Generation of WIMP Miracle-like Densities of Baryons and Dark Matter

0.22 MB·English

by  John McDonald

Generation of WIMP Miracle-like Densities of Baryons
and Dark Matter
2
1
JohnMcDonald
0
2 ConsortiumforFundamentalPhysics,CosmologyandAstroparticlePhysicsGroup,Departmentof
n Physics,UniversityofLancaster,LancasterLA14YB,UK
a
E-mail:[email protected]
J

5
1 Abstract.
Theobserveddensityofdarkmatterisofthemagnitudeexpectedforathermalrelicweakly-interacting

] massiveparticle(WIMP).Inaddition,theobservedbaryondensityiswithinanorderofmagnitudeofthe
h
darkmatterdensity. Thissuggeststhatthebaryondensityisphysicallyrelatedtoatypicalthermalrelic
p
WIMPdarkmatterdensity. WepresentamodelwhichsimultaneouslygeneratesthermalrelicWIMP-like
-
p densitiesforbothbaryonsanddarkmatterbymodifyingalargeinitialbaryonasymmetry. Productionof
e unstablescalarscarryingbaryonnumberattheLHCwouldbeaclearsignatureofthemodel.
h
(TalkpresentedatDSU2011,KITPC,Beijing,China.)
[

1
v
4 The ratio of the mass density of baryons to that of dark matter (the BDM ratio) is observed to be
2 W /W ≈1/5. However, in most models the physics of baryogenesis and of dark matter production
B DM
1
isphysically unrelated. Whythen isthedensity inbaryons within anorder ofmagnitude ofthat indark
3
matter? Either:
.
1
0 •Aremarkable coincidence
2
•Ananthropic selection mechanism
1
: •Thephysicsoftheobserved baryonasymmetryanddarkmatterdensities isinsomewayrelated.
v
i ThereforetheBDMratiomaybeapowerfulcluetothecorrectparticlephysicstheory.
X
Uptonowtherehavebeenbroadlytwoclassesofmodel:
r
a
1). Direct mechanism: The dark matter particle and baryon number densities are directly related by a
conservedcharge,
⇒Q =Q +Q ⇒n ∼n ⇒M ∼m n /n ∼1−10GeV
tot B X cdm B DM n B cdm
There are many models in this catagory, which typically predict asymmetric dark matter [1, 2, 3,
4, 5, 6, 7, 8]. Models also exist which break the simple mass relation M ∼ 1−10GeV, see
DM
[9,10,11,12,13,14]1.
2). Indirectmechanism: Thedarkmatterandbaryondensitiesarerelatedbysimilarbutseperatephysical
mechanisms for their origin ⇒ Less rigid relation between n and n ; can have n ≫n ⇒ larger
B cdm B cdm
M . Anexample based on d =4 Affleck-Dine leptogenesis is given in[16], where dark matter is due
DM
toacondensate ofright-handed sneutrinos 2
1 In[15]amodelisdiscussedwherethecorrectdarkmatterdensityisgeneratedviaitsinteractionwiththebaryonasymmetry.
2 Theauthorisnotawareofotherexamplesinthisclassandwouldbeinterestedtoknowifothermodelsexist.
However, there are in fact two seperate coincidences. 1). Whyare the baryon and dark matter densities
similar toeach other? 2). Whyare they both similar to the"WIMPMiracle" density? (Most models do
notaddress 2.)
The "WIMP Miracle" refers to the natural similarity of the observed dark matter density and the
thermal relic density of particles with weak-scale masses and interactions. This is widely interpreted
as a strong indication that dark matter is due to thermal relic WIMPs. For dark matter with constant
<s v >, where s is the non-relativistic annihilation cross-section, the observed dark matter density
rel
requires
<s v >≈10−9 GeV−2
rel
M
TheDMannihilation cross-section maybeexpresed intermsoftheannihilation matrixelement as
|M |2
<s v >= . (1)
rel 32p m2
DM
Thematrixelementisdimensionless andtypically hastheform|M |2=g4 . whereg isaneffective
eff eff
couplingconstant. Therefore
g 4 100GeV 2
<s v >=1.6×10−9 eff GeV−2 . (2)
rel
0.2 m
DM
(cid:18) (cid:19)
(cid:16) (cid:17)
Therefore if M is in the range 100GeV−1TeV and if g is not too much smaller than the weak
DM eff
interaction coupling g≈0.65 (which is natural as g can have additional factors from mixing angles,
eff
massratiosetc),thenwegettherightamountofthermalrelicdarkmatter.
IftheWIMPmiracledoesexplaindarkmatter,andifwediscountcoincidenceandantropicselection,
then we need to explain why the baryon asymmetry is also similar to the WIMP miracle density. The
similaritytothedarkmatterdensitythenfollowsfromthisi.e. theobservedbaryontodarkmatterratiois
actuallyduetoamorefundamentalrelationbetweeneachofthedensitiesandtheWIMPmiracledensity.
In [17] and [18] we presented one approach to making this connection, based on a mechanism we
call baryomorphosis. [Recently an alternative approach to achieving a WIMP-like baryon asymmetry,
WIMPybaryogenesis, hasbeenproposed in[19].]
This idea of baryomorphosis that the observed baryon density is determined by a process similar to
thermalrelicWIMPfreeze-out. Themodeldoesnotexplainthebaryonasymmetry, butmodifiesalarge
initial baryon asymmetry into a final thermal WIMP-like baryon asymmetry; hence "baryomorphosis"
ratherthan"baryogenesis".
Theingredients ofthebaryomorphosis mechanism are:
• An initial baryon asymmetry, for example in a heavy particle S which is out of thermal equilibrium,
whichdecays atalowtemperature T <O(100)GeV.
d ∼
• Pairs of new scalar particles, f and fˆ , called "annihilons", to which S decays. The annihilons have
B B
opposite Standard Model (SM) charges but, crucially, do not have opposite baryon numbers. f and
B
fˆ are distinct particles which can have different masses, although for simplicity wewill consider their
B
massestobeequalinthefollowing.
•AB-violatinginteractionwhichisbroadlyofweakinteractionstrength,viawhichf andfˆ annihilate,
B B
leavingathermalWIMP-likebaryonnumberdensity.
•Amechanism totransfer thebaryonasymmetryfromannihilons toconventional quarks.
Thisisillustrated schematically inFigure1.
In [17] a simple model implementing the baryomorphosis mechanism was presented. In this model
theannihilons annihilate toacomplexbosonHˆ viaarenormalizable B-violating interaction oftheform
L =l f fˆ Hˆ†Hˆ + h.c.. (3)
f BfˆBann B B B
1 . B a r y o n a s y m m e tr y in S d e c a y s to a n n ih ilo n s a t T
d
S
B - in je c t io n in t o
w e a k l y - in t e r a c t i n g s c a la r s
T < B - v i o l a t i n g
a t l o w T < O ( 1 0 0 ) G e V d
d
f f a n n i h i l a t i o n
B f B f r e e z e - o u t
f t e m p , T ?
B
B
B
2 . A An nn nihihiliolon ns s a an nn nihiha itlae t ev i av iaH iBg g-vsio plao tritna gl iinn ttee rraa cc ttiioo nn
^
f H
B
= > Q u a s i - t h e r m a l r e l i c
B - v io l a t in g a n n i h il a t i o n s
W I M P b a r y o n d e n s i t y
^
f H
B
= > R e lic b a r y o n a s y m m e tr y d e te r m in e d b y B - v io la tin g ~ w e a k
in te r a c tio n s tr e n g th a n n ih ila tio n s
3 . R e m a in in g a n n ih ilo n B a s y m m e tr y d e c a y s to a c o n v e n tio n a l
B a s y m m e tr y a t T
D
B t r a n s f e r t o q u a r k s f y y y y 1 M e V < T < T
B u c e c L L D d
Figure1.
NotethattheHˆ cannotbetheHiggsboson,sincethef ,fˆ willmixoncetheHiggsVEVisintroduced,
B B
resulting in a B-violating mass insertion which will wash out the annihilon asymmetry via scattering
from thermal background quarks. Therefore the final state in the B-violating annihilation must have no
VEV.
However, the original model in [17] has some features which do not have a symmetry explanation
andmusttherefore simplybeimposed:
•ThereisnosymmetrytopreventB-violating massmixingtermslikef fˆ (⇒Bwashout).
B B
• There is no suppression of renormalizable couplings of f to SM fermions (⇒ f decay too rapidly,
B B
beforeannihilating).
Inaddition, although itisnotreallyproblem,noWIMPdarkmattercandidate isspecified.
Inordertoaddresstheseissues,in[18]amodelwaspresentedwhichusesasimplediscretesymmetry
to ensure no f fˆ mixing terms leading to baryon washout. Since additional discrete symmetries are
B B
necessarytoevadeBwashout,andsinceadditionalsymmetriesarealsonecessarytostabilizedarkmatter,
itisnatural toidentify asdarkmatter particles theadditional fieldsnecessary asfinalstates inthef fˆ
B B
annihilation process. The model can be naturally combined with gauge singlet (or inert doublet [20])
darkmattertoprovideaunifiedmodelofbaryomorphosis andscalarWIMPdarkmatter.
Weintroduce apairofrealsingletscalarsssˆplusaZ discrete symmetryoftheannihilons, Z ,
2 A
Z : f →f ; fˆ →−fˆ ; s→s; sˆ→−sˆ, (4)
A B B B B
withallSMfieldsinvariantunderZ . ThiseliminatesthedangerousB-violatingmassmixingtermsf fˆ
A B B
andf fˆ H†H butallowstheB-violatingannihilation process
B B
L =l f fˆ ssˆ + h.c.. (5)
f BfˆBann B B B
Notethatf andfˆ mustcarrygaugecharges topreventthedangerous termsf f andfˆ fˆ ,whichare
B B B B B B
allowedunderZ .
A
Weneedasceonddiscretesymmetrytostabilize thedarkmatter,Z ,
S
Z :s→−s; sˆ→−sˆ. (6)
S
TheZ ×Z symmetrythenallowsthecoupling totheSM:
A S
l l
sssH†H+ sˆsˆsˆH†H . (7)
2 2
Thisallowsthesandsˆtoannihilate downtoathermalWIMP-likedarkmatterdensity.
The formation of the final baryon asymmetry and dark matter density in this model is shown
schematically in Figure 2. As before, the initial annihilon asymmetry is injected at a low temperature
T ∼0.1−100GeV. Thesandsˆsubsequently annihilatedowntothermalWIMP-likedensityifT <T,
d d s
ortoastandardthermalWIMPdensityifT >T,whereT ≈m /25isthefreeze-outtemperatureofthe
d s s s
sandsˆdarkmatter.
Theannihilation cross-section forf fˆ →ssˆis
B B
1/2
l 2 m2
<s v>f = B 1− s . (8)
B 32p m2 m2
f f !
B B
Thefreeze-out numberdensity atT isthen
d
H(T )
d
nf B(Td)≈ <s v>f . (9)
B
(The fˆB number density is the same when mf B =mfˆB.) If f B later decays to baryon number B(f B) and
fˆ toB(fˆ ),thebaryonasymmetrytodarkmatterratioatpresent, r ≡W /W ,isgivenby
B B BDM B DM
r =3(B(f )+B(fˆ )) mn g(Tg ) 4p 3 1/2Tg3 1 1 . (10)
BDM B B W DM g(Td)1/2(cid:18)45MP2l(cid:19) r c Td hs vif B
Hereg(T)istheeffectivenumberofrelativisticdegreesoffreedom,m isthenucleonmass,r thecritical
n c
density, Tg is the present photon temperature and MPl =1.22×1019 GeV. Theprefactor 3 accounts for
thethreecoloursoff . RequiringthatW =0.23thendeterminestheannihilon mass
B DM
1/4
T 1/2 m2
mf B =2.81TeV×g(Td)1/4rB1/D2M(B(f B)+B(fˆB))−1/2 1GdeV l B 1−m2S . (11)
(cid:18) (cid:19) f B!
S c h e m a t i c o f a n n i h i l a t i o n p r o c e s s
T ~ 0 . 5 - f e w x 1 0 0 G e V
d
= > R e l i c d e n s i t y
= > R e l i c d e n s i t y
Figure2.
Inthiswehaveassumedthatf andfˆ arenon-relativistic whentheB-violating annihilation occurs.
B B
This is generally true for gauge-charged f and fˆ , as discussed in [18]. It is also true in s and sˆ
B B
annihilation providedT >0.4GeV[18].
d ∼
InFigure 3weshow the annihilon mass asa function ofthe Binjection temperature T for different
d
values of the baryon-to-dark matter ratio r . We have set l = l =0.1, which are dimensionally
BDM B s
natural values in particle physics models. Since the mystery of the baryon-to-dark matter ratio may be
consideredwhytheyarewithinanorderofmagnitudeofeachother,wehaveshownr intherange0.1
BDM
to10. Weseethatawiderangeofannihilon massesinthe100GeVto10TeVrangeiscompatible with
r in the range 0.1 to 10 when T is in the range 0.1 GeV to 100 GeV. There is also an upper bound
BDM d
on Td from the requirement that Td < Tf B, where Tf B is the freeze-out temperature of the B-violating
annihilation process, Tf ≈mf /20. Tf equals a few hundred GeV for the range of mf considered in
B B B B
Figure3.
Therefore we see that for a wide range of T , O(0.1)GeV to O(100)GeV, the baryon density is
d
naturally within an order of magnitude of the dark matter density. (Note that a low T is essential for a
d
baryonasymmetrytoexistatall.)
In Figure 3 we have also shown lines for mf equal to 2 TeV and 3 TeV, corresponding to bounds
B
that may be achieveable for coloured scalars at the LHC. The observed r =0.2 favours annihilon
BDM
masseslessthan∼3TeVovertherangeofT from0.1to100GeV.Therefore, shouldtheannihilons be
d
coloured, thereisagoodprospectofproducing themattheLHC.
Inthecasewheresandsˆaredegenerateinmass,bothscalarsarestableandcontributetodarkmatter.
Figure3.
A key requirement is that ms <mf B, so that the f B fˆB annihilation process is kinematically allowed. If
T <T, then the s and sˆdark matter density is non-thermal, coming from the s and sˆproduced as final
d s
state particles in f fˆ annihilation. This gives an enhancement of the density by T/T relative to the
B B s d
thermalrelicsdensity,
W = 2ms g(Tg ) 4p 3 1/2Tg3 1 . (12)
DM r g(T )1/2 45M2 T hs vi
c d (cid:18) Pl(cid:19) d s
IfT >T thenthedarkmatterispurelythermalrelicinnature. Inthiscasewecanapproximatelyreplace
d s
T byT inEq.(12). Theresulting m isshowninFigure4forHiggsmassm =150GeV,l =0.1and
d s s h S
W DM =0.23. In Figure 5weshow ms together with mf B. Forall Td the smass ismuch less than the f B
mass, as required for consistency of the model. In addition, for most T the s freeze-out temperature is
d
less than T , so that s dark matter is in fact thermal relic in nature. Non-thermal s dark matter is found
d
onlyatT <10GeV.
d ∼
Weconclude thataconsistent baryomorphosis modelcanbeconstructed usingonlyasimpleZ ×Z
2 2
symmetry.
So far we have produced a thermal WIMP-like baryon asymmetry in f and fˆ particles. This
B B
must still be transferred to conventional quarks. We will focus on the example of coloured annihilons,
whichhave thebest prospect ofbeing produced atthe LHC.Weassume theannihilons transform under
SU(3) ×SU(2) asf (3,1)andfˆ (3,1). InordertoproduceathermalWIMP-likebaryonasymmetry,
c L B B
thedecay of f , fˆ mustoccur after the baryon asymmetry has frozen out, at T <T . This means that
B B D d
Figure4.
f andfˆ mustbeverylong-lived particles:
B B
2
100GeV
1.5s>t >8×10−11 s, (13)
∼ ∼ T
d
(cid:18) (cid:19)
where the upper bound is from nucleosynthesis. This provides a key experimental signature of
annihilons. The long annihilon life-time requires either an extremely small renormalizable Yukawa
couplinglf yy toSMfermionsy with
B
T 1TeV 1/2
l <1.2×10−10 d , (14)
∼ 1GeV mf
(cid:18) (cid:19)(cid:18) B (cid:19)
or a non-renormalizable coupling suppressed by a sufficiently large mass scale. The former possibility
seems overtly unnatural, so we will consider the latter. However, in this case we need to explain why
therearenorenormalizable couplings leadingtorapidf decay.
B
The simplest way to achieve this is if f has a large hypercharge e.g. Y(f )=5/3. In this case f
B B B
and fˆ can decay only via mass-suppressed non-renormalizable interactions. For example, for the case
B
f (3,1,5/3)andfˆ (3,1,−5/3),wecanform
B B
1
f dcd LcL (15)
M3 B R R L L
Figure5.
and
1
fˆ d ecQ Q . (16)
M3 B R R L L
The mass M should then be in the range 106−108 GeV to account for the low decay temperature T
D
[17].
Note that for fˆ to decay, we must assume that Z is slightly broken by the non-renormalizable
B A
operators. However,sincetheseoperatorsaresuppressedbyalargemassscale,thissmallbreakingofZ
A
will not introduce any dangerous mass mixing between f and fˆ . If baryon number is conserved,
B B
then from Eq.(15) and Eq.(16) the baryon numbers3 of f and fˆ would be B(f ) = −2/3 and
B B B
B(fˆ )=−1/3.
B
However, if we do not assume baryon number conservation, then there are other possible operators,
forexample
1
f (e Q e L )† , (17)
M3 B R L R L
which allows f to decay to a final state with B=1/3. In this case the effective baryon number of f
B B
andfˆ willbedetermined bytheirdominantdecaymodes.
B
Observationofsuchunstable particlesmightbeachievedviathedecayofparticleswhicharestoppedin
detectors(seee.g. [21]).
Insummary,thekeyexperimental featureofthebaryomorphosis modelaretheannihilons f ,fˆ :
B B
3 f BandfˆBalsocarryleptonnumber,L(f B)=−2andL(fˆB)=1.
• Their mass must be 100 GeV - few TeV to produce weak-strength annihilations ⇒ good prospect of
producing atcolliders.
•TheyhavealonglifetimeanddecaytonetBnumber.
•TheymayhaveB-violating decays.
•Theirlonglifetimesuggests largehypercharge |Y|≥5/3.
•Thebestcaseisthatofcolouredannihilons: CanpairproduceatLHCupto2-3TeV.(Similartosquark
production.)
Conclusions
• It is possible to modify a large initial baryon asymmetry to be similar to a thermal relic WIMP mass
density⇒Baryomorphosis.
• Requires additional particles and discrete symmetries ⇒ Can naturally combine with a WIMP dark
matter candidate (gauge singlet scalars, inert doublets) ⇒ Simultaneous generation of thermal WIMP-
likebaryonanddarkmatterdensities.
•Thereforecanunderstandbothofthepuzzlesofthebaryondensity: whyitissimilartothedarkmatter
densityandwhyitissimilartothe"WIMPmiracle"density.
•NeedalowB-injection temperature, T <few×100GeV.
d
• Generically requires pairs of new particles ("annihilons") with gauge interactions and with mass
∼100GeV-fewTeV⇒Couldbeproduced attheLHC.
•Twotypesofannihilon arenecessary, withopposite gaugecharge butdifferentB.
• Annihilons have long lifetime and decay to baryon number, with possibly large hypercharge and B-
violating decaymodes.
To sum up, the WIMP miracle can account for DM without requiring either coincidence or anthropic
selectiontoexplainW /W =1/5.
B DM
Acknowledgement
This work is supported by the Lancaster-Manchester-Sheffield Consortium for Fundamental Physics
underSTFCgrantST/J000418/1.
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