Phys. Lett. B646 (2007) 34, (hep-ph/0610249)

Non-perturbative effect on thermal relic abundance of dark matter

Masato Senami(University of Tokyo, ICRR)

Collaborated with Junji Hisano (ICRR) Shigeki Matsumoto (KEK) Minoru Nagai (ICRR)　　 Osamu Saito (ICRR, KEK)

Previously, wino dark matter massis believed as ,if wino is thermal relic dark matter.

But, this is not true

If we include nonperturbative effects(Sommerfeld enhancement)

for thermal relic wino dark matter.

Dark matter Dark matter

Non-baryonic cold dark matter No candidate in the standard model

Supersymmetric (SUSY) model Lightest SUSY particle (LSP) : Bino, Wino, Gravitino …

Universal extra dimension (UED) model Lightest Kaluza-Klein(KK) particle (LKP) : KK photon …

Beyond the standard model

Yamanaka’s talk

by WMAP

Which model is the answer?Which model is the answer? Direct and indirect detection Collider signature (LHC, ILC)

Prediction from thermal relic scenario Precise data by WMAP (within 10%) Precise calculation of relic density is required.

e.g. Moriyama-san’s talk

One criterion : Constraint for model parameter

In this work, we calculate wino relic abundance precisely.

Wino dark matter Wino dark matter Superpartner of W boson

Pure wino LSP

Anomaly mediation Thermal relic scenario

SU(2)L gauge interaction

Degeneracy : neutral and charged wino

Non-thermal production

(Mixing with other neutralino is suppressed by heavy wino mass )

SU(2) triplet Mass spectrum

Other superparticlesMas

s

Thermal relic scenarioThermal relic scenario

n/s = constant

1 10 100 1000m/T (time ) (

Net

dar

k m

atte

r de

nsit

y)C

omov

ing

num

ber

dens

ity

Equilibrium density

Increasing

equilibrium

Thermal averagedFreeze out

Large cross section reduces relic abundance. Degeneracy between and

Coannihilation should be considered.

Cross section : average by weighted with degree of freedom

Annihilation cross sectionAnnihilation cross section is important.

(Thermally averaged effective annihilation cross section)

If dark matter (or coannihilating particle) particle has a gauge charge, non-perturbative effects are important.

Sommerfeld enhancement

: SU(2) : SU(2), U(1)em

SU(2) interaction is importantif wino is much heavier than the weak gauge bosons.

Sommerfeld enhancement : U(1) Sommerfeld enhancement : U(1)

Coulomb correction

+

-

Enhancement factor

annihilation

Pho

tons

Wave functions are affected by attractive force and modified from plane wave.This enhances the annihilation cross section.

annihilation

Sommerfeld enhancement : SU(2) Sommerfeld enhancement : SU(2)

W-boson exchange For heavy wino, W-boson mass is negligible. W-boson exchanges modify wave functions.

Diagrams have an additional factor 2m/mw for each W boson exchangeDM

DM

+ + ● ● ● +W W W

W

W

Non-perturbative effects are important.

m : wino mass.

Enhancement Enhancement

Temperature dependence with fixed m

Perturbative

Non-p

ertu

rbat

ive

[cm

3 /s]

m = 2.8 TeV

Thermally averaged cross section

m / TFreeze-out

Decoupling

The cross section is increased by 20-30% even at the freeze-out temperature.

1 102 104 106 108

10-26

10-25

10-24

For m/T = 102 - 105,the cross section is increased.

At m/T = 105,charged wino is decoupled.

n/nn/nTreeTree

Since the cross section depends on the temperature in a non-trivial way, we should solve the Boltzmann equation numerically.

m = 2.8 TeV

1

0.8

0.6

1 102 104 106 108

m / T

n/n

Tre

e

Delayed freeze-out

Late time annihilation

At the freeze-out,the enhancement of thecross section is about 20%.

The abundance isreduced by about 20%.

For m/T = 102 - 105,the cross section is increased.

The abundance isreduced by about 20%.

The abundance is reduced by more than40% compared to perturbative results.

Relic abundance of WinoRelic abundance of Wino

Allowed region : 2.7 TeV < m < 3.0 TeV

Perturbative

Non-perturbative

WMAP

21 30

0.1

0.2

m (TeV)

Summary and DiscussionSummary and Discussion Wino dark matter in thermal relic scenario

Nonperturbative reduces the relic abundance 2.7 TeV < m < 3.0 TeV

(c.f. perturbative result 1.9 TeV < m < 2.3 TeV)

Other dark matter candidatesHiggsino about 10%Bino-stau coannihilation at most

1%KK dark matter in UED model within

4%

Other dark matter candidatesOther dark matter candidates Higgsino LSP (SU(2) and U(1) charge)

Higgsino is doublet in SU(2)x1/4 compared with wino

Bino-Stau coannihilation (U(1) charge for only stau) almost cancel each other

KK dark matter in UED model (U(1) charge for E(1))

Gluino NLSP Strong nonperturbative effects by QCD Involved by QCD phase transition

O(10)%

at most 1%

within 4%

Enhancement factorEnhancement factor

Mass dependence of the cross sectionnormalized by the perturbative one

m/T = 2000

m (TeV)

m/T = 200

m/T = 20

The resonance appears at m=2.4TeVdue to the bound state, which are composed by and pairs.For m=2.4TeV, the binding energy of the bound state is almost zero.So, resonances appear at these masses.

The enhancement is more significant for smaller temperature. 21 3

10

5

1

Only the s-wave annihilation is relevant to the DM phen.

OnlyS = 0

S = 0S = 1

S = 0S = 1

OnlyS = 0

Annihilation processes we have to calculate.

Annihilation of WinosAnnihilation of Winos

Schwinger-Dyson eq.For Wino-like DM pair

MSSM action

Forward Scattering amplitude.

Annihilationcross section

Im. partOptical theorem

Derivation of the Schwinger-Dyson eq.

Integrate all field except 0 and fields.

Derive the Schwinger-Dyson eq. for the 2-body states.Schwinger-Dyson equation

Schrödinger equation

Expanding 0 and by their velocities (NR-Lagrangian is produced)

Introducing auxiliary fields for the pairs composed of 0 and ,and derive the 2-body states effective action by integrating out 0 and –.

Strategy to calculationStrategy to calculation

Schrödinger equation

Schrödinger equations for Wino DM

(S = 0)

(S = 1)

(S = 0, 1)

(S = 0)

&

det V < 0

Cross section formula

Sommerfeld factor

Sommerfeld factor

If we neglect the non-perturbative effect (V = 0), the factors become 1 and annihilation cross sectionscoincide with perturbative results.