phys. lett. b646 (2007) 34, (hep-ph/0610249)
DESCRIPTION
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). Phys. Lett. B646 (2007) 34, (hep-ph/0610249). - PowerPoint PPT PresentationTRANSCRIPT
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.