H}^{2}\sim\Lambda_{H}^{2}/N$. In a
universe with many sectors, the universe is populated by whatever sectors are
abundant. It is necessary that the cosmological mechanism preferentially
reheats sectors with smaller scales. The simplest way to accomplish this is to
imagine an inflationary epoch, followed by reheating due to the decay of some
reheaton.

Other ideas involve “trigger” operators [101] that play a privileged role in
cosmological solutions to the hierarchy problem. Only three such operators are
known and each leads to distinctive phenomenological predictions that are
completely different compared to traditional solutions to the hierarchy
problem. Triggers are therefore our best shot at discovering cosmological
selection of the weak scale, either through axion-like signatures
($G\widetilde{G}$) a new (quite special) Higgs doublet at HL-LHC [101]
($H_{1}H_{2}$) or new vector-like leptons at the HL-LHC [102].

###  2.5 Strong CP and Axions

The strong CP problem – why the effective $\theta\ll 1$ – remains one of the
vexing naturalness puzzles in the SM. There are numerous approaches to solving
the the strong CP problem. Perhaps the most famous solution posits a new
pseudoscalar field, the QCD axion, that dynamically adjusts its vev to cancel
the strong CP phase [103, 104, 105, 106, 107, 108, 109, 110]. Other approaches
to the strong CP problem are based on the observation that $\theta$ can
violate certain discrete symmetries and the renormalization of $\theta$ in the
Standard Model alone is minuscule [111, 112, 113, 114, 115, 116, 117, 118,
119].

Solutions to the strong CP problem involving axions have a wide range of
phenomenological and cosmological applications [31, 25]. One of the most
important axion interactions is its coupling to photons. Measuring this
coupling could give us information about the far UV of the SM. A thriving
experimental program is underway to detect axions, with a lot of synergy
between theory and experiment, and a number of new experimental proposals on
the horizon [120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132,
133, 134, 135, 136, 137, 138, 139, 140, 141]. The broad array of employed
technologies, and their associated range of sensitivities in mass-coupling
plane, has motivated a rejuvenation of axion model building where the axion’s
properties are varied away from the naïve expectations [142, 143, 144].

Axions can also play a role in large-field inflation. The periodic shift
symmetry $a\rightarrow a+2\pi f_{a}$ naturally protects axions from Planck-
suppressed operators, which generically spoil large-field inflationary models.
Axions acquire a periodic potential from instantons of the form
$V(a)=\Lambda^{4}\sin(a/f_{a})$, which for $f_{a}>M_{\textrm{Pl}}$ leads to a
large-field model of inflation called natural inflation [145], which can be
distinguished from other models of inflation by the spectral tilt and tensor-
to-scalar ratio of the primordial power spectrum. However, quantum gravity
appears to censor such natural inflation models. Within string theory, axion
decay constants are constrained in all known examples to satisfy
$f_{a}<M_{\textrm{Pl}}$ [146], and $f_{a}<M_{\textrm{Pl}}$ is a generic
prediction of the axion version of the “Weak Gravity Conjecture” [147]. Models
of natural inflation involving multiple axions [148, 149, 150] are similarly
constrained by the Weak Gravity Conjecture [151, 152, 153, 154, 155, 156].
Although loopholes to these constraints exist [157, 152, 155, 158, 159], it is
unclear whether or not these loopholes can be successfully threaded in a UV
complete theory of quantum gravity [160]. Indeed, surveys of axion landscapes
in string theory have so far found them to be barren of large-field natural
inflation [151, 161, 162].

For the axion to produce a sufficiently small effective value of $\theta$, the
Peccei-Quinn symmetry must be very nearly conserved, with no sources of
explicit $U(1)_{\text{PQ}}$ violation other than QCD itself, otherwise the
minimum of the axion potential shifts away from the desired value of
$\theta(a)=0$. This is the axion quality problem: the $10^{-10}$ fine tuning
associated with $\theta$ has only been shifted into a different (and more
severe) fine-tuning in the corrections to the axion potential. This
requirement may be in tension with general expectations about quantum gravity
since gravitational effects are not expected to respect global symmetries and
thus provides an example of insights from high scale physics affecting BSM
physics, more of this will be discussed in the next section. Several solutions
have been proposed and recently there have been developments both in field-
and string-theoretic model building. For instance, in “accidental” axion
models the PQ-charged fields are also charged under some locally conserved
symmetries, so that all gauge-invariant PQ-charged operators are necessarily
higher-dimensional, and the PQ breaking $\sim(f_{a}/M_{p})^{n}$ is suppressed
by multiple powers of the Planck mass $M_{p}$. The local symmetry may be
discrete [163, 164, 165, 166] or continuous [167, 168, 169, 170, 171, 172]. In
composite axion models [173, 174, 175, 176, 177, 178] the axion is a baryon-
like particle, composed of quarks charged under a strongly coupled non-Abelian
gauge group. In these models the confining dynamics often instigate the
spontaneous breaking of $U(1)_{\text{PQ}}$, so that the scale $f_{a}$ is
generated dynamically.

###  2.6 Quantum Gravity Implications: Swampland

From the absence of global symmetries to the sub-extensive entropy of black
holes, there is unambiguous evidence that the rules of effective field theory
(EFT) consistency as currently understood are not enough to describe even the
low energy regime of theories that admit a gravitational UV completion
(reviewed in [28]). Quantum gravity provides us with powerful reasons for
seeking theories that are truly natural, in the sense that they explain small
dimensionless numbers in terms of $O(1)$ inputs.

The expectation that there are no global symmetries in quantum gravity, and
that at the UV cutoff scale there are not even approximate ones, provides a
strong impetus, beyond simple aesthetic considerations, for the traditional
model-building goal of explaining small numbers of the theory in terms of
reasonable inputs. Technical naturalness can be a useful guiding principle for
IR effective field theories, but a complete theory must go beyond it. This is
not to say that a number cannot be small simply because of an accidental
cancelation, although quantum gravity may also constrain how many such fine-
tunings can occur [179]. It does mean that hierarchies that are not
technically unnatural, like the flavor hierarchies, are important puzzles that
could shed light on UV physics.

A general consequence of approximate global symmetries is a lowering of the
cutoff scale as $\sim M_{\text{Pl}}/\sqrt{\log x^{-1}}$, with $x$ some
parameter such that the limit $x\rightarrow 0$ restores the corresponding
symmetry. For example, $x=y_{f}$ for a fermion chiral symmetry, or
$x=\mu^{4}/M_{\text{Pl}}^{4}$ for the shift-symmetry of an axion, with
$\mu^{4}$ the contribution to the axion potential. This conclusion seems a
reasonable lower bound on the “cost” of realizing an approximate global
symmetry, but it is not the whole story.

An alternative realization of an approximate global symmetry can be obtained
by taking the weak coupling limit of a gauge theory. In this case, the
obstruction to recovering an unbroken global symmetry is embodied by the Weak
Gravity Conjecture (WGC) [147] (see e.g. [99] for a recent review). Loosely
speaking, the WGC implies the presence of “super-extremal” degrees of freedom,
whose charge-to-mass ratio is larger than that corresponding to an extremal
black hole. Perhaps the most notable consequence of this statement is the
existence of an upper bound on the cutoff scale of a $U(1)$ gauge theory given
by $\Lambda\lesssim gM_{\text{Pl}}$, related to the presence of new dynamics
linked to the existence of magnetic monopoles that satisfy the super-
extremality bound [147]. A more sophisticated version of this statement, but
that nevertheless seems to be satisfied in all known examples, suggests that a
full _tower_ of super-extremal states should be part of the theory [180, 181,
182, 183]. In combination with the species bound (the expectation that gravity
becomes strong at the scale $\Lambda_{\mathrm{QG}}\sim
M_{\mathrm{Pl}}/\sqrt{N}$ [184, 185] in a theory with $N$ degrees of freedom),
this translates into $\Lambda_{\text{QG}}\sim g^{1/3}M_{\text{Pl}}$ [181,
186]. (Remarkably, the same $g^{1/3}$ scaling on the cutoff appears from an
entirely different argument involving massive Stueckelberg gauge fields
[187].) In other words, the cost of approaching a global symmetry by taking
the $g\rightarrow 0$ limit of a gauge theory appears to be power-law rather
than logarithmic. This is a much more severe cost, and a stronger constraint
on model-building.

##  3 Dark Matter

The existence of DM is one of the most compelling pieces of evidence for
physics beyond the SM. The most detailed understanding of DM arises from its
gravitational imprints on cosmological observables, most notably from its
effects on the acoustic peaks of the CMB angular anisotropies. Such
observations have informed us of the abundance and general characteristics of
DM when the universe was only $O(10^{5})$ years old. While its general
particle physics description currently remains unknown, any DM candidate must
be consistent with a plethora of terrestrial, astrophysical, and cosmological
probes. At a minimum, any theory of DM must posit something that is non-
relativistic, essentially collisionless, feebly-coupled to normal matter, and
stable. Even with these restrictions, the theory space is incredibly vast.
Over the past decade the broadening of theory priors has enlarged the
exploration of this theoretical landscape. This is due in part to: 1) the null
results at large underground direct detection experiments and high-energy
colliders and 2) the realization that the strong empirical evidence for DM
motivates an examination of viable models beyond just those tied to other top-
down motivations of new physics.

Continued development of experimental technologies has also driven theoretical
investigations into the nature of DM. For instance, low-threshold detectors
sensitive to the sub-eV energy deposition of sub-MeV DM have fueled the
exploration of cosmologically viable and detectable light DM candidates, while
developments in precision sensors for ultralight bosonic DM across a wide
range of mass scales have led to the identification of new cosmological
targets within the larger parameter space [14, 15, 16].

###  3.1 Interaction Mechanisms

In classic _freeze-out_ , the DM abundance is depleted through a two-to-two
scattering process until its rate drops below the Hubble expansion rate, at
which time its co-moving number density is (again) conserved. To get an
abundance in agreement with observations requires a thermally-averaged
annihilation cross-section, $\langle\sigma v\rangle\sim 10^{-26}\;{\rm
cm}^{3}/s$. For $O(1)$ coupling sizes, this famously points to a DM mass
around $0.1$-$1$ TeV. As described, the classic freeze-out scenario is highly
predictive, though it can be significantly altered through various
modifications to the framework above. There are a host of “exceptions” to
thermal freezeout that began with the classic work from Griest and Seckel
[188].

DM may not annihilate substantially with the visible sector; instead, it might
annihilate or be converted into a secondary state ($\chi^{\prime}$) which
itself has interactions with the SM. The evolution of DM depends sensitively
on the mass of the secondary state. If $m_{\chi}\gg m_{\chi^{\prime}}$, dark
matter is in the secluded regime [189], where the annihilations proceed as in
classic freeze-out requiring $\left\langle\sigma v\right\rangle\sim
10^{-26}~{}{\rm cm}^{3}/{\rm sec}$ while the direct detection signal can be
negligible.

If $m_{\chi}\simeq m_{\chi^{\prime}}$, thermal freeze-out of both $\chi$ and
$\chi^{\prime}$ must be studied in parallel and the dynamics depend on whether
$\chi^{\prime}$ annihilates or decays to deplete its abundance. If
$\chi^{\prime}$ annihilates, and the DM annihilation cross-section is similar
to classic freeze-out (though to dark states), the process is termed
coannihilation [188]). Coannihilating DM can have direct detection and
indirect detection rates comparable to that of classic freeze-out suppressed
by a loop factor.

_Forbidden DM_ [188, 190] is the same $2\rightarrow 2$ process of classic
freeze-out, but with the mass of the DM slightly below that of the outgoing SM
state. This process, forbidden at zero temperature, has an exponentially
suppressed rate proportional to $e^{-\Delta E/T}$, where $\Delta E$ is the
energy threshold for the process.

DM densities can be substantially influenced by $3\rightarrow 2$ or
$4\rightarrow 2$ interactions, also known as a phase of cannibalism [191]. The
dynamics during a cannibal phase depend on whether DM is chemically coupled to
the SM, kinetically coupled to the SM, or neither. If DM is both chemically
and kinetically coupled, its bulk properties are unchanged over time. If it is
only kinetically coupled, its number density drops, but its energy is
transferred to the SM as is the case for SIMPs [192], co-SIMPs [193], and
ELDERs [194].

The dark sector may be populated by the leakage of energy from the visible
sector through sub-Hubble rate annihilations or decays of SM particles over
time [195, 196, 197]. This production mechanism is known as freeze-in because
in many respects it is the opposite of freeze-out; the DM in non-thermal. Many
freeze-out processes can be time-reversed to provide a channel for freeze-in,
and the relationship between couplings and DM abundances have opposite
behaviors for freeze-out and freeze-in. Due to the smallness of coupling
strengths relevant for freeze-in, the DM candidate in such models is sometimes
called a Feebly Interacting Massive Particle (FIMP). The freeze-in parameter
space is an extreme limiting case because it represents the smallest relevant
coupling the DM can have with the SM plasma that affects early-universe
observables in any meaningful way. Historically, some classic examples of DM
candidates with freeze-in production mechanisms include sterile neutrinos
[198, 199, 200, 201], singlet scalars [202], and various particles in
supersymmetric models including sneutrinos [203, 204, 205, 206], axinos and
neutralinos [207, 208, 209, 210], gravitinos [211, 212, 213, 214, 215, 216],
goldstinos [217], and photinos [218].

_Asymmetric dark matter_ posits a common origin for the baryon content of the
Universe and DM (see Ref. [219] for an early suggestion in this direction).
Since the former is set by an asymmetry, based on various direct and implicit
empirical arguments, the DM abundance would also be taken to correspond to an
asymmetry of DM over its antiparticle. A generic requirement of such models is
the presence of sufficiently strong interactions that can lead to efficient
elimination of the symmetric populations in both the visible and the dark
sectors. For baryons, this is achieved by the presence of strong interactions
in the low energy regime of QCD, while the requirement that the same occurs
for asymmetric dark matter places restrictions on the new physics.

There is a multitude of models of asymmetric dark matter (for reviews see
Refs. [220, 221, 222]). There is no clear way to assign various asymmetric
dark matter models to a few distinct classes. Nevertheless, there are some
general features that broadly define different scenarios: (A) where a quantum
number has an asymmetry that gets shared between the dark and visible sectors
and (B) those that postulate a generalized “baryon number” that is preserved,
with equal and opposite baryon and dark asymmetries.

_Sommerfeld enhancement_ [223, 224] appears whenever the dark sector system is
such that effectively long-range forces arise in the non-relativistic limit.
Here, at non-relativistic velocities, a potential between the incoming DM
particles leads to the formation of off-shell bound states, and significantly
affects the interaction amplitude. This can lead to a strongly enhanced late-
time annihilation signal and needs to be taken into account for the freeze-out
calculation, as well as present-day indirect detection observables.

On-shell bound-state formation is a related process that has been investigated
more recently [225, 226, 227]. Its effect on the DM abundance [228, 229] and
late-time signatures [230] become increasingly important with growing dark-
sector coupling. A particularly interesting case is DM with EW charges. In
particular for $SU(2)$ representations larger than 3, the effective coupling
strength is large enough to support effective bound state formation [230,
231].

_Inelastic dark matter_ (e.g., [232, 233, 234, 235, 236, 237, 238, 239, 240,
241, 242]) posits that the predominant interaction of dark matter with
Standard Model particles is mediated by an interaction
$X_{1}X_{2}\mathcal{O}$, where $\mathcal{O}$ is an operator built from
standard model field(s). There are numerous models of ineleastic dark matter,
where the inelastic interaction could be dimension-4, e.g., interacting with
the $Z$ or Higgs boson, or a higher dimensional interaction. The initial
kinetic energy of the $X_{1}$-nuclear system must be greater than the mass
difference ($\delta\equiv m_{\rm X_{2}}-m_{\rm X_{1}}$) between $X_{1}$ and
$X_{2}$ in order for scattering to take place. The fact that _only_ DM with
sufficiently large kinetic energy can scatter has important consequences.
First, because inelastic dark matter must impinge with sufficiently large
kinetic energy to scatter with a direct detection target nucleus, the
available kinematic phase space for DM-nuclear scattering is reduced, and the
effective DM-nuclear scattering rate is suppressed. The amount of suppression
will depend on what fraction of dark matter in the Galactic halo has enough
kinetic energy to overcome the inelastic scattering energy threshold. Next,
the minimum required energy for inelastic DM-nuclear collisions implies a
minimum recoil energy in the detector, $E_{\rm R}^{\rm min}$. Traditional dark
matter searches have optimized sensitivity to _elastic_ DM-nuclei collisions
by focusing on the limit $E_{\rm R}^{\rm min}\rightarrow 0$, and pushing the
observed recoil energy window as low as backgrounds and detector sensitivities
allow. For inelastic dark matter with a sizable mass splitting, a low maximum
recoil energy reduces detector sensitivity. At best, a low maximum recoil
energy will be sub-optimal for detecting inelastic dark matter. At worst, if
the dark matter’s _minimum_ inelastic recoil energy lies above the window of
recoil energies, considered in a direct detection analysis, the experiment is
insensitive to inelastic dark matter.

###  3.2 Models

_Supersymmetric dark matter_ appears in R-parity conserving weak scale
supersymmetric theories, where the lightest superpartner is expected to be
absolutely stable. The minimal content of a supersymmetric theory includes
superpartners of all the SM particles, the Minimal Supersymmetric Standard
Model (MSSM) (see for eg. Refs. [38, 243]). Further, unlike the SM,
supersymmetry requires at least two Higgs doublets, one coupling to all the
up-type fermions and the other to down-type fermions. Therefore, at a minimum,
supersymmetry would include fermionic superpartners of these Higgs bosons and
the SM gauge bosons. In the presence of non-minimal field content, there may
be additional neutral fermionic states. A popular example is the Next-to-
Minimal Supersymmetric SM (NMSSM) (see for e.g., Ref. [244]) which includes an
additional singlet superfield coupling only to the Higgs superfields. Any one
of the weakly charged, electrically neutral set of these neutralinos can be
excellent thermal WIMP DM candidates. A key difference between a SUSY
neutralino dark matter candidate and a “random stable fermion” is the expected
presence of a set of correlated states in SUSY.

Since the couplings of the winos and Higgsinos are large and they are further
accompanied by almost mass-degenerate charged states (the charginos),
consistent relic density is obtained for DM masses of the order of the TeV
scale [245, 246, 247]. However, weak scale bino or singlino DM candidates may
realize an observationally consistent relic density without necessitating TeV
scale winos and Higgsinos. An observationally consistent relic density for
either binos or singlinos may be obtained by a wide variety of processes [248,
249, 250].

_Dark matter in composite Higgs theories_ can be easily obtained in
holographic composite Higgs scenarios by introducing a suitable discrete
symmetry that makes some of the massive KK modes stable.***From the
4-dimensional effective description perspective, this corresponds to identify
the DM candidate with a heavy massive resonance coming from the composite
dynamics. Two types of symmetries are often considered in the literature:
discrete exchange symmetries that relate different copies of the bulk fields
[251], and geometrical parity symmetries†††This type of symmetries are
analogous to KK parity in universal extra dimension models (see for instance
[252]). connected to the $S_{1}/Z_{2}$ orbifold structure representing the
extra spatial dimension (see for instance [253]).

Since all the fields propagating in the bulk of the extra dimension give rise
to KK modes, there are different options for the DM candidate. A natural
option is to identify the DM with a $\mathbb{Z}_{2}$-odd vector KK mode
associated to a 5-dimensional gauge field. Gauge singlet candidates are easily
obtained if the 5-dimensional gauge symmetry of the model (corresponding to
the global symmetry of the composite sector) contains ${\rm U}(1)$ subgroups.
This happens, for instance in the minimal models with custodial symmetry,
based on the coset ${\rm SO}(5)\times{\rm U}(1)_{\textsc{x}}/{\rm
SO}(4)\times{\rm U}(1)_{\textsc{x}}$ [51]. Models featuring vector DM states
have been constructed both on warped space [254, 255] and on flat space [251,
256].

_Strong-coupled composite dark matter:_ It is also possible that the DM is a
stable bound state of a confining dark sector. Depending on the details of the
model, different symmetries can guarantee the stability of various DM
candidates [257, 258, 259, 260, 261]. Given their rich dynamics, the confining
dark sectors can give rise to many interesting observable phenomena. Below we
review different DM candidates in such sectors and some intriguing dynamics
that can happen therein, see Refs. [260, 262, 263] for recent reviews of such
models.

Dark pions can become stable kinematically or through various symmetries,
giving rise to dark meson DM candidates, see for instance Refs. [238, 264,
265, 266, 267, 259, 268, 269, 270, 271, 272, 262, 273]. These dark mesons are
composed of a dark quark and a dark anti-quark and are always bosons,
regardless of the spin of dark quarks.

A more natural possibility, in direct analog with the SM, is that $N$ dark
quarks are charged under a dark confining $SU(N)$ form a color-neutral and
stable baryon that can account for the observed DM abundance today, see for
instance [257, 274, 275, 266, 258, 259, 276, 269, 277, 278, 262]. Depending on
$N$, such baryons can be either fermions or bosons. Stability of such
candidates can be guaranteed in many different ways, including by conservation
of dark baryon number.

Finally, yet another potential DM candidate from confining dark sectors are
glueballs, see for instance Refs. [279, 280, 281, 282, 283]. The spectrum of
glueballs in pure confining gauge groups has been studied extensively in the
literature, see for instance Refs. [284, 285]. It is shown that many glueball
states with different parity and charge-conjugation properties can exist in
the spectrum of any confining gauge theory. Interactions of various glueball
states within a pure Yang-Mills theory have been studied in Ref. [283].

_Atomic/Mirror dark matter_ posits that DM could exist in atom-like bound
states. Such dark atoms have a long history (see Refs. [286, 287]) and occur
naturally in mirror twin Higgs models (see e.g. Refs [288, 289, 290, 291, 292,
91, 293, 294, 295, 296, 297, 93, 298, 299, 300, 301, 302, 303, 304, 305, 306,
307, 308, 309, 310, 311, 312, 313, 314, 315, 316]). In its simplest
implementation, atomic DM [317, 318, 319, 320, 321, 322, 323, 324, 325, 326,
327, 328, 329, 330, 331, 332, 333, 334, 335, 336, 337, 338, 339] is made of
two fermions of different masses oppositely charged under a dark $U(1)_{\rm
D}$ gauge symmetry [340, 341]. More complex scenarios in which one or both
constituents of the dark atoms are themselves composite particles (such as
dark nucleons) have also been considered. Similar to the visible sector, the
presence of atomic DM generally requires a matter-antimatter asymmetry in the
dark sector to set its relic abundance, although it is also possible for a
symmetric component to survive [342], resulting in a mixture of darkly-charged
DM [343, 344, 345] and dark atoms.

_Light dark matter_ is an entire class of models in which dark matter has sub-
GeV mass, and is invisible to ton-scale nuclear recoil detectors (reviewed in
[346, 347]). As $m_{\chi}$ decreases, $n_{\chi}$ increases, so experiments
with relatively small targets (gram-scale rather than ton-scale) can have
comparable discovery prospects for the same thermally-motivated cross
sections, if the energy threshold can be reduced. Furthermore, from the point
of view of maximizing the DM signal, it is optimal to have systems with
available excitations that match the low energies and momentum transfers
associated with DM masses in the keV–GeV range. Since the DM mass is much
lower than a nucleus mass in this regime, nuclear recoils are a poor kinematic
match, but the wide range of available excitations in condensed matter systems
offers a promising way forward.

There are several mechanisms that light dark matter can employ to get the
correct relic abundance, see Sec. 3.1. The thermal histories for sub-GeV dark
matter require, at a minimum, one additional ingredient: a new force which
mediates the thermal contact between the dark matter and the SM. Indeed, dark
matter cannot interact with the SM through the strong force (otherwise it
would not be “dark” with respect to baryons), and neither can it be the weak
force, which has too small of an annihilation cross section to generate the
correct relic abundance of sub-GeV dark matter [348]. In principle, it could
be the photon if dark matter had a small enough electric charge to be
cosmologically “dark”, but the CMB excludes this possibility for freeze-out
because such a small charge would not lead to sufficient annihilation and
would yield an overabundance of DM unless other annihilation channels are
introduced [349]. Hence, a benchmark model of such a new force is a _dark
photon_ [350, 351]. In this model, dark matter has a charge $g_{D}$ under a
“dark” version of electromagnetism, but unlike electromagnetism, the dark
photon is massive, in many models comparable to the dark matter mass itself.
The experimental and observational program to search for dark photons,
motivated in part by developments in BSM model building, is one of the major
developments over the past decade [352].

_Axion and wave-like dark matter:_ The existence of dwarf galaxies means that
Dark Matter whose mass is below $\sim\mathrm{keV}$ scale must be bosonic and
furthermore that such dark matter must be heavier than
$10^{-22}\;\mathrm{eV}$. Such ultra-light dark matter has a high number
density in our galaxy and is best understood in terms of classical waves. The
(QCD) axion is the quintessential example, and there has been a resurgence in
interest over the last decade as direct searches for particle dark matter
become ever more constraining.

The non-thermal production of the axion is closely related to when and how the
$U(1)_{PQ}$ symmetry is spontaneously broken in the early universe. If such
breaking occurs after inflation, the radial mode is initially trapped at the
origin and later rolls towards the potential minimum, spontaneously breaking
the symmetry. At this time, the axion obtains random field values in different
patches of the universe. There is an irreducible abundance from the
misalignment mechanism [353, 354, 355] and the domain-wall network. Since the
axion field is randomized, the axion field must have a spatial average of the
misalignment angle. To explain the observed DM abundance, this misalignment
contribution alone predicts an axion mass of order $m_{a}\simeq 30~{}\mu{\rm
eV}$ (or $f_{a}\simeq 2\times 10^{11}{\rm GeV}$) for the QCD axion and
$m_{a}\simeq 600~{}\mu{\rm eV}~{}(10^{12}{\rm GeV}/f_{a})^{4}$ for ALPs. In
addition to axion misalignment, topological defects [356, 357], such as axion
strings and domain walls, will also form. The decay of the axion-string and
domain-wall network radiates axions, which also contribute to the DM
abundance. An accurate determination of the total axion abundance in this
scenario requires lattice simulations because of the complex dynamics involved
from the $U(1)$ symmetry breaking to the late-time oscillations. There have
been extensive efforts dedicated to this numerical study [358, 359, 360, 361,
362, 363, 364, 365, 366, 367, 368]. In the case where the domain wall number
is larger than unity, the domain walls are stable and will overclose the
universe. This issue is avoided if explicit $U(1)$ breaking is introduced so
that the domain walls decay and make an additional contribution to the axion
abundance [369, 370, 371, 372, 359, 373, 374, 375], which allows for a smaller
$f_{a}$ to still explain DM.

If the symmetry is instead broken before or during inflation, the field values
of both modes will be homogenized by inflation up to possible quantum
fluctuations and the misalignment angle $\theta_{i}$ is a constant throughout
the observable universe. The axion abundance, therefore, depends on the value
of $\theta_{i}$. The observed DM abundance is reproduced by $m_{a}\simeq
10~{}\mu{\rm eV}\times\theta_{i}^{12/7}$ (or $f_{a}\simeq 6\times 10^{11}{\rm
GeV}/\theta_{i}^{12/7}$) for the QCD axion and $m_{a}\simeq 7\;{\rm
meV}/\theta_{i}^{4}\times(10^{12}\;{\rm GeV}/f_{a})^{4}$ for ALPs. Thus, a
large decay constant, as motivated by string theory or grand unification of
the gauge and $U(1)$ symmetries [376, 377], needs a small $\theta_{i}$ to
avoid overabundance. Similarly, a small decay constant calls for an angle very
close to the hilltop of the cosine potential, $\theta_{i}\rightarrow\pi$, in
order to exploit the inharmonicity. In the simplistic scenario, a very
small/large $\theta_{i}$ has to come from a tuned initial condition. However,
a small angle may also result from the early relaxation of the axion field
during or after inflation (a large angle is similarly achieved with a further
phase shift of $\pi$ [378, 379, 380]) if the axion mass is larger in the early
universe [381, 382, 383, 384] or if inflation lasts a very long time [385,
386, 387, 388].

_Other models of dark matter:_ There are a plethora of other models of dark
matter with intriguing properties and signals that we can only briefly mention
due solely to space limitations of this summary report. This includes _sterile
neutrino dark matter_ (reviewed in [37]), _ultraheavy dark matter_ (reviewed
in [27]), _dynamical dark matter_ (reviewed in [389]), and _hidden sectors and
a multi-temperature universe_ (reviewed in [21]).

##  4 Baryogenesis

There is more matter than antimatter in the Universe. This asymmetry,
quantified as the ratio of baryon density to photon density, is measured at
the time of Big Bang Nucleosynthesis (BBN) and the Cosmic Microwave Background
(CMB) to be
$(n_{b}-n_{\overline{b}})/n_{\gamma}=n_{b}/n_{\gamma}=\left(6.10\pm
0.4\right)\times 10^{-10}\,$ [390]. Inflation dictates that such an asymmetry
must be dynamically generated after reheating, necessitating a mechanism of
_baryogenesis_.

In order to produce a matter–antimatter asymmetry, a model of particle physics
must satisfy the so-called Sakharov conditions [391]. These are: (i) Baryon
number ($B$) violation, (ii) $C$ and $CP$ violation, and (iii) departure from
thermodynamic equilibrium. In the Standard Model (SM), (i) Baryon number is
anomalously violated in the weak interactions of the SM. Although the rate of
$B$-violating _sphaleron_ processes is exponentially suppressed at zero
temperature, sphalerons are very efficient at temperatures at which
electroweak symmetry is restored, $T\gtrsim 130$ GeV [392, 393]. (ii) There is
$CP$ violation in the CKM matrix, and possibly in the PMNS matrix [394]. It
has been argued that the CKM phase is not sufficient (in fact orders of
magnitude too small) for producing the baryon asymmetry of the Universe.
Within the SM there is no process to employ the $CP$ violation in the PMNS
matrix to produce the asymmetry. (iii) There are many ways a process could
occur out of thermal equilibrium, such as particle decay at temperatures below
its mass, or a first-order phase transition. There is no process in the SM
that goes out of thermal equilibrium in the early Universe. These shortcomings
of the SM are a clear sign of BSM physics. By the nature of the problem, these
observations and the related new physics have strong implications for early
Universe cosmology. Beyond-the-Standard Model models that seek to explain the
baryon asymmetry invoke certain ingredients to satisfy the Sakharov
conditions.

The question of generating the baryon asymmetry of the universe has been
around for several decades. Leptogenesis is perhaps the best known model
[395], where a lepton asymmetry is generated by right-handed neutrino decays
and transferred to a baryon symmetry though electroweak sphalerons.
Electroweak baryogenesis (reviewed in [396, 397, 398, 399, 400]) is also a
well-known mechanism where the baryon asymmetry is generated during the
electroweak phase transition. Nevertheless, there continue to be new ways to
address this mystery, inspired by new theoretical ideas and observational
opportunities. In the reviews [24, 37], numerous baryogenesis mechanisms have
been discussed, with a focus on those developed in the last decade. A salient
aspect of many of these contributions is experimental testability: while the
vast majority of traditional baryogenesis models have involved high-scale
physics and hence are difficult to probe experimentally, many new BSM models
produce the baryon asymmetry at low scales and involve low-scale new physics,
and are therefore experimentally observable. Many of these new models are
expected to produce signals at multiple experiments, allowing for a multi-
prong search for new physics (see [24] for details).

##  5 Flavor Model Building

Flavor violating processes, in particular those involving flavor changing
neutral currents (FCNC) have exquisite sensitivity to new sources of flavor
and CP violation beyond those of the SM [30]. This high sensitivity to new
physics has its origin in the small amount of flavor breaking that is present
in the SM. In the SM, the only sources of flavor violation are the
hierarchical Yukawa couplings of the Higgs. The origin of the SM arrangement
of the various quark and charged lepton masses, the hierarchical structure of
the CKM matrix, and the absence of visible hierarchies in the PMNS matrix is
often referred to as the SM flavor puzzle. Various classes of ideas exist to
solve this puzzle: horizontal flavor symmetries [401], warped extra dimentions
[402, 403], partial compositeness [50, 51, 56, 404], and radiative fermion
masses [405]. In the SM, the quark FCNCs are suppressed by a loop factor and
by small CKM matrix elements. As long as theoretical uncertainties in the SM
predictions are under control, quark flavor violating processes can indirectly
explore very high mass scales, in some cases far beyond the direct reach of
collider experiments. In the lepton sector, SM predictions for FCNCs are
suppressed by the tiny neutrino masses and below any imaginable experimental
sensitivities. Electroweak contributions to electric dipole moments are also
predicted to be strongly suppressed in the SM, several orders of magnitude
below the current bounds. Charged lepton flavor violation and electric dipole
moments are thus null tests of the SM. Any observation of such processes would
be an unambiguous sign of new physics.

In the SM, the Yukawa couplings of the Higgs to the fermions are the only
sources of flavor violation. Therefore, the Higgs might be the window into
understanding flavor, with the precision Higgs program at the LHC, and in the
future also at a Higgs factory, able to provide valuable inputs. In
particular, Higgs decays involving tau, $h\to\tau\mu$ and $h\to\tau e$, are
cases where the direct searches at the LHC are the most sensitive probes.

In addition to long-standing puzzles, in the last several years a number of
“flavor anomalies” have created considerable excitement in the community.
Discrepancies between SM predictions and experimental measurements are seen in
$B$ decays as well as in the anomalous magnetic moment of the muon. If the new
physics origin for these experimental anomalies could be established, it would
have a transformative impact on the field. First and foremost, such an
indirect sign of new physics would establish a new mass scale in particle
physics. This scale could become the next target for direct exploration at
future high-energy colliders. With sufficient energy, discoveries would, at
least in principle, be guaranteed. Second, the couplings of the new physics
constitute new sources of flavor violation beyond the SM Yukawa couplings.
Existing low energy constraints suggest that such new physics couplings have a
hierarchical flavor structure. This provides a new perspective on the Standard
Model flavor puzzle and invites the construction of flavor models that link
the structure of the SM and BSM sources of flavor violation. At present, the
global analyses point towards a small consistent set of dimension-6 effective
operators ($C_{9}$ and/or $C_{10}$) to explain the B-physics anomalies. The
leading candidate UV models generating these operators involve $Z^{\prime}$
(e.g. $L_{\mu}-L_{\tau}$) gauge bosons or leptoquarks.

## Acknowledgments

The conveners thank the authors of all whitepapers submitted to TF08 and those
who contributed to the development of this document in numerous other ways.
P.J.F. was supported by Fermi Research Alliance, LLC under Contract DE-
AC02-07CH11359 with the U.S. Department of Energy. G.D.K. was supported in
part by the U.S. Department of Energy under Grant Number DE-SC0011640. H.M.
was supported in part by Beyond AI Institute at the University of Tokyo;
Director, Office of Science, Office of High Energy Physics of the U.S.
Department of Energy under the Contract DE-AC02-05CH11231; NSF grant
PHY-1915314; JSPS Grant-in-Aid for Scientific Research JP20K03942; MEXT Grant-
in-Aid for Transformative Research Areas (A) JP20H05850, JP20A203; Hamamatsu
Photonics, K.K.; and World Premier International Research Center Initiative
(WPI) MEXT, Japan.

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