宇宙論からの崩壊する粒子への制限

Kazunori Kohri

郡 和範

KEK and Sokendai

Standard Big Bang Cosmology

Cosmit time and Cosmic temperature

• Friedmann equation （General Relativity）

Hubble expansion

22

2:1 8

3 p

da Ha dt M

24 4 1/2

radiation ( ) ( )30

gT a t a t t

21sec /MeVt T

1(adiabatic expansion, =const.)T a s

44

38

1

18

16

2

- 4

1

5

10

12

10 GeV10 GeV10 GeV200 MeV3 M

time 10 sec 10 sec 10 sec 10 sec 0.1 sec 1 sec 10 sec

eV0.5 MeV1

10

"Energy Scale"

sec

eV0.3 eV

10

13.

7 eV

Gyr

Thermal history of the Universe

Planck scale

GUT phase transition?

Electroweak phase transition

QCD phase transition

Neutrino decoupling

Electron-positron annihilation

Matter-radiation equality

Photon decoupling (CMB)

Big bang

Present

Inflation

Baryogenesis?

Big-Bang Nucleosynthesis (BBN)

17(~10 sec)

cf) 1 GeV ~ 1013K

4

2

3

10 sec

0.1 sec 1 sec

100 MeV

2 -- 3 MeV 1 MeV

0 10 sec

.5 MeV0.1 MeV

10 sec

0.07 MeV

Thermal history around BBN Epoch

( 2 )e e

Muon annihilation

Neutrino decoupling

n/p freezeout

Electron-positron annihilationBeginning of BBN

End of (Standard) BBN

( 2 )

( e e )e e

( en )p e

cf) 100 MeV ~ 1012K

http://map.gsfc.nasa.gov/media/060916

Dark Matter? Einstein’s Cosmological Constant

Or unknown scalar field?

Unknown SUSY particles?

2CDM 0.109h

2baryon 0.022h

Brief review of Standard BBN (SBBN)

Radiation

Matter

Scenario of BBN1) 1 MeV ( 1 sec) T t

, , e,n p

Weak interaction is in equilibrium

en e p

n

p

n QExpn T

(Q 1.29 MeV)n pm m

thermal Exp[ / ]n m T

2) 1 MeV ( 1 sec) T tFeezeout of weak interaction

•Weak interaction rate

•Expansion rate

5 4~ ~ /n p n p e Wn T m

* ,eff~ 3.36 1 0.14( 3) g N

331/2

,eff4*

~ ~ 1 0.14( 3)0.8 MeV

n p p

W

T M T NH g m

2*~ /

3

pp

H g T MM

QExpT

freezeout

17

n

p

nn

4 He4

Np

B

mY

4 He

N

nm

freezeout

freezeout

2( / )0.25

( / ) +1( )

n p

n pn p

n nn nn n

He4 mass fraction

4 Hen

npp

4He /2nn n

3) ~ 0.1 MeV ( 100 sec)T t

p n D 2.2 MeV DT B

4) 0.1 MeV ( 3 minutes) T t

3

3

44

, +n( He ) +n ( He+

He p)

eH

D DD

T pT D

There is no stable nuclei for A=5,8

4

4

7

73

He +He He

L+

iBe

T

7e

7e +LiB e64 LHe i+ D

Time evolution of light elements

D

4He

3He

7Li

6Li

7Be

106.2 10

Observational light element abundances41) He

Observing the recombination line in Metal poor extragalactic H II region, or blue compact galaxy

pY 0.2534 0.0083 Aver, Olive, Skillman, arXiv:1112.3713

pY 0.2565 0.0060 Steigman, arXiv:1208.0032

Steigman, arXiv:1208.0032

2) DeuteriumObserved in high redshift QSO absorption system

Lyα（z~3）

QSO

Burles and Tytler (1997)

5D / H (2.82 0.20) 10

Pettini et al.(2008)

D H

82km/sec

Redshifted1215A 4300A

3) Lithium 7Observing metal poor halo stars in Pop II

Abundance does not depend on metalicity so much for

eff 5700 K ( ), [Fe/ ] -2T M H “Spite’s plateau”

Lemoine et al., 1997

Bonifacio et al (2006)

710Log Li/H 9.90 0.09

Lithium 6Observed in metal poor halo stars in Pop II

6Li plateau?

Asplund et al.(2006)

7 10Li / H (1.1 1.5) 10

6 7Li / Li 0.022 0.090

Astrophysically, factor-of-two depletion of Li7 needs a factor of O(10) Li6 depletion (Pinsonneault et al ’02)

We need more primordial Li6?

still disagrees with SBBN

He4

D

Li7

Li6

He3

Observational Light Element Abundances

pY 0.2534 0.0083

5D / H (2.82 0.20) 10

Bonifacio et al (2006) 7sy10 st.log Li/H 9.90 0 ( 0.35.09 )

sy6

s7Li/ Li 0.046 0. ( 0.106022 ) Asplund et al(2006)

3He/D 0.83 0.27 Geiss and Gloeckler (2003)

I will dicsuss this systematics later

Aver, Olive, Skillman (2012)

Pettini et al.(2008)

SBBN

( / )Bn n

Lithium Problem

If we adopted smaller systematic errors for observational data of 6Li and 7Li , the BBN theory does not agree with observation of Li abundances.

Astrophysical uncertainties in Li7

• Diffusion and convectionKorn et al (2006)

Destruction of Li7 in inner zone of stars

There is a increasing trend of both Iron and Li7 as a function of Teff

Li7

Doppler broadeningCold ISM 7Li

7Li+6Li

6Li

LP815-43Asplund et al.(2006)

Knauth, Federman,

Lambert (2006)

Astrophysical uncertainties in Li6

• Asymmetries of the absorption line mimicked by convective motion

Cayrel, Steffen, Bonifacio, Ludwig and Caffau (2008)

10WMAP (6.225 0.160) 10

( / )Bn n

Dark Radiation

Dark Radiation?• No strong suggestion from BBN. Nν=3 is

consistent

He4(Aver et al,2008)+D/H(Pettini et al. 2008)

0.47,BBN 0.45

0.5,BBN 0.5

See also

(Steigman,arXiv:1208.0032);

(Pett

=3.71 at

ini and

1

=Cooke,

arXiv : 1205.3785)

3.0 at

1

N

N

, . .. (68%CL)

WMAP+BAO+

WMAP+ACT+SPT, arXiv: 1301.1841

Relic abundance of thermally-produced SUSY particles

Lightest SUSY particle (LSP)• R-parity conservation (stability of proton )

i)Decay

ii) Pair annihilation/production

f f

(-1) (-1)×

(-1)× (-1)

(+1)

(+1) ×(+1)

Thermal freezeoutBoltzmann equation

frezeout

3 Hn

v

2

20.10.1

TeV

v

h

Freezeout / 20T m

Ωχ h2 does not depend on mχ

Kolb & Turner

Predicting TeV Physics!!! 26 33 10 /v cm s

∝Exp[-m/T]

m/T

LSP (LOSP) in CMSSMNeutralino or Scalar tau lepton (Stau) is the Lightest Ordinary SUSY Particle (LOSP)

Ellis,Olive,Santoso,Spanos(03)

LOSP

LOSP

χ LOSP

χ LOSP

ΩLOSP= Ωobs

ΩLOSP= Ωobs

Masses of squarks and sleptons

Gravitino mass

2 33/2 / 10 10 GeVplm F M

SUSY Breaking Models

Gravity mediated SUSY breaking model

Observable sector

quark, squark, …

Hidden sector

SUSY

20 21 2( 10 10 GeV )F

Only through gravity

2 3, / 10 10 GeVq plm m F M

20 21 2~ 10 GeVF

23/2 ~ / 10 GeVpm F M

SUSY Breaking Models IIGauge-mediated SUSY breaking model

Observable sector

quark, squark, …

SUSY breaking sector

SUSY

Messenger sector

Gauge interactionGauge interaction

Lightest SUSY particle (LSP) may be necessarily the gravitino (or axino)

Realistic candidates of particle dark matter in SUSY/SUGRA

• Neutralino χ(Bino, wino, or higgsinos)Most famous Lightest SupersymmetricParticle (LSP) with mχ~100GeV (appears even in global SUSY)

• Gravitino ψμsuper partner of graviton with spin 3/2 and m3/2 100GeV (massive only in SUGRA (local SUSY))

How heavy is the gravitino?

1) NLSP gravitino (e.g., in Gravity or Anomaly Med.)

2) LSP gravitino (e.g., in Gauge Mediation)

2 2 5

3/2 NLSP

7 2 2 -5

3/2 NLSP

/

10 s ( /10GeV) ( /10 GeV)

plm m m

m m

gravitino → LSP

NLSP → gravitino

B

2 3 9 2 -3

3/2 3/2/ 10 s ( /10 GeV)

plm m mLifetime

Lifetime

B

BBN constraints on decaying particles

Radiative decay mode

D + p + n

He3/D >~ O(1)

: 2.2 MeV ( 10 keV)D E T

4He : 20 MeV ( 1 keV)E T

Photon spectrum by radiatively decaying particles

Kawasaki, Moroi (1994)

2 /(22 )eE m T

2 /(80 )eE m T

Non-thermal Li6 ProductionDimopoulos et al (1989)

Jedamzik (2000)

Kawasaki,Kohri,Moroi (2001)

34 HeHe+

np T

4 6T + He Li+ [8.4 MeV]n3 4 6 He+ He Li+ [7.0 MeV]p

Coulomb energy loss by background electrons

i. He3 (T) production

ii. Li6 production

2 24 , ~ (1)e

e

Z ndE Odx m

3T, He 4He

Photodissociation

Kawasaki, Kohri, Moroi (2001)

3/23/2

nYs

mu- and y- distortion of CMB

Hadronic decay mode

jet

One hadron jet with/2XE m

jet

Two hadron jets with/3XE m

3/ 4 10hB

1hB

Reno, Seckel (1988)

S. Dimopoulos et al.(1989)

Hadron-fragmentation Monte Carlo event generator, (PYTHIA, Sjostrand (1994, …))

)

Kohri （2001)

Contours of final energy of energetic proton

Contours of final energy of energetic neutron

strongweakn p n pn p

Extraordinary inter-conversion reactions between n and p

Hadron induced exchange

/n p n pEven after freeze-out of n/p in SBBN

More He4, D, Li7 …

cf) 0n p 0p n

（I) Early stage of BBN (T > 0.1MeV)Reno and Seckel (1988) Kohri (2001)

(II) Late stage of BBN (T < 0.1MeV)Hadronic showers and “Hadro-dissociation” S. Dimopoulos et al. (1988)

fE En (p)

Kawasaki, Kohri, Moroi (2004)

Non-thermal Li, Be Production by energetic nucleons or photons S. Dimopoulos et al (1989)

34 +X

N (or ) + HHeT

e + X

4 6T + He + [8.4 Li MeV]n

3 4 6 He + He + [7.0 L V]i Mep

4 4 *N (or ) + He He +X

4 4 6 7 7He + He Li, Li, Be + ...

3T, He4He

4He Energy loss

① T(He3) – He4 collision

② He4 – He4 collision

Jedamzik (2000)

Constraints on long-lived SUSY particles from BBN

• We add large systematic errors into observational Li7 and Li6 abundacnes

Melendez,Ramirez(2004)

7sy10 st.log Li/H 9.90 0 ( 0.35.09 )

sy6

s7Li/ Li 0.046 0. ( 0.106022 )

Asplund et al(2006)

Massive particle X

/x xY n s

x xUpper bounds on m Y in both photodissociation and "hadrodissociation" scenario Kawasaki, Kohri, Moroi (04)

Mild observational upper bound

Mild observational upper bound

Gravitino production

• Thermal productionBolz,Brandenburg,Buchmulle (01,08)

Kawasaki,Kohri,Moroi (05)

Pradler,Steffen (07)

Gravitino production 2

• Non-thermal production Nakamura and Yamguchi (06)

Endo, Hamaguchi and F.Takahashi (06)

Dine,Kitano,Morrise,Shirman (06)

Neutralino (bino) LSP and gravitino “NLSP”

9 123/210 GeV / 10RT Y

Upper bound on reheating temperatureKawasaki, Kohri, Moroi, Yotusyanagi (08)

3/2 3/2 /Y n s

2 3

3/2

9 2 -3

3/2

/

10 s ( / 10 GeV)

plm m

m

Neutralino (bino) NLSP and gravitino LSP

Gravitino LSP and thermally porducedneutralino (Bino) “NLSP” scenario

No allowed region for DM density

Feng, Su, and Takayama (03)

Steffen (06)

Kawasaki, Kohri, Moroi, Yotsuyanagi (08) 2 2 5

3/2/

pl NLSPm m m

Relic abundance

Lifetime

100GeVBm

Stau NLSP and gravitino LSP scenario

Stable stau with weak-scale mass ( <108TeV) was excluded by the experiments of ocean water

NLSP stau should be unstable

Bound-state effect (see next)

CHArged Massive Particle (CHAMP)“CHAMP recombination” with light elemcts

Ebin ~ α2 mi ~ 100keVTc~ E bin/40 ~ 10keV

CHAMP captured-nuclei, e.g., (C,4He) changes the nuclear reaction rates dramatically in BBN

N+

CHAMP-

See also recombination between

electron and proton,

Ebin ~ α2 me ~ 13.6eV,

Tc~ Ebin/40 ~ 0.3eV,

Pospelov’s effect

• CHAMP bound state with 4He enhances the rate

• Enhancement of cross section

4 6D ( He,C ) Li C

Pospelov (2006),hep-ph/0605215

5 5 7 8Bohr~ ( / ) ~ (30) ~ 10a

Confirmed by Hamaguchi etal (07), hep-ph/0702274

Stau NLSP and gravitino LSP Scenario in gauge mediation

Kawasaki, Kohri, Moroi PLB 649 (07) 436

τ>103secτ>103sec

Lifetime Lifetime

Relic abundance

100GeVm

Sneutrino NLSP and gravitino LSP scenario

Stable (left-handed) sneutrino was excluded by the direct detection experiments because of its large cross section directly-coupled with W/Z bosons.

(left-handed) sneutrino should be unstable

Gravitino LSP and thermally porducedsneutrino NLSP scenario

No allowed region for DM density with 100GeV sneutrinos

Kawasaki, Kohri, Moroi, Yotsuyanagi (08)

Ellis, Olive, Santoso (08)Relic abundance

300GeVm

Annihilating DM and BBN

Signature of SUSY particles related with Astrophysics and Cosmology

• Direct detection• Indirect detection• Big-bang nucleosynthesis (BBN)• Cosmic Microwave Background (CMB)• Diffuse gamma-ray background

• Gamma-ray from a point source

• Antiproton • Positron• 511 keV line gamma from GC• Neutrinos

Indirect detection of LSP (LOSP) dark matter

Annihilation signals of dark matter at Galaxy Center, the Sun, near solar system, dwarf galaxies, etc…

, , , 2 , WW ZZ Z e e

, broad spectrum of , ,W Z e e p p

• Synchrotron radio• WMAP/Planck HAZE • Nucleosynthesis• 130 GeV line gamma from GC• etc…

Positron Excess (PAMELA satellite reported)

Adriani et al, arXiv:0810.4995v1 [astro-ph]

/ ( ~0.6 proton diffusion)e e E

Electron and positron flux by ATIC2

Chang et al (08)

Positron Excess (Fermi satellite reported)

Ackermann et al (11)

Electron and positron flux by Fermi

Abdo et al, Fermi LAT Collaboration, arXiv:0905.0025, PRL102 (09) 181101

Positron Excess

Steady-state solution (Hisano etal, ’06)K(E) and b(E) are taken from (Moskalenko-Strong ‘98,Baltz-Edsjo ‘99)

Diffusion model

Flux

Propagating within a few kpc, K was obtaineed to fit B/C0.17

propagation ( )/ ( ) 0.7kpc( /GeV)r EK E b E E

Hisano, Kawasaki,

Kohri, Moroi, Nakayama (09)

Positron excess

in DM annihilation

Diffusion model

Fitted to B/C ratio

24 23 310 10 /v cm s

See also Marco Cirelli’s lecture

Hisano, Kawasaki,

Kohri, Moroi, Nakayama (09)

Electron/positron cutoff

in DM annihilation

24 23 310 10 /v cm s

See also Marco Cirelli’s lecture

Another ideas

• From local pulsars

Hooper, Blasi, Serpico (08)

• From local Supernovae remnants

• Fujita, KK, Yamazaki Ioka (09)

Residual annihilation of DM even at around BBN epoch

• To fit the PAMELA and ATIC2/Fermi positron signals and EGRET gamma-ray anomaly,

24 22 310 10 /v cm s

2DMD

DMDM DMann

M DMann3 ~

Hv nn

dn Hn v n

s s

dn

t

O(102) – O(103) times larger than canonical value, 26 3

canonical 3 10 /v cm s

1

Hadron emission by residual annihilation in BBN epoch Hisano et al (09)

Charged-lepton (e+e-) emission by residual annihilation in BBN epoch

Hisano et al (09)

Velocity-dependent annihilation cross section?• Sommerfeld or Breit-Wigner enhancement

0

0

( )~ with n=1,2,4, ...( / )n

vvv v

0 freezeout-3

( ) ~ (1)1 (e.g., ~ < 10 )

v v T T O

Arkani-Hamed et al (08)

Ibe, Murayama, Yanagida (08)

Velocity of DM has been redshifted

KD KD

(before kinetic decoupling)

(after kinetic-decoupling)

~ 3 /

~ /

v T m

v v T T

0v1/2T

T

freezeoutx KDx

v

KDv

1/2 -11/21 6 KD

0( / ) ~ 10TeV MeV 0.1keV

Tm Tv v

Constraints on velocity-dependent annihilation cross section from BBN

(Hadronic)DM DM W W ( )DM DM e e Radiative

Hisano,Kawasaki,KK,Moroi,Nakayama,Sekiguchi (10)

He3/D

Constraints on velocity-dependent annihilation cross section from CMB

(Hadronic)DM DM W W ( )DM DM e e Radiative

Hisano,Kawasaki,KK,Moroi,Nakayama,Sekiguchi (10)

He3/D

130 GeV gamma-ray line(s)

• Observation and ann. DM interpretation27 3

DM+DM +

Depending on density profile(NFW,Einasto,isothermal-cor

>~ 10 / sec

>~ 0.1

ed,...

canonical

v cm

v

Weniger,arXiv1204.2797

26 3

For thermal production, =3 10 / sec

canonicalv cm

Annihilating Dark Matter?• One-loop suppression

• Branching ratio

total2 4

(DM+DM + )Br(DM+DM + )

~ ~ 10

γ

γ

DM

DM

e

e

ff

See also Endo et al for decaying DM, arXiv:1301.7536

Non-thermal DM with Large σtotal

• BBN + CMB bound on total σ (Independent of profile)

• Bounds on branching fraction into gamma line

• Constraints on branching ratio to total(>>10-4)

Hisano, Kawasaki, KK, Moroi, Nakayama, Sekiguchi (09)

See also Br > 1/30 -- 1/50 for ratio to continuum Cohen, Lisanti, Slatyer, Wacker(12), Buchmuller,Line (12)

Lithium Problem

If we adopted smaller systematic errors for observational data of 6Li and 7Li , the BBN theory does not agree with observation of Li abundances.

SBBN

( / )Bn n

(4-5)×10-10

5×10-5

Lithium 7

Observed metal poor halo stars in Pop II

Abundance does not depend on metalicity for

Expected that there is little depletion in stars.eff 5700 K ( ), [Fe/ ] -2T M H “Spite’s plateau”

Lemoine et al., 1997

7 0.32 10

0.21

7

Li / H 1.26 10 (1 )

log Li / H 9.90 0.09 (1 )

Ryan et al.(2000)

a factor of two or three smaller !!!

Bonifacio et al.(2006)

Lithium 6Observed in metal poor halo stars in Pop II

6Li plateau?

Asplund et al.(2006)

7 10Li / H (1.1 1.5) 10

6 7Li / Li 0.022 0.090

Astrophysically, factor-of-two depletion of Li7 needs a factor of O(10) Li6 depletion (Pinsonneault et al ’02)

We need more primordial Li6?

still disagrees with SBBN

Solving Li problem in new particle physics models

• We do not adopt systematic uncertainties of observational Li7 and Li6 abundances

Can long-lived particles solve the Li problem?

• Neutralino LSP and stau NLSP with small mass deference (<100 MeV)

• Residual annihilation of wino-like neutralinoLSP with more massive gravitino

• Stop NLSP and gravitino LSP scenario

Hisano et al (08)

Bird,Koopmans,Pospelov(07), Jittoh etal (07,08)

Kohri and Santoso (08)

Reduction of 7Li and production of 6Li

• Copious neutrons and tritiums are produced in hadronic shower process with decay/annihilation

• Reducing Be7 through

• Tritium scatters off the background He4 and produces Li6

7 7 4 4Be( ,p) Li(p, He)n He

4 6T+ He Li+n

Jedazmik (‘04)

Dimopoulos et al (‘89)

7 7 - 7( Li is produced later by Be + e Li )e

Jedamzik (04) , Cumberbatch et al (08)

Stop NLSP and gravitino LSP

• Stop can be NLSP in Non-universal Higgs masses (NUHM)

• Stop is confined into “messino” after QCD phase transition

• Second annihilation of stop occurs just after QCD phase transition through strong interaction

• Stop number density is highly suppressed, but it is appropriate to solve the Li problem

Kohri and Santoso (08)

14 13/ 10 GeV 10 GeVt tm n s

Hadronic decay and Lithium Prob.Cumberbatch, Ichikawa, Kawasaki, Kohri, Silk, Starkman (2006)

Stop NLSP and gravitino LSPKohri and Santoso arXiv:0811.1119v1 [hep-ph]

Residual annihilation of wino LSP

• Non-thermal production of wino LSP by decaying massive such as gravitinos (> O(10) TeV)

• Annihilating even after wino’s freeze-out time with its larger annihilation rate than bino’s

Hisano, Kawasaki, Kohri, Nakayama(08)

26 33 10 /v cm s

w w

Even during/after BBN epoch!!! WW WW

Residual annihilation of wino-like LSPHisano, Kawasaki, Kohri, Nakayama(08)

Thermal (bino) DM

We need nonthermal wino production by gravitino decay

Conclusion• By using BBN we can check the early universe up to the

10MeV epoch and obtain unique information for SUSY/SUGRA

• If gravitino is unstable, we have a strong upper bound on the reheating temperature after inflation

• Annihilating/decaying particles may solve Lithium problem

• Nν=3 is consistent with BBN

• We have obtained strong upper bounds on <σannv>. 130 GeVgamma-ray line(s) may not be produced by simple one-loop diagram annihilation

5 73 10 GeV 10 GeV

( 100 GeV 1TeV)3/2

T

m

R