Goldilocks Supersymmetry: Simultaneous Solution to the Dark Matter and Flavor Problems of Supersymmetry

0.26 MB·English

by  Jonathan L. Feng

UCI-TR-2007-37
CLNS 07/2006
Goldilocks Supersymmetry: Simultaneous Solution to the Dark Matter and Flavor
Problems of Supersymmetry
Jonathan L. Feng,1 Bryan T. Smith,1 and Fumihiro Takayama2
1Department of Physics and Astronomy, University of California, Irvine, CA 92697, USA
2Institute for High Energy Phenomenology, Cornell University, Ithaca, NY 14853, USA
Neutralino dark matter is well motivated, but also suffers from two shortcomings: it requires
gravity-mediated supersymmetry breaking, which generically violates flavor constraints, and its
thermalrelic densityΩis typically toolarge. Weproposea simplesolution toboth problems: neu-
tralinosfreezeoutwithΩ∼10−100,butthendecayto∼1GeVgravitinos,whicharesimultaneously
lightenoughtosatisfyflavorconstraintsandheavyenoughtobeallofdarkmatter. Thisscenariois
naturallyrealizedinhigh-scalegauge-mediationmodels,amelioratessmallscalestructureproblems,
8 and implies that “cosmologically excluded” models may, in fact, be cosmologically preferred.
0
0 PACSnumbers: 95.35.+d,04.65.+e,12.60.Jv
2

n
Supersymmetric extensions of the standard model of neutralinos, which suppresses annihilation to gauge and
a
J particle physics are among the prime candidates for new Higgsbosons. Theseeffects togetherenhancerelicdensi-

5 microphysics. Among their many virtues, supersymmet- ties to values that may far exceedthose givenin Eq.(1).
1 ricmodelsnaturallypredictnewparticlesthatarecandi- These two shortcomingsof neutralino dark matter are
datesfordarkmatter. Themostwellstudiedoftheseare usually considered unrelated and addressed separately.
]
h thermal relic neutralinos [1], superpartners of the Higgs One may, for example, consider gravity-mediated sce-
p andelectroweakgaugebosons. Thethermalrelicdensity narios, such as minimal supergravity, where low energy
- of neutralinos is dependent on unknown supersymme- constraintsaresatisfiedbyunificationassumptions. One
p
try parameters. However, order-of-magnitude estimates thenfurtherfocusesonspecialregionsofparameterspace
e
h yield relic densities that are consistent with [2] in which the neutralino relic density is reduced to ac-
[ ceptable levels through, for example, resonant annihi-
Ω h2 =0.1050+0.0041 (1σ) , (1)
3 DM −0.0040 lation [4], stau co-annihilation [5], or significant Bino-
v where ΩDM is the observed energy density of non- Higgsinomixing[6]. Alternatively,onemaysimplyaban-
7 baryonicdark matter in units of the criticaldensity, and don the hope that the order-of-magnitude correctness of
9
h 0.73 is the normalized Hubble parameter. This re- the neutralino thermal relic density is a significant lead
2 ≃
markable fact has not only motivated supersymmetry, in the hunt for dark matter and explore other mecha-
0
. but has also focused attention on “cosmologically pre- nismsfordarkmatterproduction. Forexample,onemay
9
ferred”models,inwhichtheneutralinothermalrelicden- considerGMSBmodelswiththermallyproducedgraviti-
0
sityisexactlythatrequiredfordarkmatter. Suchstudies nos[7]. (Note,however,thatrecentLyman-αconstraints
7
0 have implications for a large range of experiments, from requiring mG˜ ≥ 2 keV [8] imply that the gravitino ther-
v: direct and indirect dark matter searches to those at the mal relic density ΩtG˜hh2 ≈ 1.2(mG˜/keV) must be signifi-
Large Hadron Collider (LHC) at CERN. cantlydilutedthroughlateentropyproduction[9]forthis
i
X The neutralino dark matter scenario is not without possibilitytobeviable.) Morerecently,GMSB-likemod-
r its blemishes, however. First, for the neutralino to be elswithgravitinodarkmatterproducedbylatedecaying
a
stable, it must be the lightest supersymmetric particle gauge singlets have also been proposed [10].
(LSP). In particular, it must be lighter than the grav- In this work, we consider the possibility that the two
itino. This requires gravity-mediated supersymmetry shortcomingsdescribedabovearenotseparateissues,but
breaking models, in which low energy bounds on fla- are in fact pointing to a single resolution. We propose
vor and CP violation are generically violated by several that neutralinos do, in fact, freezeout with very large
orders of magnitude. Gauge-mediated supersymmetry densities. However,they then decay to gravitinos,which
breaking (GMSB) models [3] elegantly avoid these con- are light enough to accommodate the GMSB solution to
straints,butsuchmodelshavegravitinoLSPsandsoare the flavor and CP problems, but heavy enough to be all
incompatible with neutralino dark matter. of dark matter. In analogy to Goldilocks planets, which
Second, although general arguments imply that the havetemperaturesthatlie withinthe narrowwindowre-
neutralino thermal relic density is of the right order of quiredtosupportlife,thesesupersymmetricmodelshave
magnitude, in concrete models, it is often too large: gravitinomassesinthenarrowwindowrequiredtosatisfy
Neutralinos are Majorana fermions, and so annihila- bothparticlephysicsandcosmologicalconstrants,andso
tion to quarks and leptons is P-wave suppressed. In we call this “Goldilocks Supersymmetry.”
addition, gauge coupling unification and radiative elec- The essential features of this scenario may be illus-
troweak symmetry breaking typically imply Bino-like trated by simple scaling arguments. Consider models
2
in which there are two mass scales: the scale of the chirality,andf =l,u,d. Thechirality-preservingparam-
standard model superpartner masses m˜, and the grav- eters are naturally m ; for concreteness, we assume
∼ G˜
itino mass mG˜. The freezeout density of neutralinos |(mfij)LL| = |(mfij)RR| = mG˜. The chirality-violating
is inversely proportional to the neutralino annihilation masses require the breaking of electroweak gauge sym-
cross section, and so by dimensional analysis, Ωχh2 metry (and possibly horizontal symmetries); we assume
∼
ΩhnσaG˜vthui−2ra1=l∼so(mlmu˜tG˜2io./nm˜T)tΩhoeχthhg2rea∼vsuitpmineGor˜smy˜rem.limcAedttertinchseifltyasavimosretahtneimrdeefCo,rPae |gF(rimanvafijilt)lyyL,-Rwa|ne<∼dasλgsfiaujummgeGe˜-O,mw(e1hd)eirCaetPetd-hvemioλalafisjtsieansrg,eapYshuadkseaetwsaafiolecrdobubopetlhlionwtgh.se.
problems requires m m˜. We find, then, that we can
G˜ ≪ Given these assumptions, the most stringent con-
alwaysmake Ω large enoughto explain dark matter by
G˜ straints are the flavor-changing observables ∆mK and
raising m and m˜ together with their ratio fixed. The
G˜ ǫK, andthe CP-violating,but flavor-preserving,electron
essential question, then, is whether the scenario may be
andneutronelectricdipolemoments(EDMs)[13,14,15]:
realizedwithm˜ <TeV,asrequiredforanaturalsolution
tothegaugehier∼archyproblem,andwhetheritpassesall ∆mSUSY < 3.5 10 12 MeV (5)
othTeor apnaartlyiczlee pthhiyssiqcuseasntidonasctroonpchreytseiclya,lwcoensctornasiindtesr. the ǫKSKUSY < 2.3××10−−3 (6)
d < 1.6 10 27 e cm (7)
exampleofminimalGMSBmodels[11]. Suchmodelsare e −
×
specified by the 4+1 parameters Mm, Λ, Nm, tanβ, and dn < 2.9 10−26 e cm . (8)
×
sign(µ), where M is the messenger mass, Λ = F/M ,
m m
whereF isthesupersymmetrybreakingscaleinthemes- In the mass insertion approximation, these constrain
sengersector,Nm isthenumberof5+5messengerpairs, (δifj)AB ≡ (mfij)AB/m¯f˜, where m¯f˜ is an average f˜
gtasninβo =mahsHs.u0iI/nhHted0rim, asnodf µthiessethpearsaumpeertseyrms,mtheterigcaHugige-- mReass(.δ1d2)LTLh(eδ1d2le)RadRin,gfrcoomnstǫrKainotns Iamre (fδr1do2m)LL∆(δm1d2K)RRon,
mediatedcontributionstosquarkandsleptonmassesare and(cid:2)from the EDM(cid:3)s on the gauge-medi(cid:2)ated masses. (cid:3)
The supersymmetric contributions to the kaon ob-
3 g2(M ) 2 servables are ∆mSUSY = Re(M) and ǫSUSY =
m2f˜(Mm)=2NmΛ2Xi=1Cif(cid:20) i16π2m (cid:21) , (2) Im(M)/(√8∆meKxp)K, with M as given in Ref.K[16]. For
concreteness,wechoosetheδ phasestomaximizethesu-
where Cf = 5Y2, with hypercharge Y = Q T , and persymmetriccontributionforeachkaonobservable. The
Cf =0 f1or gau3ge singlets, 3 for SU(2) doubl−ets,3and 4 constraints from ∆mK and ǫK are therefore not simul-
i 4 L 3 taneously applicable, but the most stringent constraint
for SU(3) triplets. The gaugino masses are
C
smoothly interpolates between these as the phase varies.
g2(M ) For the EDMs, we first use micrOMEGAs 1.3.7 [17] to
M (M )=N Λc i m , (3)
i m m i 16π2 determine the supersymmetric contribution to aµ, the
anomalous magnetic moment of the muon. The EDMs
gwrhoeurpes,ic==1,25,,3anfodrcthe=Uc(1)=Y,1.SUA(s2)iLn,diacnatdedS,Ut(h3e)sCe are, then, de = 2mme2µaµtanθCP and dn = 31(4dd +du),
1 3 2 3 where d and d are determined from d with α α ,
d u e s
masses are generatedat the energy scale Mm. We deter- M M ,m m ,andtheintroductionofapp→ropri-
minephysicalmassesthroughrenormalizationgroupevo- 1 → 3 ˜l → d˜,u˜
ate color factors [16]. We set tanθ = 1 in the EDMs.
CP
lution to the weak scale and radiative electroweak sym-
Note that the EDMs may be suppressed, depending, for
metry breaking with SoftSUSY 2.0 [12].
example, on the origin of the µ and B parameters.
In addition to the gauge-mediated masses, there are
The resulting constraints are given in Fig. 1. The ob-
gravity-mediatedcontributions. Thesegeneratethegrav-
servables∆m andǫ requirem <30GeV(500GeV)
itino mass mG˜ = √3FM0∗, where F0 is the total super- forneutralinoKmassmKχ 100GeVG˜ ∼(1TeV). Incontrast,
symmetry breaking scale and M 2.4 1018 GeV is ∼
the EDMs are insensitive to m , since they do not rely
∗ ≃ × G˜
the reduced Planck mass. Because F receives contribu-
0 ongravity-mediatedcontributions. Theyarefoundtore-
tionsfromallsupersymmetrybreakingF-terms,F0 F. quire m > 1 TeV, in agreement with earlier work [18].
≥ χ
For direct gauge mediation, F0 F, but this is model- These resu∼lts are, of course, subject to the assumptions
∼
dependent. Here, we assume F =F, and so
0 we have made. However, they imply that in any model
inwhichgravity-mediatedcontributionsareattheirnat-
F M Λ
m
mG˜ = √3M = √3M . (4) uralscaleandallmassparametershaveO(1)phases,the
∗ ∗ standard model superpartners must be heavy, and the
Our results are not changed significantly for F >F. LSP is the gravitino, not the neutralino.
0
Gravity-mediation also generates flavor- and CP- For N =1,the lighteststandardmodelsuperpartner
m
violating squark and slepton mass parameters (mf ) , is the lightest neutralino χ throughout parameter space.
ij AB
where i,j = 1,2,3 label generation, A,B = L,R label In Fig. 1 we also show the freezeout density Ω h2, that
χ
3
FIG.1: NeutralinothermalrelicdensityΩχh2 inthe(mG˜,Λ) FIG. 2: Contours of ΩG˜h2 in the (mG˜,Λ) plane,. The thick
plane,forNm =1,tanβ =10,µ>0andmt =175GeV. The contouristhe2σ allowed region. Low-energyconstraintsand
right-handaxis givestheneutralinomass mχ ≈1.3×10−3Λ. fixedGMSB parameters are as in Fig. 1.
Regions totheright of theǫK and∆mK contoursandbelow
the de and dn contours are disfavored. The neutralino is the
LSP in theshaded region.
is,therelicdensityifneutralinoswerestable,determined
usingmicrOMEGAs[17]. Theseresultsillustratethedif-
ficulties for neutralino dark matter. At the weak scale,
typicallyµ,M >M ,andχisBino-like. Itsannihilation
2 1
is therefore suppressed for the reasons noted above. For
m = 100 GeV, Ω h2 1 is already far too large, and
χ χ
∼
forthe heaviersuperpartnermassesfavoredbythe EDM
constraints, it grows to values of 10 100.
∼ −
Inthescenarioproposedhere,however,neutralinosare
not stable, but decay to gravitinos. The resulting grav-
itino relic density is given in Fig. 2. In the dark green
shaded region, Ω h2 is in the range required to account
G˜
forallofnon-baryonicdarkmatter. We seethatpartsof
this shaded region are consistent with low energy flavor FIG. 3: Contours of λFS (solid) and lifetime τ(χ→G˜) (dot-
and CP constraints. In this scenario, very large neu- ted)inthe(mG˜,Λ)plane,forNm =1,tanβ=10,µ>0,and
tralinofreezeoutdensitiesareavirtue,notaproblem,as top quark mass mt =175 GeV. In the light yellow (medium
blue)shadedregion,hadronic(electromagnetic)showersfrom
theyallowlightgravitinostohavetherequiredrelicden-
χ decays produce discrepancies with BBN observations. The
tshitiys,sdimespplieteetxhaemspilgeniofifcmanitnidmilaultiGonMfSaBct,otrhme GG˜/omldχil.ocIkns bandwiththecorrectΩG˜h2 isasinFig.2,andtheneutralino
LSPregion and fixed GMSB parameters are as in Fig. 1.
window, in which both relic density and low energy con-
straints are satisfied, has m 1 10 GeV.
G˜ ∼ −
So far, we have considered constraints from parti-
scale structure [20]. We find that the last two are most
cle physics and Ω . We now turn to astrophysi-
DM stringent, and so focus on them here.
cal constraints. In the preferred band, the gravitino
Standard BBN agrees reasonably well with observa-
is light and dominantly couples through its Goldstino
tions. This agreement constrains electromagnetic (EM)
components. The neutralino decay widths are Γ(χ
γG˜) = (cos2θ /48π)(m5/m2M2) and Γ(χ ZG˜)→= andhadronicenergyreleaseinlatedecays,whichmaybe
(insinF2igθW. 3/,48thπe)s(Wem5χim/mpl2Gy˜Mlifχ∗2e)ti(cid:2)m1G˜e−s(cid:0)τ∗m>2Z/0m.02χ1(cid:1)(cid:3)s4.i→nAtshsehopwren- ptchaayer,aEBmMeti/sehrtaihzdeerdobnrbiaycnecξhni ie≡nrggǫyfirBraeicYlteχiao,snewdihnietnoreeEaiMc=h/hnEaeMudtr,rohanaliidcn,ocǫoidmeis--
i
ferredband. Suchlatedecaysareco∼nstrainedbyentropy ponents, and Y n /nBG, where nBG = 2ζ(3)T3/π2.
χ ≡ χ γ γ
production, µ distortions of the cosmic microwave back- We have determined the ξ following the prescription of
i
ground,Big Bang nucleosynthesis (BBN) [19], and small Refs.[21]andcomparedthem tothe constraintsgivenin
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