aainstitutetext: Department of Basic Research, CIEMAT,
Madrid, Spain, 28040bbinstitutetext: Santa Cruz Institute for Particle Physics
and Department of Physics, University of California, Santa Cruz,
1156 High Street, Santa Cruz, CA 95064ccinstitutetext: Department of Physics,
University of Massachusetts at Amherst
Amherst, MA, USA, 01003ddinstitutetext: Illinois Center for the Advanced
Studies of the Universe, Department of Physics, University of Illinois at
Urbana-Champaign,
Urbana, IL, USA, 61801

# Exotic Higgs Decays

María Cepeda b Stefania Gori c Verena Martínez Outschoorn d Jessie Shelton
<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Exotic decays of the Standard Model-like Higgs boson into beyond-the-Standard
Model particles are predicted in a wide range of well-motivated theories. The
enormous samples of Higgs bosons that have been and will be produced at the
Large Hadron Collider thus constitute one of the key discovery opportunities
at that facility, particularly in the upcoming high-statistics high-luminosity
run. Here we review recent theoretical work on models that predict or
accommodate exotic Higgs decays, the status of current experimental searches,
and look forward to future capabilities at dedicated Higgs factories and
beyond.

##  1 Introduction

With the discovery of a Standard Model (SM)-like Higgs boson ATLAS:2012yve ;
CMS:2013btf , experimental probes of the electroweak (EW) scale have entered a
new era. The stunning validation of SM predictions at the Large Hadron
Collider (LHC) and past collider experiments has upended decades of thought
about the hierarchy problem, the origins of dark matter (DM), and the nature
of new physics, and puts precision probes of the SM Higgs at the heart of the
experimental discovery program for the foreseeable future.

One of the major outstanding discovery opportunities in this program is the
search for exotic decays of the Higgs boson, where the Higgs decays to light
new particles. Rare decays of SM particles are frequently an excellent place
to search for the footprints of new physics with suppressed couplings to the
SM, which has motivated searches for e.g. rare decays of the $Z$ boson, of
$B$, $K$, and $\pi$ mesons, and so on. Among the SM particles, however, the
Higgs stands out as a special case given the ease with which it can mediate
interactions with SM-singlet new particles. The Higgs portal operator
$|H|^{2}$, along with the hypercharge field strength $B_{\mu\nu}$, is the
lowest-dimension total singlet operator that can be constructed out of SM
fields, and thus will frequently mediate the leading interaction between SM
and beyond the Standard Model (BSM) physics at the energy scales testable at
the LHC. Thus exotic Higgs decays can easily be the leading signal of a wide
variety of theories. Moreover, we have many theoretical motivations to suspect
that new physics might couple preferentially to the Higgs, as the Higgs sits
at the heart of many outstanding mysteries in particle physics.

Additionally, the Higgs has an unusually tiny width since all of its SM decay
modes are accidentally small, suppressed by small Yukawa couplings, multibody
phase space, or loop factors. For this reason, even tiny couplings to new
physics can lead to experimentally interesting branching ratios into exotic
final states. With the new discovery landscape provided by the copious Higgs
samples newly available at the LHC and at future Higgs factories including the
high-luminosity (HL) LHC, a broad and generic search for exotic Higgs decays
represents one of the leading discovery opportunities for new physics in the
near future.

Exotic Higgs decays have long been appreciated as potential signals of new
physics, beginning with the pioneering work of Suzuki and Shrock Shrock:1982kd
. A large body of work on exotic Higgs decays has been motivated by solutions
to the hierarchy problem, particularly in the context of extended SUSY models
(though see also composite Higgs models) as well as Higgs portal dark matter
(see the paper Curtin:2013fra  for details about both models and signatures).
In this review article, we focus on theoretical motivations for exotic Higgs
decays that have been substantially developed since Curtin:2013fra  and the
major advances in the experimental search for these signatures.

After reviewing theoretical motivations in section 2, we detail three simple
benchmark scenarios in section 3 that realize features of many of the best-
developed theories predicting exotic decays. Current experimental searches are
summarized in section 4, including interpretations of both prompt and long-
lived searches in our benchmark scenarios. In section 5 we survey future
prospects, and we conclude in section 6.

##  2 Theoretical motivations

There are many reasons to expect new physics to lie near the electroweak
scale. New weak-scale states might be directly tied to the electroweak
symmetry-breaking (EWSB) process, and/or responsible for controlling the
stability of the electroweak scale relative to the Planck scale. Thermal relic
DM independently motivates new particles with mass at or below the weak scale.
Many models inspired by these three directions directly involve the Higgs
boson and often naturally predict Higgs decays as one of the leading
terrestrial signatures of the model, as this section will discuss in detail.
However, while these three topics most straightforwardly relate Higgs decays
to long-standing mysteries in particle physics, they by no means exhaust the
scenarios that can motivate exotic Higgs decay modes. More broadly, the SM
Higgs provides a powerful window onto the possible existence of low-mass SM
singlets. Motivations for new light particles can also include the strong CP
problem, which strongly motivates the existence of axions or axion-like-
particles (ALPs), and the observed baryon-anti-baryon asymmetry, which cannot
be generated in the SM. Outstanding experimental anomalies, such as the muon
$g-2$, may also hint at light BSM physics. Exotic decays of the SM Higgs boson
can provide a unique and powerful discovery window onto such light new degrees
of freedom.

###  2.1 Naturalness

The lightness of the Higgs boson is one of the most intriguing puzzles of
modern particle physics. At the same time, null results in searches for
electroweak-scale new physics have called the naturalness of the weak scale
increasingly into question. In symmetry solutions to the hierarchy problem,
the symmetry protecting the Higgs from sensitivity to high mass scales
typically commutes with the Standard Model $SU(3)_{c}\times SU(2)_{L}\times
U(1)_{Y}$ gauge group, giving rise to top partners that are charged under QCD.
This guarantees a sizable LHC production cross-section for top partners with a
mass at around the TeV scale, and therefore leads to tension with LHC searches
that generically constrain top partners to have a TeV-scale mass. The most
famous example of such theories is supersymmetry (SUSY).

Some of these theories can be brought to agreement with LHC data at the cost
of some tuning in the Higgs potential, as for example in models of split SUSY
Arkani-Hamed:2004ymt ; Giudice:2004tc ; Arkani-Hamed:2004zhs  where scalar
superpartner masses could be as high as the gauge unification scale with
gaugino masses remaining around the electroweak scale. Achieving such large
splittings between scalars and gauginos requires, however, elaborate model-
building Arkani-Hamed:2004ymt . SUSY models, in both their minimal and non-
minimal realizations, have been a prime motivation for exotic Higgs decays.
For example, gauge-mediated SUSY-breaking models can predict sizable branching
ratios for $h\to\chi_{2}\chi_{2},~{}\chi_{2}\to\chi_{1}\gamma$, where
$\chi_{2}$ is a bino-like neutralino and $\chi_{1}$ a gravitino Mason:2009qh .
Exotic Higgs decays have been especially well motivated in extensions of the
minimal supersymmetric SM, such as the next-to-minimal supersymmetric SM with
an approximate Peccei-Quinn symmetry, which predicts exotic Higgs decays such
as $h\to\chi_{1}\chi_{2},~{}\chi_{2}\to\chi_{1}f\bar{f}$ where $f$ is a SM
fermion and $\chi_{2}$ ($\chi_{1}$) is a bino-like (singlino-like) neutralino
Draper:2010ew .

A different approach to the hierarchy problem is to invoke symmetries that do
not commute with the SM $SU(3)_{c}$ gauge group, leaving the weak scale to be
stabilized by SM singlets or states with only EW quantum numbers. Examples of
such theories are the Twin Higgs Chacko:2005pe  and Folded SUSY Burdman:2006tz
models, in which the top partners are singlets under the SM gauge group or
have an EW charge, respectively, but carry charge under a mirror copy of the
SM strong force. In these “Neutral Naturalness” models, twin particle
production proceeds through the Higgs portal operator that leads to a
(generically small) mixing between the SM and twin Higgs sectors, thus
allowing for both SM production of the heavier mirror Higgs as well as exotic
Higgs decays into twin particles.111These models are specific realizations of
the Hidden Valley scenario Strassler:2006im . The resulting exotic Higgs
branching fraction depends on the mixing angle between the SM Higgs and the
heavier mirror Higgs, which is proportional to the ratio of SM to mirror Higgs
vacuum expectation values (vevs). The mirror Higgs vev in turn controls the
scale of the twin particle masses and thus the residual tuning in the Higgs
potential, so that bigger exotic branching fractions correspond to a less-
tuned scalar sector.

The Twin Higgs model itself predicts invisible Higgs decays, as the produced
twin particles ultimately cascade down to mirror photons and mirror neutrinos
Burdman:2014zta . The Fraternal Twin Higgs model adds mirror partners for only
the subset of SM particles that contribute most strongly to the running of the
Higgs mass Craig:2015pha . The lightest visibly-decaying partner particles in
these theories are typically composite, dark glueballs and/or dark bottomonium
Craig:2015pha . Both the $0^{++}$ glueball $G_{0}$ and the scalar dark
bottomonium state $\chi_{\tilde{b}0}$ have the right quantum numbers to decay
back to the SM through mixing with the Higgs. Since these states are
composite, their lifetimes depend very steeply on their masses. In the better-
understood case of the dark glueball, its lifetime can range from prompt or
nearly prompt in the $\sim 40$ GeV regime, where direct two-body Higgs decays
to pairs of $G_{0}$ are expected, to kilometers in the $\sim 10$ GeV regime,
where a higher and variable multiplicity of particles is produced
Craig:2015pha ; Curtin:2015fna . In the high-multiplicity regime the typical
signature of interest will thus be one displaced vertex plus missing energy,
together with purely invisible decays.

A conceptually different way to address the hierarchy problem is realized by
relaxion models Graham:2015cka . In these models, the evolution of the Higgs
mass in the early universe dynamically selects an electroweak scale that is
parametrically smaller than the cutoff of the theory. This dynamical selection
is realized thanks to a relaxion scalar field that scans the Higgs mass
parameter from a large and positive cutoff energy down to negative values
through a slow-roll potential. Once the Higgs mass parameter becomes negative,
the Higgs gets a vev that modifies the Higgs-relaxion potential and eventually
stops the rolling of the relaxion. The relaxion generically stops its rolling
at a point that breaks CP, leading to relaxion-Higgs mixing. The relaxion can
be produced in exotic Higgs decays of the type $h\to\phi\phi$ with a branching
ratio that depends on the specific implementation of the relaxion coupling to
the Higgs Flacke:2016szy . Higgs decays provide a leading test of these
relaxion models in the regime where relaxions are too heavy to be produced in
meson decays Flacke:2016szy ; Fuchs:2020cmm .

###  2.2 Dark matter

The most direct way for the Higgs to be connected to DM is for thermal
freezeout to occur through exchange of the Higgs itself. The Higgs portal
operator readily allows interactions between the Higgs boson and a SM-singlet
particle, of which the simplest and most minimal example is the renormalizable
interaction between the SM Higgs and a scalar DM particle,
$\Delta\mathcal{L}=-1/2\,\kappa S^{2}|H|^{2}$ Silveira:1985rk .

In this minimal scalar model, the Higgs-singlet quartic interaction $\kappa$
that yields the observed relic abundance is fixed as a function of the DM
mass.222The singlet quartic self-coupling is a third parameter in this model,
but for perturbative values of this coupling its cosmological impacts are
limited Bernal:2015xba . This coupling is generally large enough to yield
unacceptably large Higgs invisible branching ratios when decays to DM are
kinematically accessible. In the region $50\;\mathrm{GeV}\lesssim
m_{s}\lesssim m_{h}/2$, however, DM annihilations are resonantly enhanced in
the early universe, allowing DM-Higgs couplings as small as
$\mathcal{O}(10^{-4})$ to generate the correct relic abundance. In this
resonant region, DM-SM couplings are small enough that DM does not necessarily
maintain kinetic equilibrium during freezeout, making DM annihilations less
efficient Binder:2017rgn . Incorporating this effect in a careful calculation
of the relic abundance increases the requisite value of $\kappa$ by as much as
a factor of 2 compared to the prediction assuming kinetic equilibrium,
depending on the modeling of scattering rates during the QCD phase transition.
The current limit on the Higgs invisible width,
${\mathrm{Br}}(h\to{\mathrm{invisible}})<0.11$ ATLAS:2020kdi , excludes the
scalar model for $m_{s}<48$ GeV at 95% CL. While invisible Higgs decays are
very effective at excluding the low mass region, the constraints from direct
detection experiments are even more stringent in the surviving resonant region
(with standard modeling of the local DM halo). The spin-independent nuclear
cross-sections generated by Higgs exchange give rise to appreciable signals in
ton-scale liquid noble gas experiments. Current results from XENON1T restrict
the lower boundary of the resonant region to $m_{s}>55.9\,(57.2)$ GeV with
minimal (maximal) kinetic decoupling effects XENON:2018voc , leaving a viable
albeit finely tuned window up to $m_{h}/2$. Future liquid Xenon experiments
have the potential to close the resonant window almost entirely DARWIN:2016hyl
; PandaX:2018wtu . Meanwhile, the $s$-wave annihilation cross-section in this
model makes indirect detection a competitive experimental test of the scalar
singlet model, and in particular Fermi observations can be a powerful probe of
the resonant regime Hardy:2018bph .

The DM annihilation cross-section required to obtain the observed relic
abundance can be reduced if the early universe underwent a period of early
matter domination during or after DM freezeout Hardy:2018bph ; Bernal:2018kcw
; Chanda:2019xyl . The smaller Higgs-singlet couplings necessary in these
models allow the minimal scalar singlet model to survive both invisible Higgs
decay constraints as well as direct detection exclusions in a broad mass
range, depending on the timing and duration of the early matter-dominated era.

The direct detection cross-section can also be suppressed by extending the
singlet-Higgs sector. Promoting the real scalar $S$ to a complex field $\Phi$,
one can ensure that the stable DM particle is a pseudo-Goldstone boson of the
(softly-broken) global $U(1)$ symmetry that takes $\Phi\to e^{i\alpha}\Phi$
Gross:2017dan . The cross-section for elastic DM-SM particles is accordingly
momentum-suppressed, and the leading contributions to the direct detection
cross-section now appear at one loop, substantially below current experimental
sensitivity. Invisible Higgs decay modes, however, remain unsuppressed, and
provide the most sensitive test of this model when they are kinematically
accessible. However, this enlarged parameter space comes with a price: the
scalar sector in this theory has several additional free parameters and the
invisible Higgs branching ratio is accordingly no longer uniquely predicted in
terms of the DM mass and relic abundance. The additional BSM Higgs boson
$H_{2}$ in this theory provides further collider signatures, notably
$H_{2}\to{\mathrm{invisible}}$, and can be an important source of constraints.

Both fermionic and vector Higgs portal DM, described by the respective
effective interactions
$\Delta\mathcal{L}=-(1/\Lambda)(c_{s}\bar{\chi}\chi+ic_{p}\bar{\chi}\gamma^{5}\chi)|H|^{2}$
and $-\lambda_{V}V_{\mu}V^{\mu}|H|^{2}$, are in some sense non-minimal models
as additional degrees of freedom must be introduced to construct even minimal
UV completions of these Higgs portal interactions. The surviving parameter
space for both fermionic and vector models is qualitatively similar to that
for the scalar model, with direct detection constraints restricting the DM
mass to lie in the resonant regime $m_{DM}\lesssim m_{h}/2$ (or at TeV
scales). Collider and (to a lesser extent) direct detection signals however
are sensitive to the additional fields required to UV-complete the Higgs
portal interactions.

Qualitatively distinct phenomenology arises in other classes of non-minimal
models. In one such class of models, DM freezes out by annihilating to SM
final states through a BSM mediator, rather than the SM Higgs. In Higgs portal
models, this mediator is generally part of an extended Higgs sector, which
inherits its coupling to the SM through mixing with (B)SM Higgs bosons. A
scalar singlet mediator, $S$, that inherits couplings to SM particles through
Higgs mixing via the renormalizeable operator $S^{2}|H|^{2}$ will generically
lead to unacceptably large direct detection cross-sections333The major
exception is the pseudo-Goldstone DM model discussed above, where the
spontaneously broken global $U(1)$ ensures a cancellation between the
contributions of the SM and BSM Higgs bosons in the direct detection cross-
section.. A pseudo-scalar mediator, $a$, however, gives rise to a tree-level
direct detection cross-section that is both spin-dependent and velocity-
suppressed, making the one-loop spin-independent cross-section the leading
source of direct detection constraints Ipek:2014gua . Coupling a pseudo-scalar
singlet mediator to SM fermions in a UV-complete model requires either new
(and generically stringently constrained) CP-violating couplings with the SM
Higgs, or enlarging the SM Higgs sector to (e.g.) a two Higgs doublet model,
which allows the mediator $a$ to mix with the doublet pseudo-scalar $A^{0}$.
In this case, exotic Higgs boson decays to pairs of mediators can easily be a
leading probe of DM freezeout Ipek:2014gua . The exotic branching ratio
depends in detail on the properties of the heavy $A^{0}$ and is not uniquely
predicted as a function of mediator mass. The mediators can decay to either
visible SM states or invisibly to DM, in principle allowing for invisible,
visible, and semi-visible Higgs decays. However, Fermi-LAT constraints on DM
annihilations make it challenging to realize thermal relic DM with masses
below 25 GeV in this model Fermi-LAT:2016uux ; Fermi-LAT:2017opo , thus
substantially limiting the parameter space where both $h\to aa$ and
$a\to\bar{\chi}\chi$ can be realized. The parameter space of the 2HDM$+a$
model was recently surveyed in Robens:2021lov .

Adding BSM mediators to DM freezeout models also allows for the generic
possibility that DM annihilations proceed directly to BSM mediator states,
with no direct involvement of the SM. In models with such secluded
annihilations the BSM mediator is generally lighter than DM and will often
have a small coupling to the SM that lets it decay into visible final states
Pospelov:2007mp . For these theories, the small mediator-SM coupling that
determines both exotic Higgs decays and direct detection signals is
parametrically decoupled from the annihilation cross-section that sets the DM
relic abundance in the early universe, thereby ameliorating direct detection
constraints. Visible Higgs decays to mediator pairs are again a leading probe
of this class of models. In the most minimal of such scenarios, the mediator
is a single Higgs-mixed scalar Martin:2014sxa ; Evans:2017kti . In scenarios
where a dark photon $Z_{D}$ mediates DM annihilations, the Higgs may also
decay to $Z_{D}Z_{D}$ through mixing with the dark Higgs boson responsible for
the mass of the $Z_{D}$ Bell:2016fqf .

If the mediator decays dominantly through Higgs mixing, then the Higgs-
mediator coupling cannot be arbitrarily small, as the mediator particle must
be cosmologically short-lived in order not to ruin the successful predictions
of BBN Fradette:2018hhl . Much more stringently, however, the assumption that
DM shares the same temperature as the SM in the early universe relies on the
mediator-Higgs coupling being large enough to keep the DM and the SM in
kinetic equilibrium. The “thermalization floor”, i.e. the minimum value for
the mediator-Higgs coupling that ensures secluded annihilations proceed while
the DM is in equilibrium with the SM, represents an important experimental
target Evans:2017kti . For couplings below this value, the initial DM
temperature must be separately specified from the SM temperature in order to
obtain consistent predictions for the DM annihilation cross-section, which
introduces dependence on additional model parameters. Searches for $h\to ss$
at the LHC test mediator-Higgs couplings that are well above the
thermalization floor Evans:2017kti .

To summarize, $h\to$ invisible at levels at or below current limits can still
be straightforwardly explained in simple models of thermal DM, though these
theories are now either finely tuned or require non-minimal cosmological
and/or particle content. However, invisible decays are far from the only
exotic decay mode motivated by DM model-building. Simple theories of dark
sector freezeout generically predict Higgs decays to pairs of new dark
mediators, which typically result in (semi-)visible decays. It is worth
observing that while the “WIMP miracle” ensures that DM freezing out via
(extended) Higgs portal interactions has a mass scale not too dissimilar from
the electroweak scale, a priori there is no compelling theoretical reason to
prefer DM masses either above or below $m_{h}/2$. Detailed discussion of Higgs
portal DM across the full viable mass range can be found in the recent reviews
Arcadi:2019lka ; Lebedev:2021xey .

###  2.3 Electroweak phase transition

One long-standing motivation for introducing new states near the electroweak
scale is to drive the electroweak phase transition (EWPT) strongly first-
order. Historically, electroweak baryogenesis has been a primary motivation
for first-order EWPTs. While constraints on BSM sources of CP violation have
made electroweak baryogenesis model-building increasingly challenging,
understanding the possible thermal histories of our universe remains an
enduring and important question. Strongly first-order EWPTs produce stochastic
gravitational wave signals, which may be seen in future gravitational wave
detectors Caprini:2019egz . The electroweak phase transition in the SM is a
crossover Kajantie:1996mn ; Csikor:1998eu , but new degrees of freedom
interacting with the Higgs boson can generate first-order EWPTs through either
loop effects or tree-level couplings with the SM. In models that feature new
particles with $m<m_{h}/2$, the most salient possibility is SM singlet
scalars, which can affect the EWPT at tree level. After the discovery of the
SM Higgs boson, most work on collider signatures of singlet-catalyzed strongly
first-order EWPTs has focused on the regime where Higgs decays to exotic
states are kinematically forbidden, as the vast majority of parameter space
with open BSM decay modes yields exotic branching ratios that are now
experimentally unacceptable Profumo:2007wc ; Ghorbani:2018yfr . However, there
is still a narrow region of viable parameter space where a light SM-singlet
scalar can drive the electroweak phase transition strongly first-order,
yielding exotic Higgs decays into either visible Kozaczuk:2019pet ;
Carena:2019une  or invisible Kozaczuk:2019pet  final states. The branching
fraction for such exotic decays is bounded from below, as the singlet coupling
to the SM Higgs boson cannot be arbitrarily small and still successfully drive
the phase transition first order. The HL-LHC will be able to test the lower
bound on the visible exotic branching fraction consistent with a strongly
first-order EWPT for scalars with mass $m\gtrsim 20$ GeV, while at lower
scalar masses lepton colliders will be needed to conclusively probe the lower
bound Kozaczuk:2019pet .

##  3 Benchmark Scenarios

Searches for visible exotic Higgs decays are often carried out in the context
of phenomenological models that guide overall analysis strategies. The best-
studied of these models consider the minimal scenarios where the Higgs decays
to pairs of singlet states, $h\to ss$, $aa$, or $Z_{D}Z_{D}$. Here $s$ denotes
a CP-even scalar, $a$ a CP-odd scalar, and $Z_{D}$ a vector boson. The key
properties of these particles for exotic decay searches are governed by the
operator(s) (or “portal”) through which they interact with the SM, which
determine both their production rate in Higgs decays as well as their decays
to SM particles. In particular, the choice of decay portal controls the
dominant final states.

Here we discuss three of the most common benchmark scenarios: (i) SM$+$s,
where $s$ is a Higgs-mixed scalar boson; (ii) SM$+$ALP; (iii) SM$+$v, where
the vector, $Z_{D}$, kinetically mixes with the SM hypercharge gauge boson.
While these benchmark scenarios certainly do not lead to all the possible
exotic decays of interest, they capture the key phenomenology predicted in a
wide variety of theories, motivate searches in a broad range of final states,
and provide a useful guide to assessing the reach and motivation of various
experimental analysis strategies.

###  3.1 SM+s

One of the simplest models leading to exotic Higgs boson decays occurs when a
new real scalar is added to the SM, mixing with the Higgs boson and inheriting
its couplings to SM fields. This model is intimately connected to many of the
theoretical models discussed above: the scalar can be motivated by electroweak
phase transitions, relaxion models, neutral naturalness (in which case the
scalar is typically long-lived), or it could be a mediator in a dark matter
model. The minimal Lagrangian describing the system is given by

$\mathcal{L}=\mathcal{L}_{{\rm{kin}}}+\frac{\mu_{s}^{2}}{2}S^{2}-\frac{\lambda_{s}}{4!}S^{4}-\frac{\kappa}{2}S^{2}|H|^{2}+\mu^{2}|H|^{2}-\lambda|H|^{4},$
(1)

where we have imposed a discrete symmetry taking $S\to-S$. Depending on the
parameters of the scalar potential, both $S$ and $H$ can get non-zero vevs,
$v_{s}$ and $v_{h}$ respectively:

$v_{s}^{2}=\,\frac{6\left(2\lambda\mu_{s}^{2}-\kappa\mu^{2}\right)}{2\lambda\lambda_{s}-3\kappa^{2}},\,\phantom{space}v_{h}^{2}=\,\frac{2\lambda_{s}\mu^{2}-6\kappa\mu_{s}^{2}}{2\lambda\lambda_{s}-3\kappa^{2}}\,.$
(2)

In this case, the two scalar mass eigenstates, $h$ and $s$ with masses $m_{h}$
and $m_{s}$ respectively, are related to the gauge eigenstates by the mixing
angle

$\tan\theta=\frac{\kappa v_{h}v_{s}}{\lambda
v_{h}^{2}-\frac{1}{6}\lambda_{s}v_{s}^{2}+\sqrt{\left(\lambda
v_{h}^{2}-\frac{1}{6}\lambda_{s}v_{s}^{2}\right)^{2}+\kappa^{2}v_{h}^{2}v_{s}^{2}}}\simeq\frac{\kappa
v_{h}v_{s}}{m_{h}^{2}-m_{s}^{2}}\,,$ (3)

where the latter relation holds only when $m_{s}$ is quite different than
$m_{h}$ and $\kappa$ is small. For small values of $\theta$ (as motivated by
LEP constraints Robens:2015gla ), the branching ratio for $h\to ss$ depends on
BSM parameters only through the mixed quartic $\kappa$ and on the phase space
available for the decay,

$Br(h\to ss)\simeq\frac{v^{2}\kappa^{2}}{32\pi
m_{h}\Gamma_{h}}\sqrt{1-\frac{4m_{s}^{2}}{m_{h}^{2}}},$ (4)

where $\Gamma_{h}$ is the total Higgs width.

The scalar $s$ decays preferably to the heaviest SM particles that are
kinematically accessible. The $s$ lifetime is proportional to
$\tan^{2}\theta$, while its branching fractions are independent of $\theta$.
To evaluate the branching ratios of $s$ to SM states as a function of its
mass, we use the results of Gershtein:2020mwi  for $m_{s}<20$ GeV and as given
by the LHC Higgs Cross Section Working Group
LHCHiggsCrossSectionWorkingGroup:2016ypw  at larger values of the mass. The
predictions at lower masses include decays to hadrons, particularly pions and
kaons, following the treatment of Winkler:2018qyg , while at higher masses
contributions from heavier particles such as $W$ and $Z$ are also considered.
The two calculations differ at the $\sim 30\%$ level for hadronic decay modes
at 20 GeV. It would be desirable to have a consistent treatment across the
full mass range in the future. The experimental results discussed in Sec.
4.1.2 are independent of $\theta$ as long as the mixing angle is large enough
to allow $s$ to decay promptly, while the LLP searches considered in Section
4.2.1 are sensitive to the $s$ lifetime and thus $\theta$.

####  3.1.1 Scalars vs. pseudoscalars

Collider searches for exotic Higgs decays to spin-zero states are largely
insensitive to the CP properties of $s$, and, thus, searches for the $h\to ss$
signatures predicted by the SM+s benchmark also have similar sensitivity to
pseudoscalars, $a$, as arising, for example, in theories where light singlet
pseudoscalars mix with pseudoscalars belonging to a doublet representation of
$SU(2)$. Thus the benchmark SM+s is a useful reference model to characterize
experimental sensitivity to a broader class of models featuring a new light
state with Yukawa-weighted decays.

However, the couplings of $a$ to SM fermions and gauge bosons, and thus the
branching ratios of $a$, depend on the parameters of the doublet state it
mixes with, such as $m_{A}$ and $\tan\beta$ in two Higgs doublet models (see
e.g. Dolan:2014ska ; Haisch:2018kqx ). Moreover, in the GeV-scale regime where
the new particle can decay directly to hadrons, its hadronic matrix elements
will depend on its CP properties. For this reason, $a$ and $s$ branching
ratios in the sub-GeV mass range will be substantially different.

A new pseudoscalar that mixes with a 2HDM doublet pseudoscalar can also give
rise to exotic Higgs decays $h\to Za$, which cannot be realized in the SM+s
model. The $h\to Za$ decay mode would probe parameter regions away from the
alignment limit Craig:2013hca .

###  3.2 SM+ALP

Another interesting class of exotic Higgs boson decays can arise when a new
ALP, $a$, is added to the SM. Such ALPs appear in well-motivated extensions of
the Standard Model, e.g. as a way to address the strong CP problem, as
mediators between the SM and a hidden sector (through the so-called “Axion
Portal”), or simply as pseudo-Nambu-Goldstone bosons in extensions of the SM
with a broken global symmetry. Models with light ALPs generically lead to
exotic Higgs decays into ALPs.

The ALP can couple to the Higgs through the dimension-six and seven operators

$\mathcal{L}\supset\frac{C_{h}}{\Lambda^{2}}(\partial_{\mu}a)(\partial^{\mu}a)H^{\dagger}H+\frac{C_{Z}}{\Lambda^{3}}(\partial_{\mu}a)(H^{\dagger}iD_{\mu}H+h.c.)H^{\dagger}H\,.$
(5)

Note that at dimension five there are no $a$ couplings to the Higgs
doublet.444Here we have assumed that electroweak symmetry is broken linearly.
Nonlinear EWSB can allow for additional $hZa$ interactions, making $h\to aZ$ a
leading probe of such theories Brivio:2017ije . After electroweak symmetry
breaking, these two operators will lead to the decays $h\to aa$
Dobrescu:2000jt ; Dobrescu:2000yn  and $h\to aZ$ Bauer:2017nlg , respectively.
The corresponding widths are given by

$\displaystyle\Gamma(h\to aa)$ $\displaystyle=$
$\displaystyle\frac{v^{2}m_{h}^{3}}{32\pi\Lambda^{4}}\left|C_{h}\right|^{2}\left(1-\frac{2m_{a}^{2}}{m_{h}^{2}}\right)^{2}\sqrt{1-\frac{4m_{a}^{2}}{m_{h}^{2}}}\,,$
(6) $\displaystyle\Gamma(h\to Za)$ $\displaystyle=$
$\displaystyle\frac{m_{h}^{3}v^{4}}{64\pi\Lambda^{6}}\left|C_{Z}\right|^{2}\lambda^{3/2}\bigg{(}\frac{m_{Z}^{2}}{m_{h}^{2}},\frac{m_{a}^{2}}{m_{h}^{2}}\bigg{)}\,,$
(7)

where $\lambda(x,y)=(1-x-y)^{2}-4xy$.

Once produced, the ALP can decay back to the SM thanks to the dimension-five
effective Lagrangian (following the notation of Bauer:2017ris )

$\displaystyle{\cal L}_{\rm eff}$
$\displaystyle=\frac{\partial^{\mu}a}{\Lambda}\sum_{F}\,\bar{\psi}_{F}\,C_{F}\,\gamma_{\mu}\,\psi_{F}+g_{s}^{2}\,C_{GG}\,\frac{a}{\Lambda}\,G_{\mu\nu}^{A}\,\tilde{G}^{\mu\nu,A}$
(8)
$\displaystyle\quad\mbox{}+g^{2}\,C_{WW}\,\frac{a}{\Lambda}\,W_{\mu\nu}^{A}\,\tilde{W}^{\mu\nu,A}+g^{\prime\,2}\,C_{BB}\,\frac{a}{\Lambda}\,B_{\mu\nu}\,\tilde{B}^{\mu\nu}\,,$

where $G_{\mu\nu}^{A}$, $W_{\mu\nu}^{A}$ and $B_{\mu\nu}$ are the field
strength tensors of $SU(3)_{c}$, $SU(2)_{L}$ and $U(1)_{Y}$, and $g_{s}$, $g$
and $g^{\prime}$ denote the corresponding coupling constants. The sum in the
first line extends over the chiral fermion multiplets $F$ of the SM. The
quantities $C_{F}$ are hermitian matrices in generation space. The couplings
in Equation 8 will also induce loop corrections to the $h\to aa$ and $h\to Za$
rates.

Depending on the values of these couplings, the ALP can decay to a large set
of final states, including $a\to\bar{f}f,~{}a\to\gamma\gamma,~{}a\to gg$. When
the fermionic operators dominate the ALP decays, the resulting phenomenology
is generically a realization of the Yukawa-weighted models discussed in the
previous subsection. Generically, however, and in contrast to light scalar
models, theories containing derivatively-coupled ALPs predict substantial
branching ratios of the ALP into gluons and/or photons. This makes the exotic
decays $h\to aa\to\gamma\gamma jj$, $h\to aa\to\gamma\gamma\gamma\gamma$,
$h\to aa\to jjjj$ particularly relevant to test ALP theories. When
$m_{a}\lesssim 10$ GeV, its decay products begin to appear collimated in the
detector. For photonically-decaying ALPs, the resulting photon-jet-like
signature in the detector can present an interesting reconstruction task
Sheff:2020jyw , and can in some parts of parameter space potentially
contribute to searches for the SM $h\to\gamma\gamma$ decay Draper:2012xt ;
Ellis:2012zp .

In understanding the range of signatures described by the effective field
theory of Equations 5 and 8, it can be useful to keep in mind concrete UV
completions, which make definite and model-dependent predictions for the
relative sizes of the Wilson coefficients as well as the scale $\Lambda$. A
variety of UV completions have been studied in the literature, including some
that realize viable lepton flavor-violating scenarios with $h\to aa$ followed
by $a\to\tau\ell$ Davoudiasl:2017zws ; Davoudiasl:2021haa  (similar signatures
were considered in Evans:2019xer ). In such scenarios $a$ can be either prompt
or long-lived, leading to interesting displaced flavor-violating signatures.

###  3.3 SM+v

Dark photon theories feature a gauge boson from a spontaneously broken
$U(1)_{D}$ gauge symmetry that kinetically mixes with the SM hypercharge gauge
boson, $\hat{B}$. The minimal dark photon model has become a standard
benchmark for feebly-interacting particle searches, and is a common building
block in theories of DM. The relevant gauge terms in the Lagrangian are

$\mathcal{L}\supset-\frac{1}{4}\hat{Z}^{\prime\mu\nu}\hat{Z}^{\prime}_{\mu\nu}+\frac{\epsilon}{2\cos\theta}\hat{B}^{\mu\nu}\hat{Z}^{\prime}_{\mu\nu}+\frac{1}{2}m_{\hat{Z}^{\prime}}^{2}\hat{Z}^{\prime\mu}\hat{Z}^{\prime}_{\mu}\,,$
(9)

where $\theta$ is the Weinberg angle, and $\epsilon$ is the kinetic mixing
parameter. After EWSB, the mass eigenstates $Z$ (corresponding to the SM $Z$
boson) and $Z_{D}$ will have non-zero $\hat{Z}$ and $\hat{B}$ components. The
dark photon mass term in Equation 9 can come either from a dark Higgs, $S$, or
from the Stueckelberg mechanism. In the former case, the Lagrangian will also
contain the interactions of the Higgs with the scalar as in Equation 1, as
well as the interaction of the scalar with two dark photons.

If the dark photon is light enough, the kinetic mixing leads to the exotic
decay $h\to ZZ_{D}$ with a width given by

$\displaystyle\Gamma(h\to ZZ_{D})$ $\displaystyle=$
$\displaystyle\frac{\eta^{2}\,\sin^{2}\theta\,m_{Z}^{2}\,m_{Z_{D}}^{2}}{16\,\pi\,v^{2}\,m_{h}^{3}\,\left(m_{Z}^{2}-m_{Z_{D}}^{2}\right)^{2}}\left(-2m_{Z_{D}}^{2}\left(m_{h}^{2}-5m_{Z}^{2}\right)+m_{Z_{D}}^{4}+\left(m_{h}^{2}-m_{Z}^{2}\right)^{2}\right)$
(10)
$\displaystyle\times\,\sqrt{-2m_{h}^{2}\left(m_{Z_{D}}^{2}+m_{Z}^{2}\right)+\left(m_{Z}^{2}-m_{Z_{D}}^{2}\right)^{2}+m_{h}^{4}}\,,$

where we have defined
$\eta\equiv\epsilon/(\cos\theta\sqrt{1-\epsilon^{2}/\cos^{2}\theta})$. The
kinetic mixing also leads to the decay $h\to Z_{D}Z_{D}$, but the width of
this decay is suppressed by $\epsilon^{4}$, making it highly sub-leading.
However, if the $Z_{D}$ mass is generated by a dark Higgs mechanism, the dark
scalar-Higgs mixing induced by the Lagrangian in Equation 1 also contributes
to the decay $h\to Z_{D}Z_{D}$,

$\displaystyle\Gamma(h\rightarrow Z_{D}Z_{D})$ $\displaystyle=$
$\displaystyle{\kappa^{\prime}}^{2}\ \frac{1}{32\pi}\
\frac{v^{2}}{m_{h}}\sqrt{1-\frac{4m_{Z_{D}}^{2}}{m_{h}^{2}}}\
\frac{(m_{h}^{2}+2m_{Z_{D}}^{2})^{2}-8(m_{h}^{2}-m_{Z_{D}}^{2})m_{Z_{D}}^{2}}{m_{h}^{4}},$
(11)

where we have have introduced the dimensionless parameter
$\kappa^{\prime}\equiv\kappa\,{m_{h}^{2}}/|m_{h}^{2}-m_{s}^{2}|$, with
$\kappa$ the quartic interaction of the dark scalar and the Higgs,
$\kappa|S|^{2}|H|^{2}$.

Through kinetic mixing, the dark photon acquires couplings to the SM fermions:

$\mathcal{L}\supset
g_{L}Z_{D\mu}\bar{f}_{L}\gamma^{\mu}f_{L}\>+\>g_{R}Z_{D\mu}\bar{f}_{R}\gamma^{\mu}f_{R}\>\,,$
(12)

where the couplings are given by

$\displaystyle
g_{L}=\frac{g_{W}}{\cos\theta}\left(-\sin\alpha\>(\cos^{2}\theta_{W}\>T_{3}-\sin^{2}\theta\>Y_{L})+\cos\alpha\>\eta\>\sin\theta_{W}\>Y_{L}\right)\simeq
eQ\epsilon,$ $\displaystyle
g_{R}=\frac{g_{W}}{\cos\theta}\left(-\sin\alpha\>(-\sin^{2}\theta\>Y_{R})+\cos\alpha\>\eta\>\sin\theta\>Y_{R}\right)\simeq
eQ\epsilon.$ (13)

Here $\alpha$ is the mixing angle between $Z$ and $Z_{D}$, and is proportional
to the kinetic mixing parameter, $\alpha\propto\epsilon$. $T_{3}$ and $Y$ are,
respectively, the third component of the isospin and the hypercharge of the SM
fermion, where we use the convention $Q=T_{3}+Y$, with $Q$ the fermion
electric charge. The last equalities are only valid in the limits $\epsilon\ll
1$ and $m_{Z_{D}}\ll m_{Z}$.

Because of these couplings, the dark photon will decay to SM fermions with
partial widths given by

$\Gamma(Z_{D}\to\bar{f}f)=\frac{N_{c}}{24\pi
m_{Z_{D}}}\sqrt{1-\frac{4m_{f}^{2}}{m_{Z_{D}}^{2}}}\left(m_{Z_{D}}^{2}\left(g_{L}^{2}+g_{R}^{2}\right)-m_{f}^{2}\left(-6g_{L}g_{R}+g_{L}^{2}+g_{R}^{2}\right)\right),$
(14)

proportional to $\epsilon^{2}$. This tree-level formula is a good
approximation for $m_{Z_{D}}$ above the $b\bar{b}$ threshold. Below this
threshold, one should include experimental information and higher order QCD
calculations (see e.g. Curtin:2014cca ). Overall, in the mass range of
interest, the dark photon has a large probability to decay to SM leptons,
$Br(Z_{D}\to\ell^{+}\ell^{-})\sim 30-50\%$, where we are summing over
electrons and muons. The branching ratios of $Z_{D}$ do not depend on
$\epsilon$, while the $Z_{D}$ lifetime is inversely proportional to
$m_{Z_{D}}\epsilon^{2}$.

Our focus in Secs. 4.1.4, 4.2.2 will be on the minimal scenario where the
exotic decay of primary interest is $h\to Z_{D}Z_{D}$, where the branching
ratio $Br(h\to Z_{D}Z_{D})$ is controlled by the mixing between the SM and the
dark Higgs Schabinger:2005ei ; Gopalakrishna:2008dv . Depending on the mass
splittings in the theory, the decay $h\to ss\to 4Z_{D}$ may also be available,
resulting in very high multiplicity final states Izaguirre:2018atq . In the
minimal dark photon model, direct searches for $h\to ZZ_{D}$ with
$\mathcal{O}(100\,{\mathrm{fb}}^{-1})$ data can start to test regions of the
$(\epsilon,m_{Z_{D}})$ parameter space that are not excluded by precision
electroweak constraints on $\epsilon$ Curtin:2014cca , making these searches
the leading probe of the minimal model for masses $m_{Z_{D}}\gtrsim 10$ GeV.
Non-minimal models that allow for additional mass mixing between $Z$ and
$Z_{D}$ can predict larger branching fractions for this exotic decay than
expected from kinetic mixing alone Davoudiasl:2013aya ; Lu:2017uur .

Another non-minimal variant of the dark photon model adds a dark neutralino
and higgsino to give the Higgsed dark $U(1)$ theory a supersymmetric matter
content Falkowski:2010cm ; Falkowski:2010gv ; Chan:2011aa . This scenario,
which we refer to as a SUSY dark photon model, can yield semi-invisible and
potentially high-multiplicity decays, depending on the details of the hidden
sector spectrum.

##  4 Experimental Status

Exotic Higgs boson decays to new particles have very rich phenomenology
featuring many possible final states, mass regimes, and lifetime ranges.
Several searches have been performed at the Tevatron and LHC for such signals.
Typically, the searches assume that the observed Higgs boson at 125 GeV is
produced in accordance with SM expectations but decays to new particles. This
is because new particles introduced in the models described in Section 3 have
a subleading effect on the Higgs boson production cross-section, since their
couplings are expected to be much smaller than the electroweak and top
couplings to the Higgs LHCHiggsCrossSectionWorkingGroup:2016ypw . The searches
target different Higgs boson production modes, mainly due to trigger
considerations, as well as different mass and lifetime ranges, often depending
on the object identification and reconstruction techniques available, as well
as the analysis strategy pursued. Experimental searches can be broadly
categorized into those targeting scenarios where the new particle decays
promptly to SM particles (Section 4.1), and where the new particle is long-
lived, resulting in a displaced or invisible decay (Section 4.2).

The total Higgs boson width cannot be measured in a model-independent way at
the LHC. However, a global fit of Higgs measurements involving SM final states
can constrain the branching ratio into exotic final states under the mild
assumption that BSM physics does not enhance the Higgs widths to $W$ and $Z$
bosons. Recent analyses set an upper limit at 95% CL of about 16% ATLAS-
CONF-2021-053  on the “undetected” Higgs branching fraction (i.e., final
states that do not contribute to searches for SM or invisible decays). Given
the assumptions necessary to extract this limit, and the finite sensitivity
expected even after the completion of the Run 2 and Run 3 analyses, there is
ample room for interestingly large exotic branching fractions while remaining
compatible with current measurements. This is very strong motivation for
pursuing the complementary strategy of performing direct searches.

Higgs boson decay products carry momenta ranging from a few GeV to few tens of
GeV, which can be challenging for triggers at hadron colliders. Searches for
final states with electrons, muons, taus, or photons typically target Higgs
bosons produced by gluon-fusion (ggF), which has the largest cross section. In
hadronic final states, the decay products are typically too soft to satisfy
trigger requirements, and searches rely on additional forward jets, targeting
Higgs boson production via vector boson fusion (VBF), or on additional leptons
from $W$ or $Z$ boson decays produced in association with the Higgs boson
($Wh/Zh$).

Further challenges arise at the reconstruction and identification level. Since
the decay products are often soft and may overlap in the detector, standard
algorithms can reject events or objects produced in exotic Higgs decays.
Dedicated identification and reconstruction techniques have been developed for
several signatures, targeting low $p_{T}$ or overlapping decay products, such
as $b$-jets ATLAS:2020ahi , taus CMS:2019spf , and muons CMS:2018jid . Such
dedicated algorithms extend the sensitivity of searches to cover new
scenarios.

Searches for long-lived particles (LLPs), which decay with measurable
displacements in the detector, offer a great opportunity to detect new physics
because of the striking signatures. These searches also present unique
challenges for triggering, reconstruction, and identification and often
require dedicated techniques. LLP signatures can resemble noise, pileup, or
mis-reconstructed objects in the detector, which are often rare and hard to
model reliably in simulation. Therefore, dedicated analysis methods to
estimate backgrounds are also often needed.

###  4.1 Summary of prompt searches

Searches for exotic Higgs boson decays to new particles that subsequently
decay promptly to SM particles have been performed in several final states and
mass ranges. Current searches primarily target Higgs boson decays to
intermediate on-shell neutral particles, $h\rightarrow ss/aa/vv\rightarrow
XX~{}YY$ and $h\rightarrow Za/Zv\rightarrow\ell\ell~{}XX$ where $s(a)$ is a
new (pseudo)scalar, $v$ a new vector, and $X$ and $Y$ are SM particles that
are pair-produced in each new particle decay: electrons, muons, taus, photons,
b-jets, or hadronic jets. Higgs decays to a pair of new particles decaying to
different final states are also explored ($X\neq Y$). Table 1 summarizes
experimental results for prompt decays to SM particles.

Table 1: Summary of the latest prompt searches for $h\rightarrow ss/aa/vv$ or $Za/Zv$, including merged (m) and resolved (r) final states. The interpretations included in each result are listed, following the categorization presented in Section 3, and $m$ denotes the new particle mass. The two mass ranges of the last listed search correspond to the interpretation SM+s and SM+v, respectively.  Decay | Mode | Reference |  $\sqrt{s}$ (TeV) |  $\int\mathcal{L}$ (fb-1) |  $m$ (GeV) | Interpretations
---|---|---|---|---|---|---
$h\rightarrow ss/aa/vv$
$eeee$ |  (r) | ggF | CMS CMS-PAS-HIG-19-007  | 13 | 137 | 4-8, 11.5-62.5 | SM+v, SM+ALP
|  (r) | ggF | ATLAS ATLAS-CONF-2021-034  | 13 | 139 | 15-60 | SM+s, SM+v
$ee\mu\mu$ |  (r) | ggF | CMS CMS-PAS-HIG-19-007  | 13 | 137 | 4-8, 11.5-62.5 | SM+v, SM+ALP
|  (r) | ggF | ATLAS ATLAS-CONF-2021-034  | 13 | 139 | 15-60 | SM+v
$\mu\mu\mu\mu$ |  (m) | ggF | D0 Abazov_2009  | 1.96 | 4.2 | 0.2143-3 | SM+s, SM+v
|  (r) | ggF | CMS CMS:2018jid  | 13 | 35.9 | 0.25-8.5 | SM+s, dark SUSY
|  (r) | ggF | CMS CMS-PAS-HIG-19-007  | 13 | 137 | 4-8, 11.5-60 | SM+v, SM+ALP
|  (m/r) | ggF | ATLAS ATLAS-CONF-2021-034  | 13 | 139 | 1.2-2, 4.4-8, 12-60 | SM+s, SM+v
$\mu\mu\tau\tau$ |  (m/r) | ggF | D0 Abazov_2009  | 1.96 | 4.2 | 3.6-19 | SM+s
|  (m/r) | ggF | ATLAS ATLAS:2015unc  | 8 | 20.3 | 3.7-50 | SM+s
|  (m/r) | ggF | CMS CMS:2020ffa  | 13 | 35.9 | 3.6-21 | SM+s
|  (r) | ggF | CMS CMS:2018qvj  | 13 | 35.9 | 15-62.5 | SM+s
$\tau\tau\tau\tau$ |  (m) | ggF | CMS CMS:2019spf  | 13 | 35.9 | 4-15 | SM+s
$bb\mu\mu$ |  (r) | ggF | ATLAS ATLAS:2021hbr  | 13 | 139 | 18-60 | SM+s
|  (r) | ggF | CMS CMS:2018nsh  | 13 | 35.9 | 20-62.5 | SM+s
$bb\tau\tau$ |  (r) | ggF | CMS CMS:2018zvv  | 13 | 35.9 | 15-60 | SM+s
$bbbb$ |  (m) | $Zh$ | ATLAS ATLAS:2018pvw  | 13 | 36.1 | 15-30 | SM+s
|  (r) | $Wh/Zh$ | ATLAS ATLAS:2020ahi  | 13 | 36.1 | 20-60 | SM+s
$\gamma\gamma\gamma\gamma$ |  (r) | ggF | ATLAS ATLAS:2015rsn  | 8 | 20.3 | 10-62 | SM+s
|  (r) | ggF | CMS CMS-PAS-HIG-21-003  | 13 | 132 | 15-60 | SM+s
$\gamma\gamma gg$ |  (r) | VBF | ATLAS ATLAS:2018jnf  | 13 | 36.7 | 20-60 | SM+s
$h\rightarrow Za/Zv$
$gg$ |  (m) | ggF | ATLAS ATLAS:2020pcy  | 13 | 139 | 0.5-4 | SM+s
$ss$ |  (m) | ggF | ATLAS ATLAS:2020pcy  | 13 | 139 | 1.5-3 | SM+s
$ee$ |  (r) | ggF | CMS CMS-PAS-HIG-19-007  | 13 | 137 | 4-8, 11.5-35 | SM+v
|  (r) | ggF | ATLAS ATLAS-CONF-2021-034  | 13 | 139 | 15-55 | SM+v
$\mu\mu$ |  (r) | ggF | CMS CMS-PAS-HIG-19-007  | 13 | 137 | 4-8, 11.5-35 | SM+v
|  (r) | ggF | ATLAS ATLAS-CONF-2021-034  | 13 | 139 | 15-30/15-55 | SM+s, SM+v

####  4.1.1 Branching Ratio and Mass Sensitivity

The sensitivity of current searches for Higgs decays to a pair of new scalars
is summarized in Figure 1, which shows the 95% CL upper limits on the
branching ratio excluded by each final state as a function of the mass of the
new particle. The limits on $\sigma/\sigma_{h}^{SM}\times Br(h\rightarrow
ss\rightarrow XX~{}YY)$ do not depend on the (model-dependent) branching
ratios of the decays of the new scalar, and make it possible to compare the
overall sensitivity for different channels and mass ranges. None of the
searches pursued so far are able to distinguish between odd and even parity
for the new scalar, and hence the symbols $s$ and $a$ may be used
interchangeably. Decays to new vector particles can result in significantly
different acceptance, so dedicated interpretations are needed.

Figure 1: Observed 95% CL upper limits on
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow ss\rightarrow XXYY)$ where $s$ is a
new scalar decaying to pairs of SM particles $X$ and $Y$, and
$\sigma_{h}^{SM}$ is the SM Higgs boson production cross section. The most
recent $h\rightarrow ss$ analyses from Table 1 are included.

Current searches cover a mass range for the new particle from $m\gtrsim
2m_{\mu}\approx 0.2$ GeV to $m_{h}/2\approx 62.5$ GeV. The lower mass range is
exclusively covered by the $\mu\mu\mu\mu$ decay channel, which spans the full
mass range except for challenging regions close to the $J/\psi$ and $\Upsilon$
mass peaks in some analyses. These searches currently set the strongest
constraints on the branching ratio for a given exclusive final state, down to
$\sim 10^{-6}$ ATLAS-CONF-2021-034 ; CMS:2018jid . Searches for the
$\mu\mu\tau\tau$ and $\mu\mu bb$ decays are currently able to place limits on
exclusive branching ratios down to $\sim 10^{-5}-10^{-4}$ in the mass range
from $m\gtrsim 2m_{\tau}\approx 4$ GeV to $m_{h}/2\approx 62.5$ GeV
Abazov_2009 ; ATLAS:2015unc ; CMS:2020ffa ; CMS:2018qvj ; ATLAS:2021hbr ;
CMS:2018nsh . Searches in the $bb\tau\tau$ CMS:2018zvv , $\tau\tau\tau\tau$
CMS:2019spf , and $bbbb$ ATLAS:2018pvw ; ATLAS:2020ahi  final states reach
sensitivity in the range $\sim 10^{-2}-10^{-1}$ for the mass range $m\gtrsim
2m_{b}\sim 10$ GeV. Searches sensitive to photons also place significant
constraints on the branching ratio, including limits down to $10^{-5}$ for
$m\approx 12-62.5$ GeV in the $\gamma\gamma\gamma\gamma$ final state
ATLAS:2015rsn ; CMS-PAS-HIG-21-003  and $10^{-1}$ for $m\approx 20-60$ for
$\gamma\gamma jj$ ATLAS:2018jnf .

There are currently fewer experimental searches targeting decay modes to a new
pseudoscalar or vector boson produced with a $Z$ boson. A search for hadronic
scalar decays ATLAS:2020pcy  sets upper limits on $Br(h\rightarrow
Za\rightarrow\ell\ell XX)$ as low as 0.35 for $m_{a}$ in the range $0.5-4$
GeV, assuming $a$ decays to either gluon pairs or strange or charm quark
pairs. Decays to muons and electrons are also explored ATLAS-CONF-2021-034 ,
setting limits on the branching ratio down to $\approx 5\times 10^{-5}$ in the
$15-30$ GeV or $15-55$ GeV mass range for the pseudoscalar or vector cases,
respectively.

The current reach of all the searches in Table 1 is limited by statistics, so
updated analyses using all available data will improve the sensitivity. More
sophisticated analyses, including new reconstruction and identification
techniques, can help complete the coverage of the full mass range. Additional
searches in uncovered channels may also bring additional sensitivity and are
interesting cross checks in case an excess is observed.

####  4.1.2 SM+s

Searches for decays to a new light scalar, $s$, often focus on the heaviest
particles that are kinematically allowed in the scalar decay. Decays to muons
are considered for $m\gtrsim 2m_{\mu}\approx 0.22$ GeV and are particularly
important in the lowest mass range until decays to taus may also become
important, $m\gtrsim 2m_{\tau}\approx 3.6$ GeV. Finally in the mass range
$m\gtrsim 2m_{b}\approx 8.4$ GeV, several searches also target decays to
$b$-jets.

Figure 2: Observed 95% CL upper limits on
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow ss)$ in the SM+s scenario where $s$
is a new Higgs-mixed scalar, from a selection of the most recent analyses in
Table 1. The branching fractions of the new scalar to SM particles are taken
from Gershtein:2020mwi ; LHCHiggsCrossSectionWorkingGroup:2016ypw , as
described in Section 3.1.

Figure 2 shows the upper limits on $Br(h\to ss)$ in the SM+s scenario, using
the branching ratios for the new scalar predicted by the minimal model of Sec.
3.1. The strongest constraints appear at the lowest masses from the
$\mu\mu\mu\mu$ mode, setting branching ratio limits down to 10-5. Between the
$J/\psi$ and the $\Upsilon$ thresholds, the sensitivity steadily decreases to
about 10-1. The sensitivity from the $\mu\mu\mu\mu$ channel is comparable to
the $\mu\mu\tau\tau$ and $\tau\tau\tau\tau$ channels in the $\sim(7-10)$ GeV
mass range. In the highest mass range $m\gtrsim 2m_{b}$, several final states
including $b$-quarks ($bbbb$, $bb\mu\mu$ and $bb\tau\tau$) constrain branching
ratios down to about $10^{-1}$. A combination of results from different
channels, especially in the intermediate and higher mass range where several
decay modes have comparable sensitivity, would extend the reach beyond the
current limits.

####  4.1.3 SM+ALP

There are fewer searches interpreted in the context of SM+ALP scenario
compared to the SM+s and SM+v cases, as summarized in Table 1. As an
illustrative example, the benchmark scenario with couplings to fermions
$C_{F}=1$ and to gauge bosons $C_{BB}=C_{WW}=C_{GG}=1/(4\pi)^{2}$ discussed in
Bauer:2017ris  has appreciable fermionic branching ratios, but enhanced
branching ratios to photons and gluons compared to the SM+s model. The
searches listed in Table 1 can be reinterpreted in this particular benchmark
SM+ALP model and are able to exclude $\sigma/\sigma_{h}^{SM}\times
Br(h\rightarrow aa)$ as small as $10^{-1}$. The enhanced gluon branching
fraction reduces current sensitivity to this benchmark point compared to SM+s,
as the reach is mostly driven by searches relying on fermionic final states.
Current searches for $gg\gamma\gamma$ and $\gamma\gamma\gamma\gamma$ have
lower sensitivity to probe $Br(h\to aa)$ for this specific benchmark point,
but they can be very important in other benchmarks where $C_{F}\ll 1$. There
is a strong case to expand the current experimental program to cover more
final states involving photons and gluons.

####  4.1.4 SM+v

New light vectors arising in models with kinetic mixing are expected to have
sizeable branching ratios to leptons, as described in Section 3.3. Figure 3
shows the latest upper limits on the exotic Higgs branching ratio to final
states with a dark $Z$ boson, $Z_{D}$, from different searches with lepton
final states after considering the $Z_{D}\to f\bar{f}$ decay width given in
Equation 14. The figure summarizes the limits obtained for both
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow Z_{D}Z_{D})$ (left panel) and
$\sigma/\sigma_{h}^{SM}\times Br(h\rightarrow ZZ_{D})$ (right panel). The CMS
search CMS-PAS-HIG-19-007  looks for $h\rightarrow Z_{D}Z_{D}$ in the mass
ranges 4.2-8 and 11.5-60 GeV, and for $h\rightarrow ZZ_{D}$ in the mass ranges
4.2-8 and 11.5-35 GeV, exploiting in both cases $Z_{D}$ decays to electrons or
muons in the full mass range. The ATLAS search ATLAS:2018coo  considers
$Z_{D}$ decays to electrons or muons in the higher mass range ($h\rightarrow
Z_{D}Z_{D}$: 15-60 GeV, $h\rightarrow ZZ_{D}$: 15-55 GeV), with similar
sensitivity to CMS. In the lower mass range (4.4-8 GeV, 12-15 GeV, and also
below the $J/\psi$ mass, 1.2-2 GeV), the same ATLAS search is restricted to
$h\rightarrow Z_{D}Z_{D}$ and considers only the $4\mu$ final state (see light
blue line in the left panel of the figure). Both ATLAS and CMS interpret the
results for $h\to Z_{D}Z_{D}$ as limits on the coupling constant $\kappa$ that
controls the mixing between the dark scalar and the Higgs, and for $h\to
ZZ_{D}$ as limits on $\epsilon$ that controls the mixing between the dark
vector and SM hypercharge (see Section 3.3).

Figure 3: Observed 95% CL upper limits on (left)
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow Z_{D}Z_{D})$ and (right)
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow ZZ_{D})$ in the SM+v scenario,
where $Z_{D}$ is a kinetically-mixed dark vector, from the most recent
searches in Table 1. The ATLAS ATLAS-CONF-2021-034  limits correspond to a low
mass $4\mu$ search (light blue, only available for the $h\rightarrow
Z_{D}Z_{D}$ interpretation) and a higher mass search that considers muon and
electron decays (dark blue). The CMS search CMS-PAS-HIG-19-007  includes muon
and electron decays in the full mass range for both $h\rightarrow Z_{D}Z_{D}$
and $h\rightarrow ZZ_{D}$. The branching fractions of the new vector to SM
particles follow the prescriptions in Curtin:2014cca , as described in Section
3.3.

Available searches can be improved by including electrons in the lower mass
range, by performing dedicated background estimates in the $J/\psi$ and
$\Upsilon$ pole regions, and by extending the search below $m_{Z_{D}}<1$ GeV,
using techniques similar to the ones in the CMS search CMS:2018jid . Other
searches for SM+v include displaced decays, and are discussed next.

###  4.2 Summary of displaced and invisible signatures

Experiments at the LHC have performed several searches for Higgs boson decays
to both visibly-decaying LLPs and invisible BSM particles. Dedicated searches
targeting LLPs that travel macroscopic distances in the detector rely on the
reconstruction and identification of displaced objects. Even though they were
not originally designed to specifically detect LLPs, ATLAS and CMS have
sensitivity to a variety of LLP signals. Searches have been performed in both
hadronic and leptonic channels. LHCb, covering the pseudorapidities
$2<\eta<5$, is designed to observe displaced decays and has also performed
such searches.

In the case of Higgs boson decays to LLPs, available searches cover a broad
range of masses and lifetimes $c\tau$. The LLPs are assumed to be on-shell and
neutral, giving rise to processes of the type $h\rightarrow ss/vv\rightarrow
XX~{}YY$, where $s$ is a new scalar, $v$ a new vector and $XX$ and $YY$ are
pairs of SM particles from each new boson decay. In several cases the LLP
signature is very distinctive and the searches have low backgrounds, so the
analyses require reconstruction of only one of the two decays. These searches
are referred to as $h\rightarrow s/v+X\rightarrow YY+X$, where $X$ refers to
all possible decays of the second particle in the pair. Table 2 summarizes the
latest searches for exotic Higgs decays to LLPs.

Table 2: Summary of the latest LLP searches for $h\rightarrow ss/vv$. $m$ and $c\tau$ denote the new particle mass and lifetime, respectively.  Decay | Mode | Reference | Method |  $\sqrt{s}$ (TeV) |  $\int\mathcal{L}$ (fb-1) |  $m$ (GeV) |  $c\tau$ (m)
---|---|---|---|---|---|---|---
SM+s: $h\rightarrow ss$ or $s+X$, $s$ long-lived |
$bbbb$ | $Wh/Zh$ | ATLAS ATLAS:2020ahi  | prompt reinterp. | 13 | 36.1 | 20-60 | $10^{-4}-10^{-2}$
$bbbb$ | ggF | LHCb LHCb:2017xxn  | disp. jets | 7,8 | 2.0 | 25-50 | $10^{-3}-10^{-1}$
$cccc$
$ssss$
$bbbb$ | $Zh$ | CMS CMS:2021uxj  | Z+disp. jets | 13 | 117 | 15-55 | $10^{-3}-1$
$dddd$
$bbbb$ | $Zh$ | ATLAS ATLAS:2021jig  | Z+disp. jets | 13 | 139 | 16-55 | $10^{-3}-1$
$bbbb$ | ggF | CMS CMS:2020iwv  | disp. jets | 13 | 132 | 15-55 | $10^{-3}-10$
$dddd$
$bbbb$ | ggF | ATLAS ATLAS:2019qrr  | CalRatio | 13 | 10.8, 33.0 | 5-55 | $10^{-1}-10^{3}$
$cccc$
$\tau\tau\tau\tau$
$bbbb$ | ggF | ATLAS ATLAS:2019jcm  | ID+MS DVs | 13 | 33.0 | 8-55 | $10^{-1}-10$
$cccc$
$\tau\tau\tau\tau$
$bbbb$ | ggF | CMS CMS:2021juv  | hadronic MS | 13 | 137 | 14-55 | $10^{-1}-10^{4}$
$dddd$ | 7-55
$\tau\tau\tau\tau$ | 7-55
$bbbb$ | ggF | ATLAS ATLAS:2018tup  | MS1+MS2 DV | 13 | 36.1 | 5-40 | $10^{-1}-10^{3}$
$cccc$
$\tau\tau\tau\tau$
$bbbb$ | ggF | ATLAS ATLAS-CONF-2021-032  | MS2 DV | 13 | 139 | 5-55 | $10^{-1}-10^{2}$
$cccc$
$\tau\tau\tau\tau$
$e\mu$+X | ggF | CMS CMS:2021kdm  | disp. leptons | 13 | 113-118 | 30-50 | $10^{-3}-10^{1}$
$\mu\mu$+X
$ee$+X
SM+v: $h\rightarrow Z_{D}Z_{D}$ or $Z_{D}+X$, $Z_{D}$ long-lived |
$\mu\mu\mu\mu$ | ggF | CMS CMS:2021ogd  | dimuon scouting | 13 | 101 | 0.5-50 | $10^{-4}-10$
$\mu\mu$+X
$\mu\mu$+X | ggF | ATLAS ATLAS:2018rjc  | MS dimuon | 13 | 32.9 | 20-60 | $10^{-3}-10^{2}$
SM+v: dark SUSY long-lived |
$\mu\mu$+X | ggF | ATLAS ATLAS:2019tkk  | disp. lepton-jets | 13 | 36.1 | $0.2-3.6$ | $10^{-3}-1$
$hh$+X
$hh$+X | ggF | ATLAS ATL-PHYS-PUB-2020-007  | recast of ATLAS:2019qrr  | 13 | 10.8, 33.0 | $\sim 0.4$ | $10^{-3}-10^{-1}$
$\mu\mu\mu\mu$ | ggF | CMS CMS:2018jid  | disp. muons | 13 | 35.9 | 0.25-8.5 | 0-1

Existing searches cover a large number of final states including large impact-
parameter tracks and displaced vertices (DVs) reconstructed in the inner
tracking detector (ID), displaced hadronic jets or photons in the calorimeter,
and displaced signals from jets or leptons in the muon system (MS). Dedicated
searches based on DV reconstruction using tracks in the ID matched to a
“displaced jet” achieve sensitivity to LLPs with lifetimes in the range from a
few mm to about a meter. These searches often rely on the ability to
reconstruct tracks with large impact parameter ATLAS:2017zsd . Given the
difficulty triggering on signals in the ID, these searches typically rely on
other accompanying objects, such as leptons from the decays of a $Z$ boson
produced in association with the Higgs boson ATLAS:2020ahi ; CMS:2021uxj .
Searches targeting signatures in the calorimeter and MS are sensitive to the
lifetime range from a few cm to hundreds of meters ATLAS:2019qrr ; CMS:2021juv
. Calorimeter and muon signals can be used in the trigger, in some cases with
dedicated strategies for displaced decays, and such searches therefore target
Higgs bosons produced by gluon fusion. Examples include the “CalRatio” trigger
that identifies trackless displaced jets in the ATLAS hadronic calorimeter by
searching for signals with low electromagnetic fraction compared to the
hadronic fraction ATLAS:2019qrr  and the “MS vertex” trigger that searches for
clusters of particles in the ATLAS MS ATLAS:2018tup ; ATLAS-CONF-2021-032 .
Dedicated reconstruction algorithms are also used to reconstruct displaced
decays using signals in the muon detectors, including multi-track vertices in
the ATLAS MS which are used to perform searches with one (MS1) and two (MS2)
vertices ATLAS:2018tup ; ATLAS-CONF-2021-032 , and clusters of hits in the CMS
endcap MS CMS:2021juv  which are used to reconstruct hadronic and
electromagnetic showers (hadronic MS). Combinations of signatures also offer
sensitivity to several signals, such as the ATLAS search for both DVs in the
ID and the MS ATLAS:2019jcm . The CMS search for displaced leptons CMS:2021kdm
targets transverse impact parameters between 0.01 cm and 10 cm and is thus
sensitive to LLP lifetimes from 1 mm to 10 m. Searches targeting longer
lifetimes benefit from the distinctiveness of the signal and the few SM
backgrounds. For the longest lifetimes, the sensitivity is limited by the size
of the detector.

One of the main challenges to search for low mass LLPs is that these signals
have large SM backgrounds and are therefore difficult to trigger on. One
limitation of the trigger systems is the bandwidth for offline processing and
data storage. New strategies such as “scouting”, where the event size is
reduced as a trade-off for recording larger rates of events, make it possible
to target signals such as displaced leptons with small displacements and low
masses, extending the sensitivity beyond the reach of traditional searches
CMS:2021ogd . Complementary searches targeting the largest lifetimes rely on
muon reconstruction in the MS alone, without a corresponding signal in the
inner detectors and can achieve sensitivity with a single vertex due to the
distinctive, low-background signal ATLAS:2018rjc . This strategy uses
dedicated triggers to identify tracks in the muon detectors without requiring
matches to an ID track or pairs of collimated muons in the MS.

LLPs may be invisible if they decay outside the detector volume or if the
standard algorithms are unable to reconstruct the signature. Therefore
searches for invisible decays ($h\rightarrow\mathrm{E}_{T}^{\mathrm{miss}}$),
in which the decay product escapes detection or is undetectable, and semi-
invisible decays ($h\rightarrow s/v+\mathrm{E}_{T}^{\mathrm{miss}}$), where
one of the new particles decays to SM particles and the other is invisible,
are also sensitive to exotic Higgs boson decays to LLPs. Available searches
for these signals are summarized in Table 3. Both invisible and semi-visible
searches rely on the presence of substantial missing transverse energy,
$\mathrm{E}_{T}^{\mathrm{miss}}$, to identify the Higgs decay. Current
experimental bounds on invisible Higgs boson decays are mainly from searches
for Higgs bosons produced by VBF CMS:2019ajt ; ATLAS-CONF-2020-052  or in
association with a $Z$ boson ATLAS-CONF-2021-029 ; CMS:2020ulv . Although the
combination of searches from ATLAS and CMS using the full Run 2 dataset has
not been completed, branching ratios greater than 0.11 are already excluded.
All current upper limits in each production mode can be found in Table 3.

Table 3: Summary of the latest searches for invisible and semi-visible Higgs
boson decays, including available interpretations for semi-visible final
states and observed (expected) upper limits (UL) at 95% CL for invisible
signatures.  $h\rightarrow s/v+\mathrm{E}_{T}^{\mathrm{miss}}$
---
Decay | Mode | Reference |  $\sqrt{s}$ (TeV) |  $\int\mathcal{L}$ (fb-1) | Interpretations
$\mathrm{E}_{T}^{\mathrm{miss}}$ \+ $\gamma$ | VBF | CMS CMS:2020krr  | 13 | 130 | SM+v
| VBF | ATLAS ATLAS:2021pdg  | 13 | 139 | SM+v
| $Zh$ | CMS CMS:2019ajt  | 13 | 137 | SM+v
| ggF, $Zh$ | CMS CMS:2015ifd  | 8 | 19.4 | Other
$\mathrm{E}_{T}^{\mathrm{miss}}+bb$ | $Zh$ | ATLAS ATLAS:2021edm  | 13 | 139 | NMSSM
$h\rightarrow\mathrm{E}_{T}^{\mathrm{miss}}$
Decay | Mode | Reference |  $\sqrt{s}$ (TeV) |  $\int\mathcal{L}$ (fb-1) | Br(H$\rightarrow$Inv) UL
$\mathrm{E}_{T}^{\mathrm{miss}}$ | VBF | ATLAS ATLAS-CONF-2020-008  | 13 | 139 | 0.13 (0.13)
| VBF | CMS CMS-PAS-HIG-20-003  | 13 | 138 | 0.17 (0.11)
| $Z(ll)h$ | ATLAS ATLAS-CONF-2021-029  | 13 | 139 | 0.18 (0.18)
| $Z(ll)h$ | CMS CMS:2020ulv  | 13 | 137 | 0.29 (0.25)
| ggF | ATLAS ATLAS:2021kxv  | 13 | 139 | 0.34 (0.39)
| ggF, $V(qq)h$ | CMS CMS:2021far  | 13 | 137 | 0.278 (0.253)
| $tth$ | ATLAS ATLAS-CONF-2020-052  | 13 | 139 | 0.40 (0.36)
| $tth$ | CMS CMS:2019bke  | 13 | 35.9 | 0.46 (0.48)
| Combination | ATLAS ATLAS-CONF-2020-052  | 7, 8, 13 | 4.7+20.3+139 | 0.11 (0.11)
| Combination | CMS CMS:2018yfx  | 7, 8, 13 | 4.9+19.7+38.2 | 0.19 (0.15)

In several scenarios, LLP searches have sensitivities that are greater than
those for promptly decaying particles. Searches at lower lifetimes and masses
typically lose sensitivity due to the presence of larger backgrounds. The
trigger and identification of low mass LLP signatures can also be challenging
since the decay products may overlap and the ability to reconstruct DVs
significantly degrades for nearby particles whose trajectories are parallel.
For higher masses, the decay products tend to have larger opening angles and
in some cases the objects become so non-pointing that the reconstruction and
identification efficiency may degrade. The LHC already has sensitivity to a
range of LLP signals and this capability can be extended by exploiting the
large datasets and benefiting from trigger and detector improvements in the
future (see Section 5).

The following sections describe hadronic searches with an interpretation
focusing on exotic Higgs decays to a pair of new scalars (Section 4.2.1) and
leptonic searches focusing on new vectors (Section 4.2.2). Studies of the
differences in acceptance for these scenarios have not been performed for LLP
signatures. There are no ATLAS or CMS interpretations of searches for exotic
Higgs decays to long-lived ALPs. Searches for displaced photons would be of
particular interest for scenarios with ALPs.

####  4.2.1 SM+s

Searches for $h\rightarrow ss$ where $s$ is a new long-lived scalar in the
mass range $30-40$ GeV decaying to SM fermions are summarized in Figure 4. For
the SM+s scenario, decays to pairs of $b$-quarks dominate with
$Br(s\rightarrow bb)\approx 85\%$ in this mass range, with additional
significant decays to $c$-quarks $Br(s\rightarrow cc)\approx 5\%$ and tau
leptons $Br(s\rightarrow\tau\tau)\approx 8\%$ (see Section 3.1).

Figure 4: Observed 95% CL upper limits on
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow ss)$ in the SM+s scenario where $s$
is a new long-lived scalar decaying hadronically. The analyses are summarized
in Table 2 and interpreted according to the procedure described in the text.
The branching fractions of the new scalar boson to SM particles follow the
prescriptions in LHCHiggsCrossSectionWorkingGroup:2016ypw , as described in
Section 3.1. The current best limit on invisible Higgs boson decays (see Table
3) is shown for comparison (gray marker on the right). The bounds from the
reinterpretation of a prompt search for $h\rightarrow ss\rightarrow 4b$ is
also shown at small lifetimes.

Several results only include an interpretation for a combination of final
states while others provide interpretations in terms of exclusive final
states. In order to compare the results, Figure 4 shows results for
$(\sigma_{h}/\sigma_{h}^{SM})\times Br(h\rightarrow ss)$ using the approximate
branching ratios for $s$ to decay to $b$, $c$, and $\tau$ final states quoted
above. The ATLAS CalRatio, MS and ID+MS DV results ATLAS:2018tup ;
ATLAS:2019jcm ; ATLAS:2019qrr ; ATLAS-CONF-2021-032  provide only the combined
results and are reproduced without modifications. The curves corresponding to
the ATLAS ATLAS:2021jig  and CMS CMS:2021uxj ; CMS:2020iwv  displaced jets
analyses use only the $bbbb$ final state with an assumed $Br(s\rightarrow
bb)=85\%$. The difference in per-jet efficiency for displaced jet
reconstruction in decays to different quark flavors comes primarily from the
difference in track multiplicity. Jets originating from $b$-quarks may form
tertiary vertices, effectively reducing the number of tracks in the LLP decay
vertex. We expect per-jet efficiencies for decays to $c$-quarks to be more
similar to those for light quark jets than $b$-jets; this effect is seen in
the LHCb analysis LHCb:2017xxn . However, due to the limited information
available, the final states with $s\rightarrow cc$ and $s\rightarrow\tau\tau$
decays are not included in the figure for ATLAS and CMS displaced jet results.

The LHCb displaced jet analysis LHCb:2017xxn  includes results both in the
$bbbb$ and $cccc$ final states, which are combined in Figure 4 under the
assumption that the only difference comes from the per-jet efficiency for
displaced jet reconstruction. The CMS hadronic MS analysis CMS:2021juv
provides results in the $bbbb$ and $\tau\tau\tau\tau$ final states and a
similar combination is performed. Beyond the analyses using dedicated
reconstruction methods for long-lived resonances, a reinterpretation of the
ATLAS prompt search ATLAS:2020ahi  shows sensitivity to signals with lifetimes
up to the mm scale. This analysis is mainly sensitive to the $bbbb$ final
state, since b-tagging algorithms are used to select events.

####  4.2.2 SM+v

Figure 5: Observed 95% CL upper limits on
$\sigma_{h}/\sigma_{h}^{SM}Br(h\rightarrow Z_{D}Z_{D})$ in the SM+v scenario
where $Z_{D}$ is a new long-lived vector decaying to leptons. The analyses are
summarized in Table 2. The branching fractions of $Z_{D}$ to SM particles
follow the prescriptions in Curtin:2014cca , as described in Section 3.3.
Current limits for prompt searches (see Table 1) and searches for invisible
Higgs boson decays (see Table 3) are also shown. The mass of the corresponding
signal LLP is indicated next to each curve in GeV.

Recent results targeting searches for exotic Higgs decays to LLPs decaying to
leptons are summarized in Figure 5. These searches are interpreted in the
context of the SM+v scenario, described in Section 3.3, focusing on leptonic
decays of a long-lived $Z_{D}$, $h\rightarrow Z_{D}Z_{D}$. The limits from
prompt searches, described in Section 4.1, and limits from invisible decays,
shown in Table 3, are also shown for comparison. A reinterpretation of these
searches in terms of signals with small lifetimes is currently not available,
but would be interesting to show the range of lifetimes covered by prompt
searches and close the gap with dedicated LLP searches.

Dedicated triggering techniques targeting displaced muons have been
instrumental to search for LLP decays in the $2\mu$+X and $4\mu$ final states.
A recent search by CMS CMS:2021ogd  using dimuon scouting probes a wide range
in proper lifetimes (0.1 mm to 10 m) for masses in the range 0.65-50 GeV and
constrains branching ratio limits down to about $10^{-5}$. A complementary
ATLAS ATLAS:2018rjc  search for LLP $\mu\mu$+X decays, identified through
displaced vertices reconstructed from tracks in the MS that do not have a
corresponding ID track, extends the probed lifetime range beyond 100 meters,
with branching ratio limits down to about $10^{-4}$ for lifetimes in the cm-m
range and LLP masses of 20 GeV. These results provide lifetime exclusions for
several mass hypotheses and also include interpretations as a function of
other model parameters, such as the kinetic mixing and mixing parameter
$\kappa$.

Available searches offer sensitivity to a broad range of lifetimes for a range
of masses. Extending the reach of the analyses to target lifetimes and masses
beyond those currently reported in the interpretations is important to cover
the full range of possible signals. Two-dimensional $m$-$c\tau$ plots may
provide a clearer picture of any gaps in sensitivity. Several interpretations
are coarse and do not cover the full region of sensitivity in mass and
lifetime. In addition, limits for different exclusive final states may
complete our understanding of the sensitivity of different searches and help
guide future search efforts.

The special techniques used in LLP searches are a challenge for the
reinterpretation of results for alternative models without access to the full
simulation of detector effects. Data preservation and in-depth documentation
of the details of the models, including detailed acceptances and efficiencies,
following the recommendations of LHCReinterpretationForum:2020xtr , is
particularly important in this context. As an example, Ref. ATL-PHYS-
PUB-2020-007  presents a reinterpretation of the ATLAS displaced calorimeter
jet search ATLAS:2019qrr  with the RECAST framework Cranmer:2010hk  in the
context of a dark SUSY model Falkowski:2010cm ; Falkowski:2010gv  that
considers hadronic decays of a dark photon and provides complementary coverage
to a dedicated search for displaced lepton-jets that targets such dark photon
decays to collimated dimuons or light hadrons ATLAS:2019tkk .

##  5 Future probes

The HL-LHC is expected to produce a large sample of $\mathcal{O}(10^{8})$
Higgs bosons, which will generically enable more than an order of magnitude
improvement in the sensitivity to exotic Higgs boson decays. Projections
assuming that current object reconstruction performance can be maintained
indicate that sensitivities to exotic Higgs decays into hadronic final states
can reach sub-percent branching fractions CMS:2019rsy . Meanwhile, combining
the full ATLAS and CMS datasets from the HL-LHC is forecast to constrain the
total exotic branching ratio to $<4\%$ at 95% CL deBlas:2019rxi . The improved
discovery potential from the HL-LHC is not only from the large total
integrated luminosity (up to 3 ab-1), but also the planned detector upgrades,
which will provide refined trigger and reconstruction capabilities.

The detector upgrades include new inner tracking and timing detectors, as well
as new electronics and an updated trigger and data acquisition system, which
are expected to extend the capabilities in ATLAS and CMS to study exotic Higgs
decays in challenging low-mass and/or displaced final states. Studies from CMS
have shown that improvements in displaced jets using information from the ID
and time-displaced calorimeter-based jets can significantly improve the
sensitivity to LLPs with meter-scale lifetimes CERN-LHCC-2020-004 . Both ATLAS
and CMS plan to reduce the dependence of muon triggers on primary vertex
constraints, increasing the sensitivity to LLP decays with larger
displacements CERN-LHCC-2020-004 ; CERN-LHCC-2017-020 . The increased
triggering efficiency for muons with larger displacements can also
significantly improve the sensitivity to exotic Higgs decays to dark photons,
such as the CMS HL-LHC prospect described in CMS:2018lqx . The higher
granularity in the ATLAS triggers will also make it possible to identify
collimated dimuon pairs arising in decays of low mass resonances CERN-
LHCC-2017-020 .

Beyond the main LHC program, there are several other experimental strategies
being pursued or planned that provide complementary opportunities to study
exotic Higgs boson decays. Several dedicated LLP detectors provide new
capabilities for discovering LLPs produced in the LHC collisions (Section
5.1). Future colliders offer substantial new opportunities for Higgs decays.
Electron-positron and muon-muon colliders offer a clean environment to probe
such signals (Sections 5.2.1, 5.2.3, respectively), while high-energy proton
colliders enable searches for extremely rare decays (Section 5.2.2), as we now
discuss.

###  5.1 Dedicated LLP detectors

Triggering challenges are one major limitation for search sensitivity to LLPs
produced in the relatively low-energy events following from Higgs decays.
Proposed dedicated LLP detectors, such as CODEX-b Gligorov:2017nwh ;
Aielli:2019ivi  and MATHUSLA Chou:2016lxi ; MATHUSLA:2018bqv , would be
located far away from the collision point with intervening shielding material
that would stop most of the charged and/or strongly-interacting SM particles
from reaching the detectors. These detectors would not suffer from trigger
limitations and would thus readily have sensitivity to the relatively low mass
final states of interest for LLPs produced in Higgs decays. The long baselines
and low backgrounds of these experiments also help them extending the range of
$c\tau$ that can be probed, although the small solid angle subtended by these
detectors, compared to the main detectors, is the limiting factor in this
extension. For theories such as neutral naturalness models that predict a
large ($\gtrsim 3$) number of relatively soft LLPs in a single event, the soft
$p_{T}$ spectra for the LLPs tend to exacerbate triggering challenges at the
main detectors, while the larger number of LLPs increases the acceptance at
dedicated detectors. In such scenarios the additional physics reach provided
by dedicated detectors can be substantial Curtin:2018mvb .

The Higgs is sufficiently heavy that, to have optimal acceptance for its decay
products, detectors should not be located too far forward. MATHUSLA and
CODEX-b have good acceptance for exotic Higgs decay products, while far-
forward detectors such as the FASER experiment Feng:2017uoz ; FASER:2018eoc
do not have competitive sensitivity. However, when new physics is light enough
to be produced in e.g. meson decays, a wide range of new experimental
signatures and searches become possible. In particular, exotic $B$ and $K$
decays can be powerful probes of BSM scalars coupled through the Higgs portal.
The relationship between such low-energy probes and exotic branching ratios of
the Higgs boson is highly model-dependent, and we will not discuss the topic
further here; see Beacham:2019nyx  for a recent overview.

###  5.2 Future colliders

####  5.2.1 Electron-positron colliders

The $\mathcal{O}(10^{6})$ Higgs bosons that would be produced at planned
electron-positron colliders will not come close to the statistics of the HL-
LHC Higgs sample, but thanks to the low-background environment, will offer the
most sensitive discovery opportunities for decays into hadronic final states,
as well as other final states that cannot be easily reconstructed and/or
separated from the large LHC backgrounds. This Higgs sample size is reflective
of the running scenarios summarized in deBlas:2019rxi  for three proposed
machines: 5 (5.6) ab-1 of unpolarized collisions at 240 GeV, as envisioned for
FCC-ee FCC:2018byv  (CEPC CEPCStudyGroup:2018ghi ), and 2 ab-1 of polarized
collisions at 250 GeV, which is the first stage of operation planned for the
ILC Bambade:2019fyw ; LCCPhysicsWorkingGroup:2019fvj .

A survey of electron-positron collider sensitivities for several
(partially-)visible, prompt final states was performed in Liu:2016zki , which
found sensitivities to exotic branching ratios at the level of a few$\times
10^{-4}$ over a wide range of signatures. These studies were carried out for
the particularly clean process where $e^{+}e^{-}\to Zh$ is followed by
$Z\to\ell\ell$. Further incorporating analyses in the higher statistics but
also higher-background $Z\to jj$ or $Z\to$ invisible final states would
contribute additional sensitivity. Meanwhile direct searches for invisible
decays are projected to reach $Br(h\to\mathrm{invisible})<0.3\%$
deBlas:2019rxi .

The SM+s model is a prime example of a model that predict preferential decays
to final states that have challenging backgrounds at the LHC. HL-LHC
sensitivity to SM+s above the $b$ threshhold reaches up to $Br(h\to
ss)<2.8\times 10^{-2}$ using CMS HL-LHC projections for the $bb\tau\tau$ final
state CMS:2019rsy . This projected sensitivity is exceeded by nearly two
orders of magnitude at electron-positron colliders: the estimates of Ref.
Liu:2016zki  for the $bbbb$ final state give $Br(h\to ss)\lesssim 5\times
10^{-4}$ across the range of masses $20\;\mathrm{GeV}<m_{s}<60$ GeV.

Beyond dedicated exclusive searches, the known initial state at lepton
colliders also affords the possibility of unambiguously measuring the total
width of the Higgs boson, thereby allowing for fully model-independent upper
bounds on the total exotic branching fraction. Ref. deBlas:2019rxi  projects
the resulting 95% CL constraints on the Higgs exotic branching ratio at the
one percent level.

While LLP searches at the LHC often enjoy excellent background rejection at
the analysis level, trigger challenges can limit LHC efficiency for LLPs
produced via the relatively low-mass Higgs boson. The lower background
environments of lepton colliders, together with detectors constructed with BSM
LLP signatures in mind, can potentially make LLP searches at Higgs factories
competitive with those at the LHC at the shorter LLP lifetimes where LHC
backgrounds are higher Alipour-Fard:2018lsf , or in other scenarios where the
event presents a particular trigger or background rejection challenge at the
LHC.

####  5.2.2 Future hadron colliders

Future proton-proton colliders running at a higher center of mass energy will
produce a much larger sample of Higgs bosons. For example,
$\mathcal{O}(10^{9})$ Higgs bosons will be produced at the high-energy LHC
($\sqrt{s}=27$ TeV) with $15\,\mathrm{ab}^{-1}$ data and at a 100 TeV proton
collider with $3\,\mathrm{ab}^{-1}$ data. This very large sample of Higgs
bosons can give access to very rare exotic decay modes. The biggest
improvements on the reach will be obtained for very clean decay modes, which
particularly benefit from the increase in statistics. An example is the search
for $h\to Z_{D}Z_{D}\to 4\ell$. The bound on the branching ratio for $h\to
Z_{D}Z_{D}$ could be pushed to $\sim 10^{-7}$, more than an order of magnitude
more stringent bound than what is achievable at the HL-LHC Curtin:2014cca .
Another example is the Higgs decay into two long-lived dark glueballs, as
arising in neutral naturalness theories Curtin:2015fna . Meanwhile direct
searches for the invisible branching fraction will reach
$Br(h\to{\mathrm{invisible}})<2.5\times 10^{-4}$, well below the SM prediction
$Br(h\to ZZ^{*}\to 4\nu)=1.1\times 10^{-3}$ FCC:2018vvp . Global fits of Higgs
rates will constrain the branching fraction into untagged states below $1\%$
deBlas:2019rxi .

However, direct searches for higher-background exotic Higgs decay modes can
also see major advances in sensitivity at future high energy proton colliders.
Cross-sections for sub-leading Higgs production modes can be much larger at
higher-energy proton colliders than the corresponding cross-sections at the
LHC. For example, the $t\bar{t}h$ production cross section at a 100 TeV proton
collider is $\sim 60$ times larger than at the LHC. These subleading
production modes will be essential to improve the reach for background-limited
exotic Higgs decays, such as e.g. $h\to ss\to bbbb$.

####  5.2.3 Muon colliders

Muon colliders, while more challenging to construct and instrument, would be
able to realize high center-of-mass energy collisions between elementary
particles. Although potential operational scenarios are still under active
discussion, the inclusive Higgs production at an $\mathcal{O}(10)$ TeV muon
collider with $\mathcal{O}(100\,\mathrm{ab}^{-1})$ of data would yield
$\mathcal{O}(10^{8})$ Higgs bosons, two orders of magnitude larger than the
production at proposed $e^{+}e^{-}$ Higgs factories. In addition, given the
low-background environment at a muon collider, such machines can provide an
excellent opportunity to investigate exotic Higgs decays beyond the reach of
the HL-LHC, offering sensitivity to ultra-rare exotic decay modes with
branching fractions down to $\mathcal{O}(10^{-7})$ AlAli:2021let ;
Franceschini:2021aqd .

##  6 Summary and conclusions

Exotic decays of the Higgs boson are an excellent place to search for the
footprints of new physics that couples only feebly to the SM. In the years
since the discovery of the Higgs boson, many theoretical studies of and
experimental searches for exotic Higgs boson decays have been performed. This
review summarizes recent developments in theoretical motivations for exotic
Higgs decays as well as the status of experimental searches for signatures
involving both prompt and displaced final states. We present interpretations
of many searches in terms of three benchmark scenarios that represent some of
the best-motivated minimal models for exotic Higgs decays.

The searches reviewed here already constitute a substantial accomplishment.
Experimental searches for dark vector bosons have attained sensitivity to
unprecedentedly small Higgs branching fractions, and even searches to more
difficult final states are reaching notable landmarks. Direct LHC searches for
exotic decay modes are now the leading probes of many models. Even for the
challenging hadrophilic SM+s model, direct searches in a variety of both
prompt and displaced final states now reach beyond constraints on the total
exotic branching ratio imposed by global fits to Higgs properties, while
searches for the decay $h\to ZZ_{D}$ are now beginning to surpass precision
electroweak measurements as a probe of the minimal dark photon model in parts
of parameter space. On the theoretical side, a substantial body of recent work
has led to qualitatively new understanding of how exotic Higgs decays can be
related to unanswered questions in particle physics, most notably the
hierarchy problem and the origin of dark matter.

To build on this effort and realize the full discovery potential offered by
exotic Higgs decays, work is still needed to understand gaps in current
experimental coverage, to guide future searches at the LHC and beyond, and to
use our developing understanding of the Higgs boson to shed new light on
physics beyond the SM. A major outstanding frontier for both theory and
experiment is Higgs decays involving more than one BSM species, as well as the
extension of current searches into more challenging regimes.

BSM particles are motivated across the entire mass range accessible in Higgs
decays, as well as with any experimentally testable value of $c\tau$. Many
current searches can be extended to cover a broader range of masses. In the
lower mass regime, the use of reconstruction and identification techniques
targeting non-isolated or merged decay products can be used, also in
combination with resolved objects to extend the reach. Existing searches for
Higgs decays may also offer sensitivity at the lowest masses where the decay
products are completely overlapping. Dedicated strategies may narrow gaps,
including the $J/\psi$ and $\Upsilon$ regions.

The further development of LLP searches will be critical for extending
coverage across the full range of testable lifetimes. Reinterpretations of
prompt searches are important to identify gaps in search coverage for the
smallest $c\tau$. Extending sensitivity at long lifetimes may be possible by
focusing on the outermost layers of current detectors and exploring dedicated
LLP detectors. Searches for LLPs can be harder to reinterpret than prompt
searches; thus it is vital for searches for decays to LLPs to report their
results in as transparent and reusable a form as possible. This point is
especially pressing as in many well-motivated theories the LLPs are composite
states, whose production is challenging to model in detail.

Many final states of interest are currently not covered. Examples of uncovered
final states include fully hadronic decays to jets (e.g., $gggg$, $ggbb$,
etc.), or displaced decays to photons or taus. Thus direct searches are not
currently sensitive to Higgs decays involving hadrophilic ALPs that decay
dominantly to gluons, nor do they target the interesting case of the displaced
photonically-decaying ALP. Meanwhile, few searches for semi-visible final
states have been performed to date, or for decays including a $Z$ boson and a
new boson in the decay. More complex scenarios involving decays into two
different BSM particles, including the case where cascade decays can occur
among the BSM species, have not been extensively explored. It does not take a
particularly elaborate model to realize high multiplicity final states; the
simple Higgsed dark photon model can already realize this possibility. In many
cases of interest high-multiplicity final states readily arise from decays
into confining hidden sectors. Given the experimental challenges posed by
soft, high-multiplicity final states together with the enlarged parameter
space of multi-state models, theoretical work on motivated reference models
featuring multiple BSM species can be particularly valuable to help guide this
program. However some signatures such as semi-invisible decay modes (very
common in decays to confining hidden sectors) and the potential presence of
resonances at different masses are straightforward and can be readily
implemented.

Exotic Higgs decays continue to serve as strong motivation for future work.
Sensitivity studies, including considerations about dedicated triggers and
reconstruction strategies for these signals, can provide valuable input to
guide future search strategies. Theoretical and phenomenological work
continues to be crucial to understand the implications of these analyses for
physics beyond the SM and to set priorities for future efforts. The LHC and
its HL-LHC upgrade, as well as future colliders and experiments, will offer
many exciting opportunities to explore the question of whether the Higgs has
new interactions and help answer some of the outstanding open questions in
particle physics.

## Acknowledgements

The work of MC is supported by the Spanish Ministry of Science and Innovation
“Ramón y Cajal” fellowship RYC-2017-22161. The research of SG is supported in
part by NSF CAREER grant PHY-1915852 and grant PHY-1748958. SG thanks the
Aspen Center for Physics, supported by NSF grant PHY-1607611, for hospitality
when part of this work was done. The work of VM is supported in part by the
NSF CAREER grant PHY-1830832. The work of JS is supported in part by DOE
Career grant DE-SC0017840. We thank J. Stegemann, N. Wardle, A. Escalante, C.
Botta, R. Coelho Lopes de Sa and S. Willocq for useful discussions.

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