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