#### Reconciling large- and small-scale structure in Twin Higgs models

HJE
Reconciling large- and small-scale structure in Twin Higgs models
Valentina Prilepina 0 1 3
Yuhsin Tsai 0 1 2
0 Stadium Dr. , College Park, MD, 20742 U.S.A
1 One Shield Ave , Davis, CA, 95616 U.S.A
2 Maryland Center for Fundamental Physics, Department of Physics, University of Maryland , USA
3 Physics Department, University of California Davis , USA
We study possible extensions of the Twin Higgs model that solve the Hierarchy problem and simultaneously address problems of the large- and small-scale structures of the Universe. Besides naturally providing dark matter (DM) candidates as the lightest charged twin fermions, the twin sector contains a light photon and neutrinos, which can modify structure formation relative to the prediction from the
Cosmology of Theories beyond the SM; Beyond Standard Model
CDM paradigm.
We
focus on two viable scenarios. First, we study a Fraternal Twin Higgs model in which
the spin-3/2 baryon ^
(^b^b^b) and the lepton twin tau ^ contribute to the dominant and
subcomponent dark matter densities. A non-decoupled scattering between the twin tau and
twin neutrino arising from a gauged twin lepton number symmetry provides a drag force
that damps the density inhomogeneity of a dark matter subcomponent. Next, we consider
the possibility of introducing a twin hydrogen atom H^ as the dominant DM component.
After recombination, a small fraction of the twin protons and leptons remains ionized during
structure formation, and their scattering to twin neutrinos through a gauged U(1)B L force
provides the mechanism that damps the density inhomogeneity. Both scenarios realize the
Partially Acoustic dark matter (PAcDM) scenario and explain the 8 discrepancy between
the CMB and weak lensing results. Moreover, the self-scattering neutrino behaves as a dark
uid that enhances the size of the Hubble rate H0 to accommodate the local measurement
result while satisfying the CMB constraint. For the small-scale structure, the scattering
of ^ 's and H^ 's through the twin photon exchange generates a self-interacting dark matter
(SIDM) model that solves the mass de cit problem from dwarf galaxy to galaxy cluster
scales. Furthermore, when varying general choices of the twin photon coupling, bounds
from the dwarf galaxy and the cluster merger observations can set an upper limit on the
twin electric coupling.
1 Introduction
2
3
4
5
6
1
2.1
2.2
The extended fraternal Twin Higgs model
Asymmetric dark matter and dark uid
Dark matter self-interaction and dark matter-dark uid scattering
Large-scale structure: Twin lepton with acoustic oscillations
Small-scale structure: Twin baryon with a self-interaction
Solutions from the Twin hydrogen DM Discussion and conclusions 1 4
Introduction
We study a non-minimal dark sector motivated by both Naturalness and cosmology
considerations and explore its potential. By doing so, we provide a solution to the little hierarchy
problem and, simultaneously, to various cosmological structure anomalies suggested by the
current data related to the large- and small-scale structure of the universe. The existence
of these issues may have revealed an intriguing clue to the nature of dark matter.
The Twin Higgs mechanism [1{3] provides a solution to the little hierarchy problem
in a hidden naturalness manner. The solution evades strong constraints from the Large
Hadron Collider (LHC) on top-partners that are charged under Standard Model (SM) color
by furnishing a hidden SM-like sector, in which the SM-neutral twin top is involved in
stabilizing the Higgs mass. There have been several studies on formulating an ultraviolet
completion of the model [4{14] and on the collider phenomenology related to the twin
particle spectrum [15{19]. The existence of the mirror sector also provides a non-minimal
dark sector containing stable charged fermions and twin gauge bosons, which introduces
various applications to cosmology. Previous works on twin cosmology mainly focused on
the thermal history of the dark matter candidates [20{23] and signatures in the (in-)direct
detection experiments [
24, 25
]. In this work, we explore the physics of structure formation
in the context of the Twin Higgs model.
A dark sector that contains a SM-like particle spectrum has the potential to extend
the cold collisionless dark matter paradigm in a way that resolves important cosmological
issues [26{28]. In the twin sector, the dark matter candidates are the lightest charged
baryon and lepton, which scatter with each other via twin photon exchange during the
halo formation. The twin sector also contains a light twin neutrino, whose existence a ects
the expansion rate of the universe and hence shifts H0, the value of the Hubble expansion
rate today. If the twin sector is extended to include an e cient scattering between the
twin neutrino and charged fermions during the structure formation time, a dark acoustic
{ 1 {
oscillation exists, which damps the dark matter power spectrum and alters the large-scale
structure.
Interestingly, these adjustments to the dark matter structure formation in fact furnish
solutions to the existing inconsistencies between the
CDM prediction and both the large
and small-scale structure observations. For many years, the well-accepted
CDM paradigm
has provided an excellent t to cosmological data on large scales, although there had been
several long-standing problems on small scales, including the core-vs-cusp [29, 30] and
toobig-to-fail problems [31]. With the advent of higher-precision measurements on large scales,
however, the large-scale results have entered into tension with
CDM as well. In particular,
there is a
3
discrepancy between the value of today's Hubble rate H0 obtained from
a t to the CMB and baryon acoustic oscillation (BAO) data [32] and the higher results
from local measurements [33{37]. Further, the inferred value of 8 (roughly speaking the
amplitude of matter density
uctuations at a scale of 8h 1 Mpc) is in 2{3 tension [38{41]
with the lower values from direct measurements by the weak lensing survey [
42
]. Resolving
these anomalies would require a paradigm that generically reduces the value of 8 and
enhances H0 as compared to the
CDM model in a consistent way.
One attempt to raise H0 from the
CDM prediction is to introduce additional dark
radiation (DR) to increase the energy density. Once the stringent CMB constraints are
taken into account, however, such a solution comes at the cost of increasing the matter
power spectrum, which exacerbates the
8 problem.1 A plausible solution is to have the
dark radiation, which enhances H0, also act to damp the dark matter power spectrum so
that the size of 8 gets reduced to agree with the weak lensing result [43]. One can consider
coupling all the dark matter particles to the dark radiation. For this scenario, the full
DMDR system undergoes dark acoustic oscillations, and hence all dark matter components are
subjected to the same damping. Such a proposal would require a well-chosen small DM-DR
coupling, which results in a DM-DR scattering that is slightly ine cient when compared to
the Hubble expansion. Consequently, a numerical study is necessary to obtain the correct
8 suppression [44{46]. It is because of this slightly ine cient scattering process that we
refer to this setup as the Quasi-Acoustic Dark Matter (QuAcDM) scenario. In the Twin
Higgs model, such a scenario can be realized by gauging the twin B
L symmetry. Here
the twin neutrino plays the role of the additional dark radiation, and its scattering to the
dark matter (twin baryon and charged lepton) damps the dark matter power spectrum,
solving the 8 problem.
Alternatively, one can consider a scenario where only a subcomponent of the total dark
matter couples to the dark radiation. In a well-motivated general mechanism that was
recently introduced in [47], one can allow the DM-DR scattering to be highly e cient. The
Partially Acoustic Dark Matter (PAcDM) is a robust framework that e ectively resolves
both the
8 and H0 large-scale structure anomalies in a natural way. It assumes the
presence of tightly coupled dark radiation and supposes that the dark matter mass density
is composed of two components, a cold and collisionless dominant one ( 1) and a cold
subdominant one ( 2) that is tightly coupled to the dark radiation. The success of this
1For example, see the 8
H0 contours in gure 33 of [32].
{ 2 {
HJEP09(217)3
framework hinges on the feature that both the self-interaction of the dark radiation and
the DR- 2 interaction remain e cient throughout the radiation domination phase and for
a signi cant portion of the structure formation era. For this reason, one can perform an
analytical estimation of the 8 suppression in the tightly coupled limit, as we will discuss
in section 3.
In this framework, the Hubble parameter anomaly can be reconciled by suitably xing
the amount of tightly coupled dark radiation. Further, for the 8 anomaly, if the relevant
modes enter the horizon before matter-radiation equality, the interaction between the dark
radiation and 2 restricts the growth of density perturbations, subsequently decreasing the
growth of uctuations in the collisionless DM
1. This is the case for modes sensitive to
the 8 measurement, and hence the discrepancy can be resolved by an appropriate choice
of the amount of subdominant DM, reducing the 8 value to match the observed deviation.
Furthermore, the reduced growth of the matter power spectrum in this scenario results in
a minor correction to the gravity perturbation during the CMB time, yielding a smaller
change of the CMB spectrum as compared to the QuAcDM case. Hence, future precision
CMB studies may be able to distinguish these two classes of models.
We focus on the PAcDM scenario here in the context of the Twin Higgs model. Our
particular realization is obtained by gauging either the twin lepton number symmetry
U(1)L or the twin U(1)B L. In the U(1)L case, the heavy twin lepton scatters with the
twin neutrino and plays the role of 2, while the twin baryon behaves as cold collisionless
dark matter
1 throughout structure formation ( gure 1). In the U(1)B L case, the twin
hydrogen behaves as 1, while the ionized twin proton plays the role of 2. The scattering
between light twin particles also renders the light degrees of freedom a tightly coupled
uid, which gives an extra contribution to
Ne , and suitably solves the H0 problem,
while satisfying a weaker CMB constraint [48{50].
In addition to the large-scale structure anomalies, there are several long-standing
puzzles on small scales related to the structure of dark matter halos that cannot be addressed
by the collisionless dark matter models. In particular, direct observations of dwarf
galaxies (
kpc size) and galaxy clusters (
Mpc size) indicate lower dark matter masses in
the inner regions of these objects than those predicted by N-body simulations with
noninteracting DM. Although this anomaly may potentially be explained by lack of baryon
interaction in the simulations [51, 52], none of the proposed solutions so far are able to
cover such a broad range of halo sizes simultaneously.2 One attractive solution to the mass
de cit problem on all halo scales is to suppose that the dark matter is self-interacting
through a light mediator. As we show in this work, the charged twin baryon provides a
plausible realization of this self-interacting dark matter (SIDM) scenario [54, 55] through
an O(10) MeV-scale twin photon. Alternatively, the dark matter self-interaction can be
realized for a DM particle with an extended geometrical size for the scattering, e.g. for
atomic DM. As we will show, the formation of twin hydrogen gives a natural realization of
atomic DM [56{60] and provides solutions to the mass de cit problem from dwarf galaxy
to galaxy cluster scales [61].
2See [53] for a review of current status on the small scale structure problems.
{ 3 {
HJEP09(217)3
consideration. The blue (gray)-colored particles correspond to the stable (unstable) members of
the spectrum. The gray arrows indicate the decay products of the unstable particles. Further, the
primed elds correspond to the set of speci c anomaly compensators used in this paper. Right: the
set of dominant processes involved in the solution of the large- and small-scale structure anomalies.
The rst Feynman diagram represents the dominant process relevant for the self-interacting dark
matter scenario through the exchange of twin photons. The second diagram corresponds to the
relevant scattering for the partially acoustic oscillation scenario, and the third one is the process
that keeps the dark radiation a tightly coupled
uid.
The rest of this paper is organized as follows. In section 2, we describe the Twin
Higgs model that contains the necessary ingredients to solve both the large- and
smallscale structure puzzles at the same time. The model is based on the Fraternal Twin Higgs
model [16] but has a gauged twin lepton number symmetry that generates the 8 damping.
In section 3, we explain how this model serves as a realization of the PAcDM framework to
resolve the (H0; 8) anomalies. We give an analytical description of the partially acoustic
oscillation and calculate the required mass ratio between the stable twin baryon and lepton
that solves these problems. In section 4 we discuss the solution from the Twin Higgs model
to the mass de cit problem and calculate the mass of the twin photon necessary to resolve
it. At the end, when we admit more general choices of the twin electric coupling, we
demonstrate how the dwarf galaxy and cluster merger observations enable us to set an
upper bound on this coupling. In section 5, we discuss the more attractive solution to
the cosmological structure formation problems with the twin hydrogen playing the role of
the dominant DM component. An eminent virtue of this model is that it requires neither
the breaking of twin electromagnetism nor the presence of anomaly compensators, which
su er from strong experimental constraints. Moreover, it successfully accommodates two
generations of fermions and does not compel one to introduce additional mass scales, thus
keeping the twin gauge bosons massless. We conclude in section 6.
2
2.1
The extended fraternal Twin Higgs model
Asymmetric dark matter and dark uid
We investigate a dark sector motivated by the Twin Higgs model, which contains a twin top
Yukawa and mirror gauge symmetries SU(3)0c
U(1)Y 0 with SM-like couplings.
In this framework, the SM Higgs arises as a pseudo-goldstone boson from a global SU(4)
symmetry breaking, which then enjoys protection from various radiative corrections due to
the approximate Z2 symmetry. Since the Higgs mass receives subdominant corrections from
the Yukawa interactions of light twin fermions, all Yukawa couplings except for the twin
top coupling are mildly constrained by Naturalness. For this reason, one can simplify the
twin fermion spectrum by including only the third-generation fermions. In this Fraternal
Twin Higgs model [16], the approximately Z2-symmetric gauge and top Yukawa couplings
can adequately stabilize the Higgs mass, while the smaller number of light fermions is able
to more exibly satisfy the restrictive
Ne bound from the CMB.
Since we mainly focus on the thermal history of the twin sector below a temperature
of O(10) GeV, the twin particles relevant for this discussion are the spin-3=2 twin baryon
^ = (^b^b^b), the twin tau ^, the twin neutrino ^ (with both chiralities), and the twin photon ^.
Their mass spectrum is similar to the SM spectrum due to the approximate Z2 symmetry.
If we take the ratio between the twin and SM electroweak symmetry breaking scales, f
and v, to be f =v = 3, which corresponds to a minor 2(v=f )2 ' 20% tuning and satis es
current constraints on the Higgs coupling [16], the twin top and twin gauge bosons feature
masses larger than the SM values by a factor of three.
The approximately Z2-symmetric Yukawa couplings of light twin fermions ^b and ^,
which result in small corrections to the Higgs mass, can be modi ed from the SM values,
leading to some arbitrariness in the determination of the twin particle masses. We will
therefore set the masses according to the solutions of the large- and small-scale structure
problems. The relevant parameters are the twin photon mass m^, the twin baryon mass
m^ , and the ratio of the twin tau mass density to the total dark matter density. We write
the latter two quantities as
m^ ' 3m^b + 5 ^ ;
r
m^
m^ + m^
:
(2.1)
Here, the contribution from the SU(3)0c con nement scale ^ is due to an approximation that
comes from the lattice result in ref. [62] for a spin-3=2 baryon in the single- avor case [22].
When solving the mass de cit problem through the ^ self-scattering, the discussion in
section 4 will demand mass ranges 10 . m^ . 20 MeV and 10 . m^ . 40 GeV. On the
other hand, for the discussion in section 3, the appropriate damping of the 8 result will call
for a mass ratio of r ' 2:5% and the existence of relativistic twin neutrinos. To simplify the
discussion of thermal history, we assume the twin neutrinos to be massless during structure
formation and focus on the following mass parameters:
m^ = 40 GeV;
m^ = 10 MeV;
r = 2:5%:
(2.2)
twin con nement scale of ^
These imply that m^ ' 1 GeV. The ^ mass further implies that m^b ' 5 GeV for the
' 5 GeV, which comes from the two-loop RG running of
Z2-symmetric QCD couplings at the cuto
scale that we assume to be 5 TeV [16]. The
Z2-breaking Yukawa couplings of ^b and ^ yield a cuto ( )-dependent correction to the
For
= 5 TeV, we nd no signi cant tuning of the Higgs mass, m2h ' (0:27 mh)2.
Higgs mass, m2h ' 4 22 ( yb2 +
y2), where
y
2
b
3(y^2
b
yb2) and
y
2
(y2^
y2) [16].
{ 5 {
Assuming an unbroken twin electric symmetry, the twin electrically charged ^ and
^ particles are stable and can serve as dark matter candidates in this setup. The relic
abundance of ^ can be generated through a similar baryogenesis mechanism as in the SM
sector. With a small di erence in either the CP violation or rst order phase transition, we
can achieve a di erent baryon asymmetry Y B^ ' Y B=8 relative to the SM. This generates
the observed dark matter density. If we suppose that the twin-sector remains charge neutral
from the twin baryogenesis, then given the absence of other stable charged particles, we
expect the number of ^ in the late-time Universe to coincide with the number of ^. Besides
the dark matter particles, light hadrons like the 0++ glueball, of mass mG^0++ ' 6:9 ^ =
35 GeV, and the pseudo-scalar bottomonium, of mass mB^0 + ' 2(m^b + ^ ) = 20 GeV, decay
quickly into the SM bb or twin photons when they become non-relativistic. Hence, we do
not consider them in the discussion of structure formation.
Let us now discuss some observational constraints relevant to the dark sector. We rst
turn to the direct detection constraint on the dominant dark matter component ^ . This
is determined by the spin-independent cross section of ^ p ! ^ p through the Higgs portal
exchange, given by [20]
h '
1
3 y^bv 2
p2f
2
ghp mN4^ ;
2
h
(2.3)
where
N ^ is the reduced mass of the ^ -nucleon system and ghp = 1:2
10 3 [20, 63] gives
the e ective Higgs coupling to nucleons. Since the momentum transfer in the scattering
is much smaller than the inverse of the ^ radius, we assume that the Higgs mediation is
dominated by the coherent scattering to three ^b's in the bound state, which includes a factor
of 32 in the cross section. Taking m^b = 5 GeV, this expression gives h ' 3:4
This value falls below the current bound ' 1:0
experiment [64] at 40 GeV dark matter mass, but the cross section lies within the sensitivity
of the proposed LZ experiment [65]. As is discussed in [22], the ^ -Higgs coupling can also be
generated from a scalar glueball exchange. The resulting cross section may be comparable
to the Higgs mediation result, but a concrete result relies on a future lattice study.
10 46 cm2 (90% CL) from the LUX
2.2
Dark matter self-interaction and dark matter-dark uid scattering
Let us next turn to the dark matter interactions relevant to the formation of large- and
small-scale structure. For the small-scale structure case, the model in question assumes
that the dark matter particles ( ^ ; ^) carry twin electric charges and are endowed with
self-couplings; hence, they elastically self-scatter. Although this self-scattering does not
a ect the linear evolution of large-scale structure [66], it can in uence the dark matter
structure formation. As we show later, we choose the same value for the twin and SM
ne
structure constants, ^ = , and a twin photon mass m^
10 MeV that softly breaks the
Z2 symmetry. The photon mass enables us to generate the appropriate velocity-dependent
cross section that explains small-scale structure anomalies from dwarf to galaxy cluster
scales. If the U(1)Y^ -breaking spurion m^ carries a fractional charge, then ^
and ^
can
be easily made to be long-lived when compared to the cosmological time scale. Since m^
is larger than the binding energy m^ ^2
' 40 keV, the two particles do not form a bound
{ 6 {
state through the ^ exchange. We also note that ^ can also self-scatter via the exchange
of twin mesons. However, this corresponds to a mediation scale that is above a GeV, in
which case the resulting self-interaction is too weak to explain the anomalies.
Having a new mass scale m^ in the twin sector complicates the UV-completion of the
model. Since the hyper charge U(1)Y gives a negligible contribution to Higgs tuning, if
the goal of the model is to only solve one of the small-scale structure problems, one can
solve the dwarf anomaly by a Z2-breaking coupling ^
potential of the twin sector in addressing the structure formation issues, we will still aim
for a solution to the small-scale structure anomalies on all scales and focus on the massive
does not require a massive ^. In this scenario, the twin hydrogen plays the role of the
SIDM, and the additional velocity dependence in the scattering cross section in both the
elastic and inelastic scattering processes resolves both the dwarf and cluster anomalies,
once the hyper ne structure of the twin atoms is taken into account.
Turning to the large-scale structure in the ^ {^ scenario, we nd that in order to address
the 8 puzzle in the PAcDM framework, we introduce a non-decoupled interaction between
the subdominant dark matter ^ and dark radiation ^ that acts to damp the matter density
contrast. Any such interaction between ^ and ^ but not ^ and ^ can serve this purpose.
To provide a speci c scenario, we implement this interaction by gauging the twin lepton
There is then an e cient scattering ^^ ! ^^ through a massless Z^L mediator.
number symmetry and assuming that U(1)L^ is preserved throughout structure formation.
Gauging the U(1)L^ symmetry results in local gauge anomalies. We can keep the U(1)L^
symmetry anomaly-free during structure formation by introducing anomaly compensators.
For example, one way to achieve this is to include twin leptons ^lR0T = (^0; ^0)R
(1; 1; 1=2; 1) and ^0
L
(1; 1; 1=2; 1) charged under the twin SU(3)0c
(1; 2; 0; 1),
3 We assume that the tau compensator, ^0, obtains a Yukawa mass from
the term y^^lR0H^ ^L0 that is slightly heavier than that of ^, so that ^0 decays quickly into ^^^0
when it becomes nonrelativistic. We also assume that the twin neutrino compensator ^0
remains massless just like ^. This particle provides an additional contribution to
and consequently helps to explain a higher value of H0 from the local measurements. A
potential cause for concern is the allowed decay of ^ into the neutral (^) and charged (^0)
neutrinos, which comes from a dimension-10 operator (^lLH^ ^R)(^L0 ^R)(^L0 ^R). However,
this concern is eliminated if the mediation scale is above a TeV. In our discussion of the
acoustic oscillation, we take the size of the U(1)L^ coupling to be gL^ & 10 4 to ensure that
the ^-neutrino scattering rate is always larger than the Hubble expansion rate.
Further, it turns out that in order to evade the stringent bound from searches for
a fth force in the SM sector (see [68] for a review of the constraints), we are led to
3Instead of having anomaly compensators simply as chirality- ipped twin fermions [67], here we assign
di erent U(1)Y^ charges to the neutrino compensators, so that they do not introduce vectorized neutrino
masses, and the twin photon can decay into ^0's before BBN. Having the twin photon decay into dark
radiation can avoid the stringent direct detection constraints as compared to the decay into SM particles
through a kinetic mixing.
{ 7 {
retain the SM U(1)L as un-gauged, otherwise the same anomaly compensators in the SM
su er from stringent collider constraints. Since the U(1)L^ interaction only a ects the
twin Higgs mass at two-loop level, this minor Z2 breaking has a negligible e ect on the
naturalness of the electroweak scale. In the discussion of twin hydrogen DM in section 5, the
scattering between the ionized twin atom and ^ is given by a gauged U(1)B L symmetry.
Since U(1)B L is anomaly-free, there is no need to introduce the unattractive anomaly
compensators. Hence, it is easier to UV-complete the model by gauging U(1)B L in both
sectors, and break the SM U(1)B L through the same Z2 breaking as in the Higgs potential.
Another possible cause for concern is the Weibel plasma instability. Inside the halo,
the twin tau in the dark
uid behaves like a charged plasma, and there may be potential
constraints on the U(1)L^ coupling from the plasma instability [69, 70]. However, since the
twin tau density is only 2:5% of the overall dark matter density, we do not expect this
bound to be strong. Incidentally, we should note that the precise bound has not yet been
formulated and is currently still under construction.
In our PAcDM scenario, the ^
^ scattering is highly e cient, rendering the dark
radiation (^; ^0; Z ^ ) a tightly coupled
L
contributes to the e ective number of neutrino species
uid. Like free-streaming radiation, this dark
uid
e
N scatt.
However, being self
interacting, the uid is subject to a weaker CMB constraint when compared to the free
streaming case with
space to accommodate
To determine the
e
e
N scatt
e
N scatt < 1:06 (2 ) [49, 50]. This feature has the e ect of freeing up
N scatt in our model, we refer to the state of the Universe around the
' 0:4{1, which furnishes a solution to the H0 problem [35].
kinetic decoupling time between the SM and twin sectors. Kinetic equilibrium between
the two sectors is maintained by the Higgs mediation, which decouples around the GeV
scale. Immediately after the decoupling, the twin sector contains the relativistic particles
(^; ZL^ ; ^; ^0). As soon as the temperature drops to T . 10 MeV, the twin photon ^
decays into ^0's, avoiding the stringent direct detection constraints it would su er if it were
to instead decay into SM particles through a kinetic mixing before Big-bang
Nucleosynthesis [71]. Now, after the twin photons decay, the twin sector is left with (^; ^0; ZL^ ), which
contribute an overall
enhance the Hubble rate, solving the H0 problem.
An alternative solution to the (H0; 8) problems is to gauge the anomaly-free U(1)B L
symmetry instead of gauging the twin lepton number. This is a realization of the QuAcDM
framework. In contrast to the PAcDM for which only the subdominant dark matter
component undergoes dark acoustic oscillations, here the acoustic oscillations are experienced
by the full DM-DR system, namely by both ^ and ^ interacting with the dark radiation.
These damp the power spectrum with a weak U(1)B L coupling. If we invoke the result in
refs. [
43, 44
], we can reduce the size of 8 to the desired value by choosing ^B L
for a 10 GeV-scale dark matter mass.
3
Large-scale structure: Twin lepton with acoustic oscillations
The presence of a cold dark matter component ^ and a subcomponent dark matter ^ that
couples to the self-scattering radiation (^; ^0; ZL^ ), modi es the values of (H0; 8) relative
{ 8 {
ple), Partially Acoustic dark matter (PAcDM, blue), and Fully Acoustic dark matter (QuAcDM,
orange) cases. In the QuAcDM scenario, which corresponds to the case when both ^ and ^ interact
with the dark radiation, the oscillation delays the linear growth of the density contrast during the
matter domination phase. This feature results in a suppression of the matter power spectrum. In
the PAcDM scenario, which corresponds to the case when only ^ scatters with the dark radiation,
the slower growth of the power spectrum allows a smaller deviation from the CDM case during
the CMB time (a
10 3) and the same suppression of power spectrum today (a ' 1) as in the
QuAcDM case. In order to illustrate the idea, we choose parameters that give a large 8 suppression.
to the
CDM model. The self-scattering radiation contributes an overall
that serves to reconcile the values of H0 between the local and CMB measurements [
33
].
Moreover, during the matter-dominated era, the dark
uid-^ scattering generates a dark
acoustic oscillation that delays the structure formation of ^. As we show later, this not only
reduces the ^ matter density contrast but also retards the growth of the ^
uctuations.
The slower growth of the ^ structure results in a stronger suppression of the matter power
spectrum at low redshift, as is shown in the blue curve of gure 2.
Here we describe the way in which the acoustic oscillations experienced by the ^{DR
system act to suppress 8
. A more detailed study is presented in ref. [47]. We employ
the general formalism of Ma and Bertschinger [72] for scalar perturbations in the
conformal Newtonian gauge. Working in momentum space, we express the coupled evolution
equations in terms of the comoving wavenumber k and conformal time derivative _ = 1=d .
Then the evolution of the over-density of ^ can be described by the linear equations
_ ^ =
_^ =
a_
a ^ + k2 :
(3.1)
Here the over-density, s
s= s, parametrizes the density perturbation relative to the
average density of matter or radiation. Further, the parameter s = @j vsj is the divergence
of a comoving 3-velocity, which modi es the density perturbation by having particles move
out of the overdense region. In addition,
and
are the metric perturbations in the
conformal Newtonian gauge ds2 = a( )2[ (1 + 2 )d 2 + (1
2 )dxidxj ]. Since the dark
{ 9 {
radiation is tightly coupled, we take
=
in the equations and ignore the minor correction
from SM neutrinos.
We note that eq. (3.1) coincides with the corresponding evolution
equation for the density perturbation of standard cold dark matter particles for a given
metric perturbation , where
evolves according to the Einstein equation
k
2
with the largest s s contribution on the r.h.s.
The evolution equations for the interacting dark matter component ^ are given by
HJEP09(217)3
_^ =
_^ =
a_
a ^ + k2
+ a ( DR
^);
where
hp^i
dh p2^i=dt is the thermal averaged momentum transfer rate experienced
by a ^ particle as it travels through the dark uid. Note that here t is the Minkowski time,
since the rate
is a microscopic quantity independent of the cosmological expansion. In
the twin sector, this scattering rate is given by [43]
to obtain (R^
3 ^=4 DR)
_DR =
_DR = k
2
4
3 DR + 4 _;
DR +
4
+
3
4 DR
^ a ( 2
DR);
^ +
^
R
a_
a 1 + R^ _^ +
k
2
3(1 + R^)
^ '
k2 :
where T^ is the temperature of ^. In the tightly coupled limit, T^ equals the temperature of
dark radiation.
The tight-coupling approximation is valid as long as the interaction rate
is
comparable to or exceeds the Hubble rate during structure formation. We focus on the case for
which
is signi cantly larger than the Hubble expansion rate, which enables us to gain an
analytical understanding of the oscillation physics. This is easily achieved provided that
the U(1)L^ coupling satis es
^
L
where T0 is the photon temperature today and T^ ' 0:4 T0. In this tightly coupled limit, we
1, which implies that the scattering term in eq. (3.3) dominates
the ^ evolution. The consequence is that ^ =
DR, which authorizes us to combine the
evolution equations of the dark matter component ^ and the DR as follows:
(3.2)
(3.3)
(3.4)
(3.5)
(3.6)
(3.7)
The resulting evolution equations indicate that in the tight-coupling limit, the ^{DR
system behaves like a single coupled
uid. Here we neglect terms containing higher-order
conformal time derivatives of
in order to focus on modes well within the horizon, for
which k
1. We nd that the evolution of the over-density ^ is similar to that of the
SM baryon. Let us now consider varying R^. In the regime R^
1, the ^{DR
uid is
relativistic. In this limit, the rst two terms in eq. (3.7) generate an acoustic oscillation of
^ without building up the density perturbation. This has the e ect of delaying the growth
of dark matter structure when the mode enters horizon, as is shown by the PAcDM (blue)
and QuAcDM (orange) curves in
gure 2. It is only when the dark radiation cools down
and one enters the R^
1 regime that the power spectrum begins to grow monotonically.
This delay of the ^ structure formation results in ^
^ upon entering the matter
domination era. Inserting the density ratio r de ned in eq. (2.1), we can then express the
total dark matter density perturbation as
DM = [(1
DM
r) ^ + r ^] ' (1
r) ^ :
For modes well within the horizon, k
1, so that eq. (3.2) simpli es to
k
2
'
4 a2G DM (1
r) ^ =
6
where we have applied the Friedman equation and noted that the scale factor a is
proportional to 2 during matter domination. Canceling the ^ in eq. (3.1) and inserting the
above metric perturbation, we then have for the dominant dark matter component (
1=d )
0^0 +
2 0^ '
6(1
r)
2
^ /
a
aeq
1 0:6r+O(r2)
^ :
:
(3.8)
(3.9)
(3.10)
(3.11)
(3.12)
Hence, the growth of the dark matter density perturbation obeys a reduced power law
Further, since the power spectrum P of the dark matter density perturbation is
proportional to the square of the over-density, D2M, we nd that the ratio of the power spectrum
with and without the interacting component ^ is given by
P (r)
P (0) '
(1
r)2 2^ (r)
2^ (0)
' (1
2r)
a
amd
1:2r
;
where amd ' 10 3 is the scale factor at which matter dominates the source term of the
Einstein equation in eq. (3.2). In order to eliminate the 8 discrepancy through the
reduction of the density perturbation by ' 10%, we need to suppress the matter power spectrum
in eq. (3.12) by ' 20%. This requires r ' 2{3% and is the reason for the benchmark value
in eq. (2.2).
To obtain a more precise result, we determine the size of the over-density
DM by
numerically solving equations (3.1){(3.3) and (3.6), where we choose a U(1)L^ coupling that
satis es eq. (3.5). We also incorporate the evolution equations for the SM photon and
baryon by making the replacements DR!
and ^ ! SM baryon (B), respectively. For the
modes that enter the horizon during radiation (matter) domination, the initial conditions
for solving the coupled system are given by
r(;DmR) =
4
3 ^;^;B = 1
r(m) ;
^;^;DR;B; = 2
r(m)k2
;
(3.13)
with the values 1r =
.
We make the following
parameter choices when solving this coupled system of evolution equations: h = 0:68,
h
2 = 2:47
has only a small e ect so that its precise value is not
important for our purpose here. We choose N scatt = 0:46, assuming the presence of the
e
anomaly compensator ^0, and a slightly larger value of
DMh
2 = 0:13 in order to keep the
redshift at matter-radiation equality unchanged. This allows us to compare our matter
power spectrum to that of a conventional single-component dark matter model without
any dark radiation.
We nd that the choice of r = 2:5% leads to an 8% suppression of the density
perturbation around the scale k
0:2h Mpc 1 as compared to
CDM, thereby solving the 8
problem. It should be noted that this corresponds to a ' 23% suppression when compared
to the r = 0 case with the same amount of dark radiation, as displayed in the left panel
of gure 3. In the same plot, we also show the ratio of the power spectrum, P (r)=P (0),
during the CMB time with a
10 3 (dashed curve). Due to the redshift dependence in
eq. (3.12), the suppression of the matter power spectrum is smaller at the earlier CMB time,
and hence the correction to the metric perturbation is minor at this time. This feature
allows the model to
exibly accommodate bounds from the CMB temperature spectrum
and CMB lensing, as is discussed in ref. [47].
If we consider an alternative scenario, in which both ^ and ^ scatter with the dark
radiation through a gauged twin B
L symmetry as a realization of the QuAcDM framework, we can obtain the same suppression by requiring
B^ L^
10 9:8. Distinct from the
PAcDM setup, the QuAcDM scenario gives comparable suppressions to the matter density
perturbation between today and the CMB time. As is shown in
gure 2, the di erent
corrections to the power spectrum provide a way to di erentiate between these dark sector
scenarios through the CMB observation.
4
Small-scale structure: Twin baryon with a self-interaction
In this section, we study the dark matter self-interaction through twin photon exchange
( gure 1) and make a connection to dark matter halo structures. Our twin sector contains
the self-interacting dark matter particles ( ^ ; ^) and a dark
uid scattering with ^, which
gives rise to complicated dynamics for halo formation. A detailed N-body simulation of the
halo structure is beyond the scope of this work. In the present analysis, we only focus on
the dominant dark matter component ^ , which contains ' 98% of the dark matter density,
and comment on the possible correction to the result from the presence of ^ and the dark
uid.
N scatt = 0:46. In the Twin Higgs setup discussed in this work, the dark matter ratio r is given
e
by r = m^=(m^ + m^). In the plot, the solid (dashed) curves are obtained by numerically solving
the linear evolution equations described in section 3, all in the tight coupling limit and assuming
no anisotropic stress. Results for di erent values of r are labelled in di erent colors, while earlier
(a = 10 3) and late (a = 1) times are indicated by dotted and solid lines, respectively. Also see
ref. [47] for more details.
The halo structure formation depends on the average time scale of dark matter
scattering hn v
i
1, where n = c DM=mDM gives the number density, and the various relevant
e ects are determined by the cross section mass ratio
=mDM. In order to solve the mass
de cit problem from dwarf galaxy to galaxy cluster scales, we require that
=mDM be
1 cm2=g for dwarf galaxies and
0:1 cm2=g for galaxy clusters. One way to achieve this
is to introduce a velocity-dependent dark matter self-scattering process with the mediator
mass comparable to or lighter than the momentum exchange of the dark matter
particles. Since the average collision velocity between dark matter particles in dwarf galaxies is
about an order of magnitude smaller than the corresponding value for the galaxy clusters,
the nonperturbative e ects in the scattering cross section, enhanced by a low dark matter
velocity, can help to reconcile the required
=mDM for di erent objects.
In this work, we estimate the size of =mDM by applying standard partial wave
methods discussed in ref. [73] to a range of twin photon masses and couplings. We focus on
scattering outside of the Born regime, demanding that ^m^ =m^ & 1, so that the
nonperturbative e ects of nonrelativistic scattering become important. Since the dark matter
density contribution
^ arises from the twin baryon asymmetry, the dark matter particles
are scattered by a repulsive potential V (r) = ^e m^r=r with
ne structure constant ^
in the twin sector, and the transfer cross section of dark matter scattering can then be
expressed as (
2 ^m^=m^ v2) [73]
;
(4.1)
in the classical limit m^ v=m^
1. For m^ v=m^ . 1, a good approximation is obtained by
(4.2)
(4.3)
0 i
im^ v
m^
1
) A ;
Since the number density of the subcomponent dark matter ^ is comparable to that of
the dominant dark matter ^ , the chance of having a ^ particle scatter with ^ is therefore
comparable to the ^ self-scattering. However, given that m^
m^, the momentum
transfer from the ^ {^ scattering is accordingly much smaller than that from the ^
selfscattering. It is then reasonable to consider only the ^ scattering to a good approximation.
Our study focuses on dark matter halo structure anomalies in dwarf galaxies, low
surface brightness galaxies (LSBs), and galaxy clusters. Instead of tting the result for each
of these objects, we approximate the results for the ratio of the cross section to the dark
matter mass in ref. [55] in terms of various ranges of this ratio. For dwarf galaxies, we take
=mDM = 0:5{5 cm2=g and v = 60 km=s. Next, for LSB galaxies, we assume =mDM = 0:5{
5 cm2=g and v = 100 km=s. Further, for galaxy clusters, we take =mDM = 0:05{0:5 cm2=g
and v = 1200 km=s. When studying the cross section, we also consider bounds from the
ensemble of merging clusters of =mDM < 0:47 cm2=g at 95% CL [74] at a collision velocity
In the upper panel of gure 4, we show the allowed sizes of m^ and m^ required to
solve the mass de cit problem in various galactic objects. The plot assumes Z2-symmetric
electromagnetic couplings ^ =
between the twin and SM sectors. It turns out that if we
x the mass parameters to be in the range 10 . m^ . 40 GeV and 10 . m^ . 20 MeV,
the self-interaction of the twin baryon can provide a plausible solution to the small-scale
structure problem.
In addition to explaining the anomaly, an analysis of the e ect of dark matter
selfscattering on halo formation also sets a bound on the twin photon interaction.
When
we consider a twin sector that contains stable charged baryons carrying a SM-like baryon
asymmetry, the self-coupling of the baryons is subject to an upper bound that ensures
that the self-scattering does not violate the small-scale structure constraints. In the lower
panel of gure 4, we investigate the upper bounds on the twin photon coupling by applying
constraints from the merging cluster with
=m^ < 0:47 cm2=g and the shape of dwarf
halos with
=m^ < 5 cm2=g. If we suppose that the twin baryon dominates the dark
matter density, there then needs to be a breaking of the mirror symmetry either through
a nonzero m^ or a smaller twin electric coupling.
When we consider the e ect of the presence of ^ and the dark uid, then no matter
whether ^ contributes to a core- or a cusp-like density pro le, the 2:5% dark matter density
does not yield observable signatures in the current measurements of halo structure. One
potential application of the ^-dark uid scattering is the following: if the dark uid is able
ponent ^ and a Z2-symmetric twin photon coupling ^ =
. See section 4 for the choice of cross
section and velocity values. The dashed curve shows a lower bound on the dark matter mass from
the cluster merger constraint. The overlap area (gray) among di erent allowed regions gives
solutions to the mass de cit problem for the three types of galactic objects. Right: upper bounds
on the twin electromagnetic coupling from the cluster merger and dwarf halo constraints. The
kinks of the curves in both plots correspond to the transition points between di erent analytical
approximation regimes in eq. (4.1) and (4.2) for the cross section calculation. For example, in the
m^ = 10 GeV cluster merger curve, the rst kink from the left corresponds to
' 1, and the second
kink corresponds to m^ v=m^ ' 1.
to cool down the ^ particles enough such that the subcomponent dark matter falls into
the galactic center, this mechanism would provide a possible explanation of the origin of
supermassive blackholes [75]. When nonlinear halo formation sets in around a redshift
of z = 10{20 [
76
], the dark uid is much colder than the virial temperature of ^, given
by ' (m^=1 GeV) keV. So, if the
uid is able to rapidly transport heat outside the halo,
the dark matter ^ can accordingly undergo e cient cooling and collapse into a black hole.
However, since the free streaming length of the dark uid is in fact very short, expected to be only 10 m for a twin coupling of size
^
T
10 4 eV, a dark
uid particle makes a random walk across a distance
10 3 pc until
L^ ' 10 2 and a
uid temperature of about
today [77], which is negligible relative to a
10 kpc-size halo. Hence, we conjecture that
the dark uid does not dissipate heat e ciently through di usion and expect that a better
cooling mechanism such as convection is required to form the black hole.
5
Solutions from the Twin hydrogen DM
The extended Fraternal Twin Higgs model described above contains two questionable
assumptions of the Z2 breaking. The rst one is that in order to accommodate the mass
de cit problem, it is necessary to break the twin electromagnetism U(1)L at the MeV
scale, thus introducing an additional scale which is not associated with any other mass
scales in the model. The second assumption is that if we choose to gauge the U(1)L
symmetry, we are compelled to include anomaly compensators in the SM. These su er
from strong experimental constraints, and an additional Z2 breaking is required to lift the
compensator mass.
EWSB scales by
p
B L
with
B L & 10 4 [78].
Rather than adding extra layers of the model, here we present an alternative solution to
the structure problems that does not require the twin U(1)EM breaking and the introduction
of additional fermions in the TH model. We will see below that in this scenario, the required
Z2 breaking will be a ' 60% deviation between the SM and twin electric couplings and
that the solution will feature di erent Yukawa couplings of the light fermions.
Let us rst describe the main idea of the model. When the temperature of the twin
sector drops below the twin con nement scale, we assume that the twin sector contains
the following spectrum: the twin proton p^+, twin lepton `^ , light twin neutrinos ^; N^ , as
well as massless gauge bosons ^; ^B L. Instead of gauging the twin lepton number, here
we gauge the twin U(1)B L that is anomaly-free assuming the presence of right-handed
neutrinos. In this scenario, we can break the SM U(1)B L above the EW scale through
the same Z2 breaking as in the Higgs potential. For example, upon getting a VEV, the
Z2-odd scalar in the Z2-symmetric potential L
can induce the breaking of SM U(1)B L through the B
(jHAj
2
jHBj2) + 0 (j Aj
2
j Bj2)
L charged scalar
and split the
h i in the two sectors. In order to achieve a successful PAcDM
scenario, the U(1)B L coupling required to resolve the LSS problem can be as small as
10 8, and existing constraints from the Z0 search only cover the TeV scale B L
Twin hydrogen H^ starts to form when the twin temperature drops below the binding
energy between (p^+ `^ ). Following recombination, a small fraction of the twin particles
remains ionized. Since H^ is neutral under both the U(1)EM and U(1)B L symmetries, it
behaves as a cold DM particle during the structure formation. Meanwhile, the few ionized
twin particles (p^+; `^ ) scatter with the twin neutrinos via the t-channel U(1)B L process.
This process realizes the PAcDM framework in this scenario, furnishing the mechanism
which suppresses 8 and enhances the Hubble value due to the presence of additional twin
radiation.
During the DM halo formation, the virial temperature of the dark plasma is lower
than the binding energy. Hence, the twin hydrogen H^ remains stable and constitutes
the dominant DM component inside halos. Characterized by an extended but nite size,
the H^ atom furnishes a good SIDM candidate if its geometric size is around the barn
scale. The reason stems from the property that the scattering between two H^ 's contains
both elastic and inelastic processes. The elastic process comes from the collision between
two atoms, which transfers energy from one atom to the other and acts to keep DM
thermalized. Meanwhile, the inelastic process comes from the hyper ne splitting between
`^ and p^. In the inelastic case, when `^ absorbs part of the collisional energy into the excited
state, the subsequent decay into the ground state releases DM energy into soft ^. This
cooling process is important when H^ carries a kinetic energy comparable to the hyper ne
splitting, in which case the scattering process introduces an additional velocity dependence
in the scattering cross section. A numerical study of the scattering cross section has been
performed in [61]. From this, it emerges that the general trend is that the cross sections of
dwarf halo particles with lower DM velocities tend to be larger than those of particles in
cluster halos with higher velocities, which feature provides the correct behavior required
to solve mass de cit problems in both cases.
structure formation.
can be approximated as [
59
]
We rely on the results in refs. [
59, 61
] to determine reasonable parameters in the twin
sector for our purposes. It turns out that in order to solve both the large- and small- scale
structure problems simultaneously, we need the twin masses mp^
the twin electric coupling ^
0:02, and the twin U(1)B L coupling ^B L & 10 9. The
last bound is necessary to ensure that the t-channel p^ ^ ! p^ ^ scattering is e ective during
20 GeV, m^
`
3 GeV,
We next discuss some details of the parameters. First, the fraction of ionized atoms
e
2
' 0:5 is the ratio between the Twin and SM temperature today when the twin
radiation contributes
Ne
' 0:4 for solving the H0 problem. BH =
2
d H=2 is the
binding energy of the dark hydrogen atom, and
H is the reduced mass of the p^ `^ system.
Upon choosing ^ = 0:02, mp^ = 20 GeV, and m`^ = 3 GeV, we nd that the resulting fraction
is e ' 2:5%. As discussed in section 3, this value results in the appropriate amount of
oscillating DM necessary to solve the 8 problem.
For simplicity, we assume the U(1)B L coupling to be smaller than the electric coupling,
^B L < ^, so that the twin EM dominates the binding force. With the above choices, the
binding energy is BH
400 keV, which signi cantly exceeds the virial temperature ' 2 keV
of the twin atom during galaxy formation.4 Moreover, for the size of ^ we choose, the rate
of collisional ionization between H^ atoms in cluster halos is always smaller than the cluster
lifetime [61]. Hence, the twin atom remains in the ground state during halo formation.
If we consider the case where the H^ atom is composed of a spin- 12 p^ and a spin- 12
`^, the hyper ne splitting for the chosen mass and coupling parameters is
100 eV. The
value is above the `^ energy due to the virial velocity inside dwarf galaxies but below that
inside galaxy clusters. Therefore, the hyper ne splitting plays a more important role in
DM scattering inside galaxy clusters than dwarf galaxies. From the numerical study in [61],
such an energy splitting generates di erent DM thermalization e ects at dwarf galaxies and
galaxy clusters, which feature enables one to successfully solve the mass de cit problem in
both systems.
scale ^
Meanwhile, in the single-generation model, the lightest twin baryon (^b^b^b) is a spin- 32
particle, and a numerical study of the hyper ne splitting between a spin- 32 nucleus and a
spin- 12 lepton in the H^ scattering is more involved and is beyond the scope of this work. In
order to give a viable example of the model, we simply adapt the result in [61] by taking
the nucleus to be a spin- 12 particle. We then assume two generations of twin fermions
and take (^b; s^) to be the lightest twin quarks. In this case, (^b; s^) quarks remain stable
and form protons, p^
= (^b^bs^)
or (^bs^s^) , while the twin neutron is absent due to a fast
c^ ! s^^^ decay. With two generations of quarks, RG running gives the twin con nement
' 270 MeV. Here we assume that m^b ' ms^. Although this choice introduces
4The virial temperature is given by Tvir
0:9 keV MMDgaMl 10 GeV Rvir
110 kpc , where M represents the mass of
the virial cluster, MDgaMl = 1012M
of a dark plasma particle (in our case this is
= p^=np^ = 20 GeV) [79].
is the mass of DM in the Milky Way galaxy, and is the average mass
additional Z2 breaking, it does not ruin Higgs tuning owing to the smallness of the Yukawa
couplings for the ^b and s^ quarks and constitutes a better alternative to the introduction of
anomaly compensators. Then, approximating the twin proton mass as mp^ ' 3(ms^ + ^ ),
we nd that the lightest twin quarks feature a mass of 6:5 GeV. Twin muon carries a mass
of 3 GeV and is combined with twin proton to form the twin hydrogen. In this case, the
muons (with lifetime
10 6 sec) during the twin con nement.
lightest twin hadron is the scalar glueball mG^0++ ' 2 GeV, which decays promptly into SM
In this model, we nd that when the SM and twin sector decouple around the GeV
scale, the light degrees of freedom from the dark radiation ^ ; ; N^ ; ; ^; ^B L contribute a
Ne = 0:4, which is the required value for solving the Hubble problem. We thus see that
this Twin Hydrogen scenario successfully resolves both the large- and small-scale structure
problems without introducing additional mass scales or anomaly compensators.
6
Discussion and conclusions
In this work, we take the viewpoint that the Hierarchy problem and the large- and
smallscale structure anomalies are all indicative of the existence of a dark sector that extends
beyond the
CDM paradigm.
We investigate potential solutions to these problems in
the context of an extension of the Fraternal Twin Higgs model, which contains only the
heavier-generation partners of SM fermions and a massless gauge boson that gives the DM
and twin neutrino scattering. We rst discuss the ^ {^ scenario, which assumes a SM-like
baryogenesis, the twin baryon ^
(^b^b^b) and the twin tau ^ become metastable dark matter
particles due to twin baryon number and an approximate twin U(1)em symmetry. Through
the exchange of a
10 MeV-scale twin photon, these dark matter particles have a
selfinteraction cross section that successfully resolves the mass de cit problem on all scales,
from the dwarf galaxies to the galaxy clusters. In the speci c implementation of the PAcDM
framework that we consider, the gauged U(1)L^ force acts to suitably damp the dark matter
power spectrum, supposing it remains e ective at the beginning of matter domination. In
particular, if m^ ' 2:5% m^ , such a damping can indeed reduce the size of 8 by ' 8%,
reconciling the 8 discrepancy. Moreover, the overall
e
N scatt, which receives contributions
from the tightly coupled
uid in the twin sector, including the massless neutrinos, U(1)L^
gauge boson, and its anomaly compensators, is able to
exibly enhance the size of H0.
Favored by a weaker CMB constraint on a tightly coupled uid, this model can e ciently
reconcile the tension between the H0 results from the CMB and local measurements.
We also discuss the scenario of the twin hydrogen DM. In this case, ' 2:5% twin protons
remain ionized, and their scattering to twin neutrinos through a twin U(1)B L force damps
the matter power spectrum realizing the PAcDM framework. The twin photon remains
massless in this case, and the scattering between two twin hydrogens contains the required
velocity dependence necessary to successfully resolve the mass de cit problem from dwarf
galaxy to galaxy cluster scales.
Our study is based on the Fraternal Twin Higgs model, which contains a smaller
number of neutrinos than the full three-generation case and hence is able to more easily satisfy
the
Ne constraint. Alternatively, it may be possible to accommodate all three
generations of fermions in the twin sector, provided that there is either a late-time reheating that
preferentially goes into the SM sector [80{83] or a Z2 breaking of the Yukawa couplings [84].
In either of the cases, the stable charged twin fermions can still interact with each other
through the twin photon exchange and a ect the halo formation. Further, if a component
of the dark matter has acoustic oscillations, either through a twin baryon acoustic
oscillation among the twin proton, twin electron, and twin photon, or through a twin lepton
acoustic oscillation between the twin electron and twin neutrino through the anomaly-free
gauge force U(1)L^i L^j , there are partially acoustic oscillations that can smoothly change
the large-scale structure. We leave the study of this scenario to future work.
Aside from explaining the possible anomalies, analysis of structure formation in the
twin sector provides additional constraints on the Twin Higgs model. Given a sizable
amount of stable charged twin particles, which can be found in a large chunk of parameter
space, constraints from the dark matter self-interaction enable us to set an upper bound
on the twin electric coupling ( gure 4). If the charged twin particles scatter with massless
twin particles, studies of the CMB and the matter power spectrum also set upper bounds
on such couplings. In the coming years, the experimental precision in the values of
Ne
and (H0; 8) is expected to improve signi cantly from both the CMB and weak lensing
measurements [85]. Moreover, with the progress of the N-body simulation, we anticipate
to better identify the signi cance of the mass de cit problem from baryonic grounds. No
matter whether these puzzles of the large- and small-scale structure remain signi cant
or disappear, the coming future results will more clearly reveal the details of the Twin
Higgs model, opening the door to a stronger understanding of these issues and to novel
connections between the dark sector and the Hierarchy problem.
Acknowledgments
We thank Kimberly Boddy, Zackaria Chacko, Nathaniel Craig, Yanou Cui, David Curtin,
Sungwoo Hong, Gustavo Marques-Tavares, Takemichi Okui, Martin Schmaltz, Neelima
Sehgal, Hai Bo Yu for helpful discussions. VP is supported by the DOE grant
DE-FG0291ER40674. YT is supported in part by the National Science Foundation under grant
PHY-1315155, and by the Maryland Center for Fundamental Physics. YT thanks the
Aspen Center for Physics, which is supported by National Science Foundation grant
PHY1066293.
Open Access.
This article is distributed under the terms of the Creative Commons
Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in
any medium, provided the original author(s) and source are credited.
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