The WIMPless Miracle: Dark Matter Particles without Weak-scale Masses or Weak Interactions

0.22 MB·English

by  Jonathan L. Feng

UCI-TR-2008-10
The WIMPless Miracle: Dark Matter Particles
without Weak-scale Masses or Weak Interactions
Jonathan L. Feng and Jason Kumar
Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
We propose that dark matter is composed of particles that naturally have the correct thermal
relic density, but have neither weak-scale masses nor weak interactions. These WIMPless models
emerge naturally from gauge-mediated supersymmetry breaking, where they elegantly solve the
dark matter problem. The framework accommodates single or multiple component dark matter,
darkmattermassesfrom10MeVto10TeV,andinteractionstrengthsfromgravitationaltostrong.
ThesecandidatesenhancemanydirectandindirectsignalsrelativetoWIMPsandhavequalitatively
new implications for dark mattersearches and cosmological implications for colliders.
9
0 PACSnumbers: 95.35.+d,04.65.+e,12.60.Jv
0
2
Introduction. Cosmological observations require dark
n
a matter that cannot be composed of any of the known
J particles. At the same time, attempts to understand

0 the weak force also invariably require new states. These
1 typically include weakly-interacting massive particles

(WIMPs) with masses around the weak scale mweak ∼
]
h 100 GeV−1 TeV and weak interactions with coupling
p gweak ≃ 0.65. An appealing possibility is that one of
- the particles motivated by particle physics simultane-
p
e ously satisfies the needs of cosmology. This idea is moti-
h vated by a striking quantitative fact, the “WIMP mira-
[ cle”: WIMPs are naturallyproduced as thermalrelics of FIG.1: Sectorsofthemodel. SUSYbreakingismediated by

3 theBigBangwiththedensitiesrequiredfordarkmatter. gaugeinteractionstotheMSSMandthehiddensector,which
v This WIMP miracle drives most dark matter searches. contains the dark matter particle X. An optional connector
6 We show here, however, that the WIMP miracle does sector contains fieldsY,charged underboth MSSMand hid-
9 den sector gauge groups, which induce signals in direct and
notnecessarilyimplytheexistenceofWIMPs. Morepre-
1 indirect searches and at colliders. There may also be other
cisely, we present well-motivated particle physics mod-
4 hidden sectors, leading to multi-component dark matter.
. els in which particles naturally have the desired ther-
3
mal relic density, but have neither weak-scale masses
0 (m ,g ) can also give the correct Ω . Here, however,
X X X
8 nor weak force interactions. In these models, dark mat- we further show that simple models with low-energy su-
0 ter may interact very weakly or it may couple more
persymmetry (SUSY) predict exactly the combinations
: strongly to known particles. The latter possibility im-
v of (m ,g ) that give the correct Ω . In these models,
X X X
Xi plies that prospects for some dark matter experiments mX is a free parameter. For mX 6=mweak, these models
maybegreatlyenhancedrelativetoWIMPs,withsearch
are WIMPless, but for all m they contain dark matter
r implications that differ radically from those of WIMPs. X
a with the desired thermal relic density.
Quite generally,a particle’s thermalrelic density is [1]
Models. We will consider SUSY models with gauge-
1 m2 mediated SUSY breaking (GMSB) [2, 3]. These models
ΩX ∝ hσvi ∼ g4X , (1) have several sectors, as shown in Fig. 1. The MSSM
X sector includes the fields of the minimal supersymmet-
where hσvi is its thermally-averaged annihilation cross ric standard model. The SUSY-breaking sector includes
section, m and g are the characteristic mass scale thefieldsthatbreakSUSYdynamicallyandmediatethis
X X
and coupling entering this cross section, and the last breakingtotheMSSMthroughgaugeinteractions. There
step follows from dimensional analysis. In the mod- arealsooneormoreadditionalsectorswhichhaveSUSY
els discussed here, m will be the dark matter parti- breaking gauge-mediated to them; these sectors contain
X
cle’s mass. The WIMP miracle is the statement that, thedarkmatterparticles. Thesesectorsmaynotbevery
for (mX,gX) ∼ (mweak,gweak), the relic density is typi- well-hidden,depending onthe presenceofconnectorsec-
callywithinanorderofmagnitudeoftheobservedvalue, tors (discussed below), but we will follow precedent and
Ω ≈ 0.24. Equation (1) makes clear, however, that refertothem as“hidden”sectors. Forotherrecentstud-
X
the thermal relic density fixes only one combination of ies of hidden dark matter, see Refs. [4].
thedarkmatter’smassandcoupling,andothervaluesof This is a well-motivated scenario for new physics.
2
GMSB models feature many of the virtues of SUSY, For the proton and electron, this accident results from
while elegantly solving the flavor problems that gener- extremely suppressed Yukawa couplings which are unex-
ically plague proposals for new weak-scale physics. Ad- plained. Thereisnoreasonforthehiddensectortosuffer
ditionally,inSUSY models thatarisefromstringtheory, from this malady. Generally, since m is the only mass
X
hiddensectorsareubiquitous. Asaconcreteexample,we scale in the hidden sector, we expect all hidden parti-
extendthe canonicalGMSBmodelsofRef.[3]toinclude cles to have mass ∼ m or be essentially massless, if
X
one hidden sector. SUSY breaking gives vacuum expec- enforced by a symmetry. We assume that the thermal
tation values to a chiral field S, with hSi = M +θ2F. relic has mass around m , and that discrete or continu-
X
We couple S to MSSM messenger fields Φ, Φ¯ and hid- oussymmetries stabilize this particle. The particlesthat
den sector messenger fields Φ , Φ¯ through the super- areessentiallymasslessatfreezeoutprovidethe thermal
X X
potential W = λΦ¯SΦ + λ Φ¯ SΦ . These couplings bathrequiredforthevalidityofEq.(1). Anexampleofa
X X X
generate messenger F-terms Fm =λF and FmX =λXF viable hidden sectoris one with MSSM-like particle con-
andinduceSUSY-breakingmassesintheMSSMandhid- tent (with possible additional discrete symmetries), but
den sectors at the messenger mass scales Mm =λM and with different gauge couplings and with all Yukawa cou-
MmX =λXM, respectively. plings O(1). The light particles are then the neutrinos,
Relic Density. NeglectingsubleadingeffectsandO(1) gluon, photon (and gravitino), while the remaining par-
factors, the MSSM superpartner masses are ticles are all at the scale m . The lightest such particle
X
charged under a (possibly discrete) unbroken symmetry
m∼ g2 Fm = g2 F , (2) willthen be stableby hidden sectorchargeconservation.
16π2Mm 16π2M One might worry that the extra light particles will
have undesirable cosmological consequences. In partic-
where g is the largest relevant gauge coupling. Since m
ular,thenumberoflightparticlesareconstrainedbyBig
alsodeterminestheelectroweaksymmetrybreakingscale,
Bang nucleosynthesis (BBN) [11] and (less stringently)
m∼mweak. The hidden sector superpartner masses are
the cosmic microwave background [12] even if they have
m ∼ gX2 FmX = gX2 F . (3) no SM interactions. These constraints have been ana-
X 16π2MmX 16π2M lyzed in detail in Ref. [13]. They are found to require
g∗h(TBhBN/TBBN)4 ≤2.52(95% CL),whereg∗h isthenum-
As a result,
ber of relativistic degrees of freedom in the hidden sec-
mX m F tor at BBN, and TBhBN and TBBN are the temperatures
g2 ∼ g2 ∼ 16π2M ; (4) of the hidden and observable sectors at BBN, respec-
X tively. This bound may therefore be satisfied if, for
that is, mX/gX2 is determined solely by the SUSY- example, g∗h < 2.5 or if the hidden sector is as big as
breaking sector. As this is exactly the combination of the MSSM with g∗h = 10.75 but is slightly colder, with
parameters that determines the thermal relic density of TBhBN/TBBN < 0.7. Such discrepancies in temperature
Eq. (1), the hidden sector automatically includes a dark are possible if the observable and hidden sectors reheat
matter candidate that has the desired thermal relic den- to different temperatures [14, 15] and need not alter the
sity, irrespective of its mass. (In this example, the su- relic density calculation significantly [13].
perpartner masses are independent of λ and λ ; this To summarize so far: GMSB models with hidden sec-
X
will not hold generally. However,giventypical couplings torsprovidedarkmattercandidatesthatarenotWIMPs
λ∼λ ∼O(1), one expects the messenger F-terms and but nevertheless naturally have the correct thermal relic
X
massesto be approximatelythe same asthose appearing density. These candidates have masses and gauge cou-
in hSi, and Eq. (4) remains valid.) plings satisfying mX/gX2 ∼mweak/gw2eak, and
Thisanalysisassumesthatthesethermalrelicsaresta- 10−3 <∼ gX <∼3
ble. Of course, this is not the case in the MSSM sector,
wherethermalrelicsdecaytogravitinos. This isa major 10 MeV<∼ mX <∼10 TeV , (5)
drawback for GMSB, especially because its classic dark where the upper limits from perturbativity nearly satu-
matter candidate, the thermal gravitino [5], is now too rate the unitarity bound [16], and the lower limits are
hot to be compatible with standard cosmology [6]. So- rough estimates from requiring the thermal relic to be
lutions to the dark matter problem in GMSB include non-relativistic at freeze out so that Eq. (1) is valid.
messengersneutrinos[7],lateentropyproduction[8],de- Detection. Ifthe hiddensectorisnotdirectlycoupled
caying singlets [9], and gravitino production in late de- totheSM,thenthecorrespondingdarkmattercandidate
cays [10], but all of these bring complications, and only interacts with the known particles extremely weakly. A
the last one makes use of the WIMP miracle. moreexciting possibilityisthatdarkmatterinteractions
But the problem exists in the MSSM only because of are enhanced by connector sectors containing particles
an accident: the stable particles of the MSSM (p, e, ν, Y that are charged under both MSSM and the hidden
γ, G˜) have masses which are not at the scale mweak. sector, as shown in Fig. 1.
3
Y superpartnermassesreceivecontributionsfromboth
MSSMandhiddensectorgaugegroups,andsoweexpect
mY ∼ max(mweak,mX). Connectors interact through
λXYf, where λ is a Yukawa coupling and f is a SM
particle. X remains stable, as long as m < m +m ,
X Y f
buttheseinteractionsmediatenewannihilationprocesses
XX¯ →ff¯,YY¯ andscatteringprocessesXf →Xf. The
new annihilationchannels do not affect the thermalrelic
density estimates given above, provided λ<∼gweak.
Connector particles create many new possibilities for
dark matter detection. For example, in WIMPless mod-
els, the dark matter may have mX ≪mweak. This moti-
vatesdirectsearchesprobingmassesfarbelowthosetyp-
ically expected for WIMPs. Because the number density
mustcompensateforthelowmass,indirectdetectionsig-
nals are enhanced by m2 /m2 over WIMP signals.
weak X
Toquantifythis,weconsiderasimpleconnectorsector FIG. 2: Direct detection cross sections for spin-independent
with chiral fermions YfL and YfR and interactions X-proton scattering as a function of dark matter mass mX.
Thesolid curvesarethepredictionsfor WIMPless darkmat-
L=λfXY¯fLfL+λfXY¯fRfR+mYfY¯fLYfR , (6) ter with connector mass mYu = 400 GeV and the Yukawa
couplings λu indicated. The shaded region is excluded by
where the fermions f and f are SM SU(2) doublets
L R CRESST[18],CDMS (Si) [19],TEXONO[20], XENON[21],
andsinglets,respectively. TheYf particlesgetmassfrom and CDMS (Ge) [22].
SM electroweak symmetry breaking. For simplicity, we
couple Y to one SM particle f at a time, but, one Y can J¯ is a constant parameterizing the cuspiness of our
have multiple couplings or there can be many Y fields. galaxy’s dark matter halo, ∆Ω is the experiment’s solid
We begin with direct detection, and assume the in- angle, and Nγ = EmthXrdEddNEγ is the average number of
teractions of Eq. (6) with f = u. These mediate spin- photons above thrReshold produced in each τ decay.
independent X-nucleus scattering through Xu → In Fig. 3, we evaluate the discovery prospects for
L,R
YL,R →XuL,R with cross section GLAST [27]. We take ∆Ω = 0.001, Nγ = 1 and
σSI = 2λπ4u(mNm+2NmX)2[ZB(upm+X(A−−mYZ))2Bun]2 , (7) vdEaitsrhciroovu=esrλy1.τGaTeshVae, fmaunnindcitmrioeunqmuoirfveamlΦuXγesa>roef1gJ0¯i−vfe1o0nrcidnmis−Fc2oigv.se−r3y1. ffAoosrr
the flux is proportional to number density squared, we
where A (Z) is the atomic mass (number) of nucleus N,
find excellent discovery prospects for light dark matter.
Bp =hp|u¯u|pi≃5.1, and Bn =hn|u¯u|ni≃4.3 [17].
uInFig.2,wepresentX-pruotonscatteringcrosssections For λτ =0.3 and mX <∼20 GeV, GLAST will see WIM-
Pless signals for J¯ ∼ 1, corresponding to smooth halo
as functions of m for various λ and m = 400 GeV.
X u Yu profiles that are inaccessible in standard WIMP models.
Y receives mass from SM electroweak symmetry break-
u
Conclusions. In GMSB models with hidden sectors,
ing, and this mass is well within bounds from perturba-
we have found that, remarkably, any stable hidden sec-
tivity and experimental constraints [23]. Note that the
tor particle will naturally have a thermal relic density
cross sections are much larger than for neutralinos and
many standard WIMPs, such as B1 Kaluza-Klein dark thatapproximatelymatchesthat observedfor darkmat-
ter. Indeed, it is merely an accident that the MSSM
matter [24]. Also, the framework accommodates dark
itselfhasnostableparticlewiththe rightrelicdensityin
matter at the GeV or TeV scale, which may resolve cur-
GMSB, and it is an accident that need not occur in hid-
rent anomalies, such as the apparent conflict between
den sectors. These candidates possess allthe key virtues
DAMA and other experiments [25].
of conventional WIMPs, but they generalize the WIMP
We now turn to indirect detection and consider the
paradigm to a broad range of masses and gauge cou-
interactionsofEq.(6)withf =τ. Theseinteractionscan
plings. This generalizationopensupnewpossibilities for
produce excess photon fluxes from the galactic center.
large dark matter signals. We have illustrated this with
The integrated flux is [26]
two examples, but many other signals are possible.
Φ = 5.6×10−10N σSMv 100 GeV 2J¯∆Ω , (8) AsshowninFig.1,thisscenarioalsonaturallyaccom-
γ cm2 s γ pb (cid:20) m (cid:21) modatesmulti-componentdarkmatteriftherearemulti-
X
ple hidden sectors. This is highly motivated — in IBMs,
where the cross section for XX¯ →τ+τ− is
onegenerallyexpectsmultiplehiddensectorsinaddition
λ4 m2 totheMSSM.Inthisframework,itiscompletelynatural
σSMv = 4πτ (m2 +Ym2)2 , (9) for dark matter particles with varying masses and cou-
X Y
4
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