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JMR, S.West, D. Cumberbatch, D.Hooper arXiv:0801.3440 [hep-ph] and more to come...
Heavy Dark Matter Through the Higgs PortalJohn March-RussellOxford University
Planck'08, Barcelona
Adventures with WIMPonium
or better...
Basic Idea
Want to consider the possibility that WIMP dark matter can form unstable bound states similar to positronium or quarkonium
We will find simple models where this is occurs
Moreover, WIMPonium can dramatically effect relic density calculations and, especially, indirect detection, potentially leading to a rather precise window into multi-TeV-scale physics
Basic constraint
Consider a pair of Majorana fermion WIMPs interacting via a massive scalar leading to a NR potential
Simple semiclassical considerations show that the approximate number of bound state energy levels is
(s)(n)
V = ! !!2
8"rexp(!mnr)
Ms
8
!(!V )rdr =
Ms
mn
!!2
64"
Thus to have interesting physics we require
Assuming this shows that WIMPs must be multi-TeV, and moderately strong coupling needed
Later, our simple model will take and
Ms
mn!!2 ! 64"
mn ! mw
!! ! 1 to"
4"Ms ! 1 TeV to 30 TeV
Major effects of WIMPonium
A. If thermal relic density annihilation cross section are modified by threshold resonances. Closely related to Sommerfeld effect
B. Annihilation of WIMPs in indirect searches can be 1) enhanced by factors of and 2) have a rich spectrum of discrete gamma-lines
mn !Ms
103 to 105
At freeze-out, small relative velocity implies KE < V leading to strong distortions of incoming WIMP plane waves. Equivalent to the DBW approximation in nuclear physics
Sommerfeld enhancement corresponds to the summation of ladder diagrams where rungs are enhanced by
A. The Sommerfeld EnhancementSommerfeld, Hisano et al; Strumia et al...
1/!
!
!
!!vis
!vis
"#! #
"
"
H
H
#
1
Calculation can be re-formulated as non-relativistic two-body QM problem with a potential
Most significant for s-wave - ang mom'm barrier suppresses effect for l>0. Thus can write
! = R!!=0tree R = |!(0)/!(!)|2
! 1Ms
d2!
dr2+ V ! = K!
V = ! !!2
8"re"mnr, K = Ms#
2
!!(!)/!(!) = iMs"
Can be an enhancement or suppression if vector states are exchanged on rungs
For Yukawa potential, R cannot be found analytically
By scaling can show that
Note
R = R(!/",!/#) where ! ! $!2
8%, and # ! mn
Ms
Analytic form for R in Coulomb limit
Simple form due to pile-up of bound states near zero energy in Coulomb potential
In small limit this reduces to
R =y
1! e!ywith y =
!"2
8v=
!"2
4vr
vr
R ! !!2
4vr
Coulomb limit of Sommerfeld Enhancement
! ! mn/Ms " 0
!1 0 1 2 3 4 5 6
0.0
0.5
1.0
1.5
2.0
Log!""##
Log!""$#
Contours in R
Away from Coulomb limit R has much richer structure
0
2
4
6
0.0
0.5
1.0
1.5
0
500
1000
3D Version
R
Log[!/"]
Log[!/"]
500
1000
0
0
0.5
1.51.0
2
4
6
Return to importance of resonance region when we discuss indirect signals
Since relic freeze-out occurs at we are in Coulomb region for FO calculations
To focus one's thoughts useful to explore a very simple model where WIMPonium occurs....
! ! 1/5
Basic idea: consider (heavy) DM that interacts with SM purely via Higgs interactions
The "Higgs Portal" to a new sector Schabinger, Wells; Patt Wilczek...
DM could be SM-neutral states from a strongly interacting hidden sector
For example take simple variant of MNMSSM
WIMPonium in SUSY Higgs-Portal Models
WMSSM,µ=0 + !NHuHd +!!
2NS2 +
Ms
2S2 + ...
this has an interesting UV completion...Fat Higgs model...
Pilaftsis,..., Dedes,..., Tamvakis
Harnik,...
SUSY is our most successful BSM theory. But two aspects of MSSM are not so well motivated
1) -conservation - doesn't really solve the problems for which it was designed
2) Minimality of higgs sector - problems, higgs mass bounds....
Also might expect hidden or sequestered sectors to exist, and Higgs is unique window
Motivations for this model...
Rp
µ/Bµ
Only scalar n states are ''rungs on the ladder"
For simplicity take so and can take EW symmetry to be unbroken
Set soft A-terms to zero
As soft masses negligible compared to
so s freezes out at similar T to and must include scalar s annihilation rates in relic density calculation
(Ms !Ms)/Ms " m2susy/M
2s # 1
Ms
s
Relic Density Calculation
Tfo !Ms/25 > TEWSBMs > 3TeV
s
s
hu
hd
ans
s
!n
an
s
s
s
!n
!(ss ! XX !) =[("!")2 + ("!)4]
64#vrm2s
y
1 " e"y, y =
"!2
4vr
4
Fermion-fermion s annihilations and result
s
s
hu,hd
hd,hu
n
s
s
!n
n
s
s
s
n
an
s
s
s
!n
!(ss ! XX !) =[("!")2 + ("!)4]
32#vrm2s
y
1 " e"y, y =
"!2
4vr
3
Text
Scalar-Fermion s annihilations
s!
s
hu
hd
!n
s
s
h!u
h!d
s!
s!
hu
hd
s
s!
!n
!n
s
s!
s
n!
n
s
s
n
n
n
s
s
!n
!(ss ! XX ") =[3(""")2 + 7("")4]
64#vrm2s
y
1 " e#y, y =
""2
4vr
2
Text
Scalar-scalar s annihilations
Re-label and define
Relic Density Numericss, s as s1, s2
ri !gi(1 + !i)3/2 exp["x!i]
ge!, !i = (mi "m1)/m1
xf = ln!0.038ge!MplMs < !e!vr >
!g!xf
",
ge! =!
i
gi(1 + !i)3/2 exp[!x!i], x = Ms/T
!e! =!
i,j
!ijrirj
Griest, Seckel; Gondolo, Gelmini,.....
!h2 =1.07! 109xf"g!Mpl(GeV )J
, J =! !
xf
x"2ae!dx
1.5 2.0 2.5 3.0!'
0.5
1.0
1.5
2.0
2.5
3.0
!
ms"# 23 TeV
ms"# 19 TeV
ms"# 15 TeV
ms"# 11 TeV
ms"# 7 TeV
ms"# 3 TeV
6
5 10 15 20 25 30 35m
s! !TeV"
0.05
0.10
0.15
"h2
Without Sommerfeld
With Sommerfeld
5
Sommerfeld (effectively zero-E resonances) leads to a factor 5 increase in DM mass. Outside discovery reach of LHC
Direct detection: No restrictive limits but sizeable fraction of parameter space covered by next generation detectors
is Higgs mixing matrix
Comments
L =!
U=u,c,t
CU ss UU +!
D=d,s,b
CD ss DD
CU =!
i
!UV1iV2i!!
2m2hi
, CD =!
i
!DV1iV3i!!
2m2hi
Vij
For cross section below current constraints from experiments such as XENON and CDMS
!sN ! 2" 10!7 pb!
Vij
0.5
"4 !""
3
"2 !120GeV
mh1
"4
Ms ! 3 TeV
Indirect most interesting by far....
1) For indirect detection interested in so far in resonance region where can get huge enhancements in total annihilation rate which quickly increase as
Could favour objects with low velocity dispersion e.g. dwarf satellite galaxies of the Milky Way, even though lose density compared to galactic center
! ! 10!3 to 10!5
! ! 0
0
2
4
6
0.0
0.5
1.0
1.5
0
500
1000
3D Version
R
Log[!/"]
Log[!/"]
500
1000
0
0
0.5
1.51.0
2
4
6
2) Structure of WIMPonium bound states can show up in direct detection as rich discrete spectrum of gamma-lines
s
s
fan
!
!
s
s
fan
!
Z
1
E
1
ConclusionsWIMPonium states arising from exchange of weak-scale quanta can occur for
Sommerfeld enhances DM freeze-out by factor 5
Simple models give rise to this phenomenology
Resonant effects can lead to dramatic increases in indirect flux by , possibly changing search strategy
WIMPonioum bound state spectrum can give many discrete gamma lines -- possible that "DM spectroscopy" can probe super-TeV interactions
103 to 105
Ms ! 3 TeV
Fat Higgs Appendix
! N=1 susy SU(2) gauge theory with six doublets
SU(2)L ! SU(2)H
SU(2)R ! SU(2)g ! U(1)R
U(1)Y SU(2)R
SU(2)H !H
Mij = TiTj (i, j = 1...6)
! Full Symmetry gauged:
global:
subgroup of also gauged
! becomes strongly coupled at
! Six doublets charged under SU(2)H form composite
meson objects with
Field SU(2)LSU(2)HSU(2)RSU(2)gU(1)R Z2
T1 2 2 1 1 0 +T2 2 2 1 1 0 -T3 1 2 2 1 1 -T4 1 2 2 1 1 +T5 1 2 1 2 1 +T6 1 2 1 2 1 +P11 2 1 1 2 1 +P12 2 1 1 2 1 +P21 2 1 1 2 1 -P22 2 1 1 2 1 -Q11 1 1 2 2 1 -Q12 1 1 2 2 1 -Q21 1 1 2 2 1 +Q22 1 1 2 2 1 +Sa 1 1 1 1 2 -Sb 1 1 1 1 2 -
Tree level superpotential WFHtot = W1 + W2
W1 = y1SaT1T2 + y2SbT3T4 + y3SaT3T4 + y4SbT1T2W2 !mT5T6
W2 = y5
!T1 T2
"P
#T5
T6
$+ y6
!T3 T4
"Q
#T5
T6
$
SU(2)H
Wdyn = !!PfM ! v2
0M56
"+ m1SaM12 + m2SbM34 + m3SaM34 + m4SbM12
After becomes strong
+m5 (M15P11 + M16P12 + M25P21 + M26P22)+m6 (M35Q11 + M36Q12 + M45Q21 + M36Q22)
where, using NDA,
v20 ! m!H
(4!)2
mi ! yi!H4!
!(!H) ! 4"
(m5, m6)! (m1, m2, m3, m4)
W !dyn = !M56
!M14M23 !M24M13 ! v2
0 + M12M34
"
+m1SaM12 + m2SbM34 + m3SaM34 + m4SbM12
m1 ! m2 ! m3 ! m4 ! m!
Sa, Sb, M12 and M34
S1
W = !N!HuHd ! v2
0
"+ !!
2 NS21 + ms1
2 S21
!H+
u
H0u
"=
!M13
M23
",
!H0
d
H!d
"=
!M14
M24
", N = M56
ms1 !
More Fat higgs...
Make assumption:
Integrate out heavy states
!
With
components mix,
! m!lightest eigenvalue
Integrate all but lightest eigenvalue
!
where
Final Assumption electroweak scale
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