A Solution to the Li Problem by the Long Lived Stau

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

Masato YamanakaMasato YamanakaCollaborators Collaborators

Toshifumi Jittoh, Kazunori Kohri, Toshifumi Jittoh, Kazunori Kohri, Masafumi Koike, Joe Sato, Takashi ShimomuraMasafumi Koike, Joe Sato, Takashi Shimomura

7

Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.××××Phys. Rev. D78 : 055007, 2008 and arXiv : 0904.××××

Contents

1, Introduction

2, The small m scenario and long lived stau

3, Solving the Li problem by the long lived stau7

4, Relic density of stau at the BBN era

5, Summary

Introduction

[ B.D.Fields and S.Sarkar (2006) ]

Big Bang Nucleosynthesis (BBN) Yellow box

Observed light element abundances

[CMB] vertical bandCosmic baryon density obtained from WMAP data

Color lines Light element abundances as predicted by the standard BBN

Prediction of the light elements abundance

Primordial abundance obtained from observations

consistent !

Li problem7

Theory

( 4.15 )×10＋ 0.49－ 0.45

－ 10

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

Observation

( 1.26 )×10＋ 0.29－ 0.24

－ 10

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

Predicted Li abundance ≠ observed Li abundance7 7

Li problem7

Requirement for solving the Li problem7

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 Coupling with a hadronic current

Able to survive still the BBN era Able to survive still the BBN era

Exotic processes are introducedExotic processes are introduced

The small m scenario and long lived stau

Setup

Minimal Supersymmetric Standard Model (MSSM) with R-parity

Lightest Supersymmetric Particle (LSP)Lightest neutralino ～

～ = N1 N3N2 N4B～

+ + +～W

～Hu

0 ～Hd

0

Next Lightest Supersymmetric Particle (NLSP)

Lighter stau ～～ = cos

～L～R+ sin e-i

Dark matter and its relic abundance

http://map.gsfc.nasa.gov

Dark Matter (DM)

Neutral, stable (meta-stable), weak interaction, massive

Good candidate : LSP neutralino

DM relic abundance

DMh 2= 0.1099 ± 0.0062

m n× DMDM∝

mDM = (constant) 1nDM

Naïve calculation of neutralino relic density

～

～

SM particle

SM particle

DM reduction process

Neutralino pair annihilation

Not enough to reduce the DM number density

[ PDG 2006 (J. Phys. G 33, 1 (2006)) ]

mDM = (constant) 1nDM

m ～ > 46 GeV

Not consistent !

Coannihilation mechanism [ K. Griest and D. Seckel PRD43(1991) ]

～

～

SM particle

SM particle

DM reduction process

Neutralino pair annihilation

+

+ stau-neutralino coannihilation

～ SM particle

SM particle～

Requirement for the coannihilation to work

Possible to reduce DM number density efficiently !

mLSPmNLSP

mLSP

–<~ 10 %

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 Stau has a long lifetime due to phase lifetime due to phase space suppression !!space suppression !!

Long lived stau

Stau lifetime

～～ survive until BBN era

BBN era

Stau provides additional processes to reduce the primordial Li abundance !!7

7Solving the Li problem by the long lived stau

Destruction of nuclei with free stau

～ ± A(Z)

A(Z±1)～

Interaction time scale (sec)

Negligible due toCancellation of destruction

Smallness of interaction rate

Stau-nucleus bound state

nuclear radius~

･･ stau ・・nucleus

New processes

Key ingredient for solving the Li problemKey ingredient for solving the Li problem

Negative-charged stau can form a bound state with nuclei Negative-charged stau can form a bound state with nuclei

77

Formation rate

Solving the Boltzmann Eq.

Stau catalyzed fusion

Internal conversion in the bound state

Stau catalyzed fusion

Nuclear fusionWeakened coulomb

barrier

･･ stau ・・nucleus

( ): bound state

[ M. Pospelov, PRL. 98 (2007) ]

Ineffective for reducing 7Li and 7Be

∵ stau can not weaken the barrieres of Li3+ and Be4+ sufficiently

Constraint from stau catalyzed fusion

Standard BBN process Catalyzed BBN process

Constraint on stau life time

Catalyzed BBN cause over production of Li

Internal conversion

Closeness between stau and nucleus

Overlap of the wave function : UPUPInteraction rate of hadronic current : UPUP

Hadronic current

~+ does not form a bound state

No cancellation processes

The decay rate of the stau-nucleus bound state

IC | | 2・= ( ) v: The overlap of the wave functions

: Cross section × relative velocity

| | 2

( ) v

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

| | 2 =1

anucl3

Internal conversion rate

anucl = nuclear radius = 1.2 × A 1/3～

( ) v is evaluated by using ft-value

( ) v ∝ ( ft )– 1

7Be → 7Li ・･･ ft = 103.3 sec (experimental value)

ft-value of each processes

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

Interaction rate of Internal conversionIn

tera

ctio

n ti

me

scal

e (s

)

Very short time scale

significant process for reducing Li abundance !significant process for reducing Li abundance !77

Scattering with background particles

Internal conversion

Internal conversion

Be7 7Li

He7

He,4 He,3

proton, etcD, etc

～～ ,

～～ ,

New interaction chain reducing Li and BeNew interaction chain reducing Li and Be7 7

Numerical result for solving the Li problem7

10.01 0.1Mass difference between stau and neutralino (GeV)

10

10

10

10

10

10

-16

-12

-13

-14

-15

-11

Y~

m = 300 GeVDM

Y~ ~ns

~n : number density of stau

s : entropy density

Allowed region

100 - 120 MeV

(7 – 10) 10× -13

The Li problem is solved7

Strict constraint on m and Y~

m = (100 – 120) MeV Y~ = (7 – 10) 10× -13

Allowed region

Produced Li are destructed by energetic proton

7

Internal conversion of occur when back ground protons are still energetic

Back ground particles are not energetic when Li are emitted 7

Produced Li are destructed by internal conversion

7

( Be)7~

Over production of Lidue to stau catalyzed fusion

6

Forbidden region

Bound states are not formed sufficiently

Insufficient reduction

Overclosure of the universe

Stau decay before forming a bound state

• Lifetime of stau 　

• Formation time of

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, which provides the solution for the Li problem7

The evolution of the number density

Boltzmann Eq. for neutralino and stau

i, j : stau and neutralino

X, Y : standard model particle

n (n ) : actual (equilibrium) number density

H : Hubble expansion rate

eq



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



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



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

Single Boltzmann Eq. for LSP DM

Absence of exchange terms ( cancel out )

∴

In the calculation of relic density of long lived stau

( all of SUSY particles decay into LSP )

∴

Obviously we can not use the method !

We are interesting to relic density of NLSP

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

Significant process for stau relic density calculation

Due to the Boltzmann factor, n i n j n X n Y, ,<<

Annihilation process

Exchange process

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 mass 100 GeV - 1000 GeV )

DM freeze out temperature

TDM ~ mDM 205 GeV - 50 GeV

Exchange process for NLSP stau and LSP neutralino

After DM freeze out, number density ratio is still varying

Boltzmann Eq. for the number density of stau and neutralino

Numerical calculation

Y n si i

s : entropy densityn : number density of particle ii

Numerical result (prototype)

Tau decoupling temperature (MeV)

Mass difference between tau and neutralino (MeV)Ratio of stau relic density and current DM density

Significant temperature for the calculation of stau number density

Tau decoupling temperature

Freeze out temperature of exchange processes・・

6060 80 80

50 50100 100

15 % 3 % 8 % 1.5 %


Condition ( tau is in thermal bath )

[ Production rate ] > [ decay rate, Hubble expansion rate ]

Production processes of tau

l l

q q


~ 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 fusionStau-catalyzed fusionInternal conversion processInternal 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

mixing angle between 　 and

CP violating phase

Weak coupling

Weinberg angle

Effective Lagrangian

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, 23confidence level are indicated by solid lines

Documents

A Solution to the Li Problem by the Long Lived Stau