Light Higgsino for Gauge Coupling Unification

0.27 MB·

by  Kwang Sik Jeong

PNUTP-17/A11
Light Higgsino for Gauge Coupling Unification
∗
Kwang Sik Jeong
Department of Physics, Pusan National University, Busan 46241, Korea
7
1 We explore gauge coupling unification and dark matter in high scale supersymmetry where the
0 scale of supersymmetry breaking is much above the weak scale. The gauge couplings unify as pre-
2 cisely asin lowenergy supersymmetryifthehiggsinos, whosemass doesnotbreak supersymmetry,

r aremuchlighterthanthoseobtainingmassesfromsupersymmetrybreaking. Thedarkmatterofthe
a universecan thenbeexplainedbytheneutralhiggsino orthegravitino. Highscale supersymmetry
M
with light higgsinos requires a large Higgs mixing parameter for electroweak symmetrybreaking to
takeplace. Itisthusnaturally realized inmodels wheresuperparticle masses are generated at loop

1 levelwhiletheHiggsmixingparameterisinducedattreelevel,likeinanomalyandgaugemediation
2 of supersymmetrybreaking.

]
h
Supersymmetry (SUSY) is a theoretically well- gaugecouplingsintheabsenceofhighscalethresh-
p
- motivated framework for extending the Standard old corrections so that extension towards a grand
p Model (SM), and can be realized in various ways. unified theory (GUT) is possible.2 Interestingly,
e
Takenas a theoreticalguiding principle to physics gauge couplings unify as precisely as in low en-
h
[ beyond the SM, naturalness suggests low energy ergy SUSY if the higgsinos, whose mass is not

SUSY spontaneously broken at a TeV scale or be- directly connected to SUSY breaking, are much
2
low, for which the minimal supersymmetric SM lighter than other sparticles and the heavy Higgs
v
7 (MSSM) becomes compatible with gauge unifica- doublet [8, 9]. That is, if
4 tion [1] and provides a viable candidate for cold
9 dark matter [2]. However, the observation of the |µ|≪m , (1)
6 susy
SM-like Higgs boson with mass near 125 GeV and
0
non-observationofnewphysicssignalsattheLHC
1. seemtoindicatethatthescaleofSUSYbreakingis whereµisthehiggsinomassparameter,andmsusy
denotes the scale of SUSY breaking. The lightest
0
around multi TeV or higher. One may then need
7 sparticle is then the neutral higgsino or the grav-
a different approach to the naturalness problem,
1 itino, which can make up all the dark matter if
: like for instance the dynamical relaxation of the produced non-thermally or from thermal scatter-
v
weak scale [3]. If realized at a high energy scale,
i ings of sparticles.
X SUSY would play only a partial role in stabiliz-
High scale SUSY with light higgsinos can have
r ing the weak scale against quantum corrections.1
a interestingphenomenology[8–14],butneedstoad-
Nonetheless it still remains attractive, in partic-
dresshowtoachieveelectroweaksymmetrybreak-
ular from the viewpoint of grand unification and
ing (EWSB) that requires a Higgs mixing param-
dark matter.
eter B much larger than m . We stress that
susy
a natural framework for large B is provided by
In this letter we examine if SUSY broken much
models where sparticle masses are generated at
abovetheweakscalecanaccountforthedarkmat-
loop level while B is induced at tree level, like in
ter of the universe, and retain the unification of
anomaly [15, 16] or gauge mediation [17, 18]. We
examinetherelationbetweenm andµrequired
susy
for EWSB and gauge unification in the scenario
∗email: [email protected] where anomaly or gauge mediation is sizable, and
1 InSUSYrelaxionmodels[4–6],thehiggsinomassparam- estimate the value and scale at which the gauge
eter µ receives two or morecontributions whose relative couplings unify.
phaseisdeterminedbytherelaxion,generatingtheweak
scale viacosmological evolution. This mechanism would
work also in high scale SUSY with light higgsinos be-
cause|Bµ|2,onwhichthedeterminantoftheHiggsmass
matrix depends, still varies along the relaxion direction. 2 See,forinstance,Ref.[7]forthresholdcorrectionsatthe
HereB denotes theHiggsmixingparameter. GUTscaleinthehighscaleSUSYscenario.
2
How light can the higgsinos be compared to ThehierarchybetweentheHiggsmixingparam-
other sparticles? The most important theoretical eter and sparticle masses is naturally realized in a
constraint on µ comes from EWSB. In the MSSM classofSUSYbreakingmodelswheresparticlesob-
scalar potential, the squared-mass terms of the tainmassesatlooplevel,thatis,forinstance,mod-
neutral Higgs fields read elsinwhichanomalyorgaugemediationissizable.
A large B in such models has been regarded as
(m2Hu +|µ|2)|Hu0|2+(m2Hd +|µ|2)|Hd0|2 problematic in low energy SUSY because it makes
−(BµH0H0+h.c.), (2) EWSB difficult unless µ is below 100 GeV, which
u d
is in conflict with the LEP bound on the chargino
including SUSY breaking terms associated with mass. The situationhoweverchangesinhighscale
the Higgs doublet fields. Thus EWSB occurs if SUSY.
In supergravity, anomaly mediation always in-
|Bµ|2 >(m2 +|µ|2)(m2 +|µ|2), (3)
Hu Hd duces sparticle masses radiatively, but the Higgs
mixing parameterassociatedwith µ arisesat tree-
where the involved parameters should satisfy
level:
2|Bµ| < m2 +m2 +2|µ|2, (4)
Hu Hd m2
m2 | ∼ 3/2 ,
for the scalar potential to be stable along the D- Hd AM (8π2)2
flat direction, |Hu0| = |Hd0|. It is obvious that the B|AM ∼ m3/2, (8)
above condition cannot be satisfied if µ is much
larger than msusy as inferred from that it gives a where m3/2 is the gravitino mass. Hence msusy ≪
supersymmetricmasstotheHiggsbosons. Forthe |B| is obtained in models where anomaly media-
conventionalscenario with tion is sizable to other mediations in size. In such
acase,the gravitinoisquite heavyaswouldbe re-
|µ|∼|B|∼ m2Hd ∼msusy, (5) quiredtomakethegravitinodecaybeforebigbang
q nucleosynthesis(BBN).Notealsothatthehiggsino
EWSB is triggered when renormalization group
islikelythelightestsupersymmetricparticle(LSP)
(RG) flow drives m2 to negative or small values
Hu because EWSB requires |µ|≪msusy.
at low energy, which is possible as it is consider-
AnotherpossiblewaytogetalargeHiggsmixing
ably affected by loop effects associated with the
parameteristoconsidermodelswithsizablegauge
large top Yukawa coupling.
mediation where µ is dynamically generated from
It is remarkable that EWSB is possible also for
the superpotential term
|µ|≪m iftheHiggsmixingparameterB hasa
susy
large value around m2susy/µ. To be in more detail, f(X)HuHd, (9)
the minimization condition
forsomefunctionf. HereX istheSUSYbreaking
2|Bµ|
sin2β = , fieldthatprovidesmassestomessengers. Onemay
m2 +m2 +2|µ|2 ∗
Hu Hd instead consider f(X,X )HuHd in the K¨ahler po-
1 m2 −m2 tan2β tential. The sparticles then obtain masses at loop
m2 = −|µ|2+ Hd Hu , (6)
2 Z tan2β−1 level, while the Higgs mixing parameter is gener-
ated at tree level:
shows that EWSB can be achieved when the hig-
gsinos are relatively light and the Higgs sector pa- (F/M)2
m2 | ∼ ,
rameters have the hierarchy [19], Hd GM (8π2)2
B| ∼ F/M, (10)
m2 GM
susy
|µ|≪m ≪|B|≈ , (7)
susy
|µ|tanβ for hXi= M +θ2F. On the other hand, the van-
ishing cosmological constant puts a lower bound
for moderate and large tanβ, while m2 is nega-
Hu on the gravitino mass
tive or much smaller than m2 in size as in the
susy
conventionalscenario. Heretanβ =h|H0|i/h|H0|i, M
u d m & F/M, (11)
and mZ is the Z-boson mass. 3/2 MPl
3
with M being the reduced Planck mass. The fora=1,2,3andsummingoverthesparticlesand
Pl
gravitinocanbe the LSPifthe messengerscaleM heavy Higgs doublet. Here b denotes the β func-
a
is intermediate or low. tion coefficient in the MSSM, and bφ is the con-
a
To summarize, there naturally arises a hierar- tribution of the particle φ to it. Using the above
chy between the Higgs mixing parameter and the relations, one finds that successful unification is
sparticle masses: maintained for a sparticle spectrum satisfying
|B|.8π2m . (12)
susy 1 1 7 1
|µ| mH 4 M2 3 M2 3 mℓ˜ 4 =1,(17)
inmodelswhereanomalyorgaugemediationgives
sizablecontributionstosparticlemasses. Forlarge m∗ (cid:18)m∗ (cid:19) (cid:18)m∗(cid:19) (cid:18)M3(cid:19) (cid:18)mq˜(cid:19)
B, we need |µ| ≪ msusy to trigger EWSB. In this withm∗ ≈1TeV[20–24]. HereM2andM3arethe
classofmodels,therefore,thelightestordinarysu- wino andgluino mass,respectively, andm is the
H
persymmetric particle wouldbe a nearly pure hig- heavy Higgs doublet mass. The unification condi-
gsino, while the gravitino can be very heavy or tionissensitivetothemassesofthehiggsino,wino
light. and gluino. But it is relatively insensitive to the
Let us now turn to the issue of gauge coupling masses of the heavy Higgs doublet and sfermions.
unification. TheMSSMleadstoquantitativeunifi- In particular, gauge unification becomes indepen-
cationofgaugecouplingsforlowscaleSUSYwhere dent of the sfermion spectrum if the squarks and
the sparticles are around TeV. The unified gauge sleptons have a common mass, which reflects the
coupling and unification scale are approximately fact that they form complete SU(5) multiplets.
given by This implies that unification works even when the
1 sfermionsareveryheavywhile othersparticlesare
≃ 2,
g2 | around m∗ as in the split SUSY [25]. It is also
GUT TeV
worthnotingthattheinclusionoftwo-loopcorrec-
M | ≃ 2×1016GeV. (13)
GUT TeV tions leads to smallshift ofthe scalem∗, and does
Letusconsiderasimplecaseinwhichallthespar- not change the qualitative features.
ticlesandtheheavyHiggsdoublethaveacommon Under the condition Eq. (17), the three gauge
mass. Then, there exists a value of the common couplings converge to a common value
sparticle mass
1 1
m∗ (14) g2 = g2 |
GUT GUT TeV
aattownheicphoitnhtewtihthreine tghaeuMgeScSoMup.lTinhgesvmaleueetoefxmac∗tliys + 1 ln |µ| 1190 M2 1192 mℓ˜ 2
8π2 m |µ| |µ|
estimated to be "(cid:18) H(cid:19) (cid:18) (cid:19) (cid:18) (cid:19) #
125 173
m∗ ≈1TeV, (15) + 1 ln M3 19 mq˜ 76 , (18)
8π2 M m
wherethedependenceontanβ,whicharisesatthe "(cid:18) 2(cid:19) (cid:18) ℓ˜(cid:19) #
two-loop level, is very mild.
at a GUT scale
Toseehowgaugecouplingunificationisaffected
by sparticle masses,we use one-loopRG evolution 2 10
of gauge couplings in the dimensional reduction M = M | mH 57 |µ| 57
GUT GUT TeV
|µ| M
scheme under the assumption, for simplicity, that (cid:18) (cid:19) (cid:18) 2(cid:19)
25 9
the sleptons (squarks) have a universal mass mℓ˜ × M2 57 mℓ˜ 76 . (19)
(mq˜). From the fact that gauge unification works (cid:18)M3(cid:19) (cid:18)mq˜(cid:19)
in low scale SUSY, the unified gauge coupling is
found to be For higgsinos much lighter than other sparticles,
1 1 b M | the GUT scale and the value of unified gauge cou-
a GUT TeV
= + ln
g2 g2 | 8π2 M plingwillgetsmaller. IftheMSSMisembeddedin
GUT GUT TeV (cid:18) GUT (cid:19) aGUT,operatorsmediatedbyheavygaugebosons
bφ m
+ a ln φ , (16) around MGUT would induce proton decay mainly
φ 8π2 (cid:18)m∗(cid:19) via p → π0e+ [26] . The experimental limits on
X
4
proton lifetime are evaded for anomaly, gauge, gravitymediation and mixed me-
diations,
g2 −1 M 2
GUT GUT &0.1, (20) Ma
(cid:18) 0.5 (cid:19) (cid:18)2×1016GeV(cid:19) g2 ∝ 1+baα, (23)
a (cid:12)msusy
(cid:12)
whichiscombinedwiththerelations,Eqs.(18)and at the one-loop le(cid:12)vel, whereas scalars have a quite
(cid:12)
(19), to put an upper bound on the ratio between model-dependent mass pattern. Here α represents
msusy and µ: the relative importance of anomaly-mediated con-
tributions,anditispositiveinmanymixedmedia-
−25
msusy .0.6×104 M3 8 , (21) tionmodels[33–35]. Negativeαisalsopossiblebut
|µ| M in rather involved models [36]. From the gaugino
(cid:18) 2(cid:19)
mass pattern, it follows
forasimplifiedcasewherethewino,sfermionsand
M 1+b αg2
heavy Higgs doublet have a similar mass about 3 = 3 3, (24)
M 1+b αg2
msusy. Theconstraintissatisfiedinmostofthepa- 2 2 2
rameterregionofourinterest. Thegaugecoupling where one would need
at M increases if there are gauge messengers,
GUT |α|≤O(1), (25)
enhancingtheprotondecayrate[27,28]. Asacon-
sequence,the upper boundonm /|µ|presented because pure anomaly mediation suffers from the
susy
aboveisreduced,forinstance,byafactorofabout tachyonicsleptonproblem. Thegaugecouplingra-
0.6 (0.2) for N =1 (3) and M =108 GeV. tiog2/g2isequalto3aroundTeV,anditdecreases
mess mess 3 2
Here N is the number of gauge messengers in to1asenergyscaleincreases. ForothersoftSUSY
mess
5+5¯ ofSU(5),andM istheirmass. Notethat breaking parameters, one obtains
mess
there are alsomodel-dependent dimension-fiveop- |B| κ
erators leading to proton decay mainly via p → m2 = m , (26)
K+ν¯, which are induced by the exchange of col- Hd susy
oredHiggs multiplets [29]. The lifetime is approx- for κ lying in the range
imately proportionalto MG2UT m4susy for sfermions 0<κ.8π2. (27)
tan2β M2+µ2
2
aroundmsusy, and it followsthat highscale SUSY The parameter κ is much larger than order unity
with msusy above 10 TeV and low tanβ is favored ifanomalyand/orgaugemediationprovidesizable
to evade the experimental bound [30]. masses to sparticles while generating B at tree
For gauginos, sfermions and the heavy Higgs level. Finally, from the minimization condition,
doublet around msusy, the unification condition the value of µ appropriate for EWSB reads
Eq. (17) is reduced roughly to m
susy
|µ|≈ , (28)
κtanβ
12 4
msusy ≈ m∗ 7 M3 m∗, (22) and it should not exceed much msusy. As no-
|µ| M
(cid:18) (cid:19) (cid:18) 2(cid:19) ticed above, the value of msusy consistent with
gauge unification becomes higher than TeV for
wherewehavekeptthedependenceontheratiobe-
|µ|≪m ,andisfurtherpushedupifthegluino
tweenthewinoandgluinomassasitcanbeimpor- susy
is heavy relative to the wino.
tant. The above shows that the sparticle masses
We now perform a simple numerical discussion
msusy canbelargerthanm∗,i.e.aboveTeV,ifthe
of the sparticle spectrum required for EWSB and
higgsinos are much lighter than other sparticles.
gauge unification. The EWSB relation Eq. (28) is
The value of m consistent with unification is
susy
combined with the unification condition Eq. (17)
further pushed up if the gluino is heavier than the
to uniquely fix the values of µ and m :
wino [31]. susy
Let us examine if gauge unification works for 28 12
the Higgs sector with the hierarchy of Eq. (7). msusy ≈ 0.1×103 M3/M2 19 κtanβ 19 ,
m∗ 2 300
Combined with gauge unification, the low energy (cid:18) (cid:19) (cid:18) (cid:19)
28 −7
gaugino masses have a distinctive and robust pat- |µ| M3/M2 19 κtanβ 12
≈ 0.4 , (29)
tern [32] in many mediation schemes including m∗ 2 300
(cid:18) (cid:19) (cid:18) (cid:19)
5
FIG. 2: High scale SUSY with light higgsinos for
FIG. 1: RG flow of gauge couplings αi = gi2/4π gauge coupling unification. The heavy Higgs doublet
in the MSSM. Dotted gray lines correspond to the andsparticlesexceptforhiggsinoshavemassesaround
running of SU(3)C, SU(2)L and U(1)Y, respectively, msusy. For msusy ≫|µ|, EWSB requires a large Higgs
for low energy SUSY where the heavy Higgs doublet mixingparameter,|B|tanβ≈m2 /|µ|. Herewehave
susy
and all sparticles are degenerate around TeV. Col- taken 50 ≤ |B|tanβ/msusy ≤ 500 for models where
ored lines show how gauge coupling unification is af- anomaly or gauge mediation is sizable, taking intoac-
fected by sparticle masses in high scale SUSY where count thathigh scale SUSYabovea few tensTeV can
theheavyHiggs doublet and sfermions are degenerate accommodate the observed 125-GeV Higgs boson for
at msusy = 200 TeV. Colored solid lines are obtained tanβ .4. Then, EWSB occurs in the region between
forM2 =msusy,M3 =2msusy andµ=230GeV,while thetwothicklines,andlighthiggsinosleadtosuccess-
dashed ones are for M2 =M3 =µ=msusy. ful gauge coupling unification in theshaded region for
0.5≤M3/M2 ≤5.
for κtanβ & 1, and α of order unity. Here we
have taken into account that low tanβ is favored cordingtoEq.(29)oncetheEWSBandunification
to accommodatethe 125-GeVHiggsbosoninhigh conditions are imposed.
scale SUSY, for instance, tanβ smaller than 4 for Finallywediscussdarkmatterandcollidersigns
m abovea few tens TeV [37], andthat one has inhighscaleSUSYunderconsideration. TheLSP,
susy
g2/g2 = 2 around 100 TeV. We emphasize that whichis stable under R-parityconservation,is the
3 2
highscaleSUSYcanbereconciledwithgaugeuni- higgsino or the gravitino. For |µ| ≪ msusy, the
fication when the higgsinos are much lighter than lightest neutralino and chargino are mostly pure
other sparticles. For instance, EWSB and unifica- higgsino, and are nearly mass degenerate:
tionareachievedfor µ aroundafew hundredGeV
and m = 10–100 TeV. If M /M gets larger, ∆m≡m −m =∆m +∆m , (30)
susy 3 2 χ+1 χ01 tree loop
the required value of µ and m increase by the
susy
same factor. where the tree-level contribution is due to mixing
Fig. 1 shows RG flow of gauge couplings in the with the bino and wino, and is positive unless the
MSSM. High scale SUSY with light higgsinos can bino and wino mass have a different sign
leadtogaugecouplingunification,wherethethree
gaugecoupling unify aspreciselyasinthe conven- 105GeV M2
|∆m |≃30MeV 1+0.3 ,(31)
tional TeV SUSY. In Fig. 2, the shaded region is tree M M
(cid:18) 2 (cid:19)(cid:12) 1(cid:12)
compatible with gauge unification. Here we have (cid:12) (cid:12)
(cid:12) (cid:12)
used the fact that the SUSY particle mass msusy while the radiative mass differen(cid:12)ce comes m(cid:12)ainly
and the higgsino mass parameter µ are fixed ac- from gauge boson loops [38], and is approximated
6
by this cosmological difficulty is to consider R-parity
violation. One possibility is to add R-parity vio-
0.15
|µ| latingtermsthatviolatetheleptonnumberaswell
∆m ≈260MeV , (32)
loop
100GeV but preserve the baryon number to forbid danger-
(cid:18) (cid:19)
ous proton decay operators [43, 44]. For instance,
forµ belowaboutTeV.Hence,themassdifference ∆W = µ L H with µi tanβ larger than about
isexpectedto be positiveandlargerthanthe pion 10−12 canialilowu the NLµSP to decay very shortly
mass, for which the lightest chargino dominantly
into ordinary particles while making the gravitino
decays to the lightest neutralino and the charged
live long enough to make up the dark matter of
pabioonu.t 0T.h3e×d1e0c−ay10steimce×o(f∆tmhe/3l0ig0hMteesVt)c−h3arfogrin∆omis the universe. Note thatone needs µµi tanβ .10−5
to avoid washout of baryon asymmetry before the
not close to the pion mass. It would thus be diffi-
cult to probe at the LHC, but e+e− → γχ0χ0 or electroweak phase transition [44, 45].
γχ+χ− mediated by virtual Z boson may p1rov2ide Let us move on to the case of m3/2 > |µ| with
1 1 R-parity conservation, for which the LSP is the
a visible signal in future linear colliders.
neutral higgsino. The LSP thermalrelic density is
WefirstexaminethegravitinoLSPcase,m <
3/2 significant only for µ above 1 TeV. For smaller µ,
|µ|. In this case, the gravitino production from
therightdarkmatterdensitycanbegeneratedvia
thermal scatterings can generate the right dark
non-thermal LSP production. Here we consider a
matter density. If the freeze-out temperature of
scenariowheregravitinosareabundantlyproduced
the gravitino [39]
fromthedecayofaheavyscalarfieldsuchasinfla-
m 2 100TeV 2 ton, Polonyi field, or string moduli. The gravitino
T ≈1011GeV 3/2 (33) decay width reads
f
10GeV M
(cid:16) (cid:17) (cid:18) 3 (cid:19) 193 m3
itserhiignhfleartitohna,nthtehegrraevhietaintiongretleicmapbeurantduarneceTrieshdaef-- Γ3/2 = 384π M3P2/2l, (36)
termined by
for m ≫m , anditcorrespondsto the decay
3/2 susy
temperature
T
Ω h2 ≃ 0.3 reh
3/2 (cid:18)109GeV(cid:19) 10 41 m3/2 32
2 T ≃0.25GeV , (37)
× 1m0GeV 10M0T3eV , (34) 3/2 (cid:18)g∗(T3/2)(cid:19) (cid:16)PeV(cid:17)
(cid:18) 3/2 (cid:19)(cid:18) (cid:19)
where g∗ counts the effective number of relativis-
where the gravitino should be heavier than about tic degrees of freedom. Thus, LSPs are produced
100 keV to be a cold dark matter [40]. The re- belowtheLSPfreeze-outtemperature∼|µ|/20. If
heating temperature producing the observed dark the gravitino abundance is large enough to make
matter density can be higher than about 109 GeV annihilation among produced LSPs effective, the
as required for standard thermal leptogenesis [41]. LSP relic density becomes independent of the ini-
One should however note that the next to light- tial gravitino abundance [19, 42]:
est supersymmetric particle (NLSP), which is the
1
neutral higgsino, decays into the gravitino and or- Ω h2 ≃ 0.06 g∗(T3/2) 4
dinary particles with a width χ01 0.84cZ+cW (cid:18) 10 (cid:19)
1 |µ|5 |µ| 3 PeV 32
Γ ∼ , (35) × , (38)
χ01 16πm23/2MP2l (cid:18)100GeV(cid:19) (cid:18)m3/2(cid:19)
and so it occurs during or after the BBN epoch in where c ≡(1−m2/|µ|2)3/2/(2−m2/|µ|2)2, and
Z Z Z
the parameter regionof our interestwhile produc- c issimilarlydefinedbytakingm →m . Note
W Z W
ing high energetic electromagnetic and hadronic that the gravitino should be heavier than about
showers. Such late-time decay of the NLSP can 40 TeV to decay before nucleosynthesis, and its
significantlyaltertheabundancesoflightelements, massisboundedfromabove,m .8π2m ,be-
3/2 susy
spoilingthesuccessofBBN.Asimplewaytoavoid cause anomaly mediation is a model-independent
7
itino decays. On the other hand, in the case of
a gravitino LSP, gravitino production by thermal
scatterings can yield the right relic density.
We have studied gauge coupling unification and
dark matter in high scale SUSY where sparticles
have masses much higher than the weak scale as
would be indicated by tensions between low en-
ergySUSYandtheLHCresults. HighscaleSUSY
admits gauge coupling unification as exactly as in
low energySUSY if the higgsinosare much lighter
than those obtaining SUSY breaking masses. In
thisscenario,theLSPistheneutralhiggsinoorthe
gravitino,whichcanmakeupallthedarkmatterof
the universe if produced non-thermally in the for-
mer case and thermally from sparticle scatterings
inthelattercase. AlargeHiggsmixingparameter
requiredforEWSBisnaturallyobtainedinmodels
where sparticle masses are generated at loop level
FIG. 3: Dark matter in high scale SUSY with light
while the Higgs mixing parameter arises at tree
higgsinos. For the higgsino LSP case with 50 ≤
msusy/|µ| ≤ 500, non-thermal LSP production from level, as is the case in anomaly and gauge media-
heavy gravitino decays yields the right dark matter tion. Then, gauge coupling unification and dark
density along the thick green line while satisfying the matter would indicate high scale SUSY around
condition m3/2 < 8π2msusy. The correct density can 10 TeV – a PeV and light higgsinos below a few
be obtained also from the higgsino thermal relic for
TeV.
µ about 1 TeV, which is along the thin vertical green
line, where the gravitino mass is bounded by m <
3/2
8π2msusy andtheBBNconstraint. Ontheotherhand,
in the case of a gravitino LSP, gravitinos produced by
Acknowledgment
thermalscatteringscanexplaintheobserveddarkmat-
terdensityinthelightredandblueshadedregionfora
reheatingtemperatureindicatedbythenumbers. Here The authorthanks toBumseokKyaeandFumi-
we have taken 102 ≤ M3/|µ| ≤ 103 and the reheat- nobu Takahashi for useful discussions. This work
ing temperature T = 1010 GeV (107 GeV) for the
reh is supportedby the NationalResearchFoundation
region between theupper(lower) dot-dashedand dot-
of Korea (NRF) grant funded by the Korea gov-
ted lines. The non-shaded region between the upper
(lower)dot-dashedanddottedlinesleadstom >|µ| ernment (MSIP) (NRF-2015R1D1A3A01019746).
3/2
(T >T ), whereT isthefreeze-out temperatureof
reh f f
thegravitino.
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