A Solution to the Li Problem by the Long Lived Stau

Transcript A Solution to the Li Problem by the Long Lived Stau

by the Long Lived Stau

Masato Yamanaka Collaborators Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi Shimomura Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.

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1, Introduction Contents 4, Relic density of stau at the BBN era 5, Summary

Introduction

Big Bang Nucleosynthesis (BBN) Yellow box Observed light element abundances [CMB] vertical band Cosmic baryon density obtained from WMAP data Color lines Light element abundances as predicted by the standard BBN [ B.D.Fields and S.Sarkar (2006) ] Prediction of the light elements abundance consistent !

Primordial abundance obtained from observations

Li problem

7 Li problem Theory ( 4.15 )

－

10 A. Coc, et al., astrophys. J. 600, 544(2004) Observation ( 1.26 )

－

10 P. Bonifacio, et al., astro-ph/0610245

Requirement for solving the Li problem Able to destroy a nucleus To occur at the BBN era Not a Standard Model (SM) process Possible to be realized in a framework of minimal supersymmetric standard model !

Stau ~

Superpartner of tau lepton Coupling with a hadronic current Able to survive still the BBN era Exotic processes are introduced

and long lived stau

Setup Minimal Supersymmetric Standard Model (MSSM) with R-parity Lightest Supersymmetric Particle (LSP) Lightest neutralino

= N 1

～

B + N 2

～

W + N 3

～

0 H u + N 4

～

0 H d Next Lightest Supersymmetric Particle (NLSP) Lighter stau = cos

q t t

L + sin

q t

-i g t t

Dark matter and its relic abundance Dark Matter (DM) Neutral, stable (meta-stable), weak interaction, massive Good candidate : LSP neutralino DM relic abundance

= 0.1099

0.0062

∝

(constant) 1 n

http://map.gsfc.nasa.gov

Naïve calculation of neutralino relic density DM reduction process Neutralino pair annihilation

SM particle SM particle

Not enough to reduce the DM number density

= (constant) 1 n

Not consistent !

c > 46 GeV [ PDG 2006 (J. Phys. G 33, 1 (2006)) ]

Coannihilation mechanism [ K. Griest and D. Seckel PRD43(1991) ] DM reduction process Neutralino pair annihilation

SM particle SM particle

+ stau-neutralino coannihilation

SM particle

Possible to reduce DM number density efficiently ! Requirement for the coannihilation to work

m NLSP

–

m LSP m LSP

Long lived stau Attractive parameter region in coannihilation case

m ≡ NLSP mass

ｰ

LSP mass < tau mass (1.77GeV) NLSP stau can not two body decay Stau has a long lifetime due to phase space suppression !!

Stau lifetime BBN era survive until BBN era Stau provides additional processes

by the long lived stau

Destruction of nuclei with free stau

n t A(Z ± 1)

Negligible due to Cancellation of destruction Smallness of interaction rate

± A(Z) Interaction time scale (sec)

Stau-nucleus bound state Negative-charged stau can form a bound state with nuclei ~

nuclear radius ･･ stau ・・ nucleus

Formation rate Solving the Boltzmann Eq.

New processes Stau catalyzed fusion Internal conversion in the bound state

Stau catalyzed fusion [ M. Pospelov, PRL. 98 (2007) ]

･･ stau ・・ nucleus Weakened coulomb barrier Nuclear fusion ( ): bound state

Ineffective for reducing 7 Li and 7 Be

∵

stau can not weaken the barrieres of Li 3+ and Be 4+ sufficiently

Constraint from stau catalyzed fusion Standard BBN process Catalyzed BBN process Catalyzed BBN cause over production of Li Constraint on stau life time

Internal conversion Hadronic current Closeness between stau and nucleus Overlap of the wave function :

UP

Interaction rate of hadronic current :

UP

+ does not form a bound state No cancellation processes

Internal conversion rate The decay rate of the stau-nucleus bound state

G IC

2 ・ s s 2 : The overlap of the wave functions : Cross section × relative velocity

The bound state is in the S-state of a hydrogen-like atom

p 1 a 3 nucl a nucl = nuclear radius = 1.2 × A 1/3 s s

is evaluated by using ft-value

∝ (

) – 1

ft-value of each processes

7 Be → 7 Li ・･･

= 10 3.3

sec (experimental value) 7 Li → 7 He ･･･ similar to 7 Be → 7 Li (no experimental value)

Interaction rate of Internal conversion Very short time scale

7 7 New interaction chain reducing Li and Be Internal conversion 7 He 7 Be Internal conversion ,

n t

7 Li ,

n t

Scattering with background particles 4 He, 3 He, D, etc proton, etc

7 Numerical result for solving the Li problem

10 -11 10 -12

t 10 -13 10 -14 10 -15 10 -16 0.01

0.1

Mass difference between stau and neutralino (GeV) 1

n n s

: number density of stau

: entropy density

Allowed region

(7 – 10) 10 -13 100 - 120 MeV d

m = (100 – 120) MeV

= (7 – 10) 10 -13

Back ground particles are not internal conversion Allowed region

back ground protons are still energetic energetic proton

Forbidden region Overclosure of the universe Stau decay before forming a bound state

• Lifetime of stau • Formation time of

Bound states are not formed sufficiently Insufficient reduction 6 Over production of Li due to stau catalyzed fusion

Relic density of stau at the BBN era

For the prediction of parameter point Stau relic density at the BBN era Not a free parameter !

Value which should be calculated from other parameters For example DM mass, mass difference between stau and neutralino, and so on Calculating the stau relic density at the BBN era We can predict the parameters more precisely,

The evolution of the number density Boltzmann Eq. for neutralino and stau

i, j

: stau and neutralino

X, Y

: standard model particle : actual (equilibrium) number density

: Hubble expansion rate

The evolution of the number density Boltzmann Eq. for neutralino and stau Annihilation and inverse annihilation processes

i j X Y

Sum of the number density of SUSY particles is controlled by the interaction rate of these processes

The evolution of the number density Boltzmann Eq. for neutralino and stau Exchange processes by scattering off the cosmic thermal background

i X j Y

These processes leave the sum of the number density of SUSY particles and thermalize them

The evolution of the number density Boltzmann Eq. for neutralino and stau Decay and inverse decay processes

i j Y

Can we simplify the Boltzmann Eq. with ordinal method ?

In the calculation of LSP relic density All of Boltzmann Eq. are summed up

∴

( all of SUSY particles decay into LSP ) Single Boltzmann Eq. for LSP DM Absence of exchange terms

∴

( cancel out ) In the calculation of relic density of long lived stau We are interesting to relic density of NLSP Obviously we can not use the method !

We must solve numerically a coupled set of differential Eq. for stau and neutralino

Significant process for stau relic density calculation Boltzmann Eq. for neutralino and stau Annihilation process Exchange process Due to the Boltzmann factor,

n i

n j

n X

n Y

Annihilation process rate << exchange process rate Freeze out temperature of sum of number density of SUSY particles ≠ Freeze out temperature of number density ratio of stau and neutralino

Exchange process DM freeze out temperature

T DM

m DM 20

5 GeV - 50 GeV ( DM mass 100 GeV - 1000 GeV ) Exchange process for NLSP stau and LSP neutralino

g t t g

After DM freeze out, number density ratio is still varying

Numerical calculation Boltzmann Eq. for the number density of stau and neutralino

s n i

: number density of particle

i s

: entropy density

Numerical result (prototype)

Tau decoupling temperature (MeV) Mass difference between tau and neutralino (MeV) Ratio of stau relic density and current DM density 60 50 15 % 60 100 3 % 80 50 8 %

Significant temperature for the calculation of stau number density

・・

Tau decoupling temperature Freeze out temperature of exchange processes

80 100 1.5 %

Tau decoupling temperature Condition ( tau is in thermal bath ) [ Production rate ] > [ decay rate, Hubble expansion rate ] Production processes of tau

g g

l l q q

t t t t t t

Tau decoupling temperature ~ 120 MeV

Summary

We investigated solution of the Li problem in the MSSM, in which the LSP is lightest neutralino and the NLSP is lighter stau Long lived stau can form a bound state with nucleus and provides new processes for reducing Li abundance Stau-catalyzed fusion Internal conversion process We obtained strict constraint on the mass difference between stau and neutralino, and the yield value of stau Stau relic density at the BBN era strongly depends on the tau decoupling temperature and mass difference between stau and neutralino Our goal is to predict the parameter point precisely by calculating the stau relic density and nucleosynthesis including new processes

Appendix

Effective Lagrangian

mixing angle between and CP violating phase Weak coupling Weinberg angle

Bound ratio

Red : consistent region with DM abundance and mass difference < tau mass Yellow : consistent region with DM abundance and mass difference > tau mass The favored regions of the muon anomalous magnetic moment at 1

, 2

s, 2.5s,

confidence level are indicated by solid lines