Cosmology with long-lived
charged particle

Kazunori Kohri （郡和範）

Physics Department, Tohoku University

Dark Matter

Unknown SUSY particles?

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

Running of Renormalization Group (RG)
Equation in CMSSM

Negative Higgs mass term

Martin, ”A Supersymmetry Primer”

LSP (LOSP) in CMSSM
Neutralino or Scalar tau lepton (Stau) is the Lightest Ordinary SUSY
Particle (LOSP)ΩLOSP= Ωobs

χ LOSPχ LOSPτPSOLτPSOLΩLOSP= Ωobs

Ellis,Olive,Santoso,Spanos(03)NASA WMAP Science TeamThermal history of the Universecf) 1 GeV ~ 1013KBig bangtime

1 eV ~ 104K

"temperature"

10−44 sec − 1018 GeV Planck scale

10−38 sec − 1016 GeV GUT phase transition?
10−11sec −10 GeV Electroweak phase transition2− 1 MeV
10 sec − 1 keV
10 sec − 0.3 eV
1 sec
612Inflation and Reheating≈

Neutron decoupling

Baryogenesis?

Big-Bang
Nucleosynthesis (BBN)

Galaxy-size perturbation reenters the horizon (LSS)
Matter-Radiation equality and Photon decoupling (CMB)

13.717Gyr − 10- 4 eV~2.7 K(~10 sec)

Present宇宙の外には何がある？
Voltaire(1694-1778)• 神の存在を信じたデカルトに対してヴォルテールは「この世の無という隙間がなく、物質だけで全て満たされているのだとすると、物質とは違うはずの神は一体どこに存在しているのか？」とデカルトに反論した。物質世界の内と外という概念を導入せざるを得ない。
• To a question, “What exists outside the horizon?”,we can say, quantum fluctuation exists outside thehorizon in modern picture of Inflationary cosmology

Stau NLSP and gravitino LSP scenario
Stable stau with weak-scale mass ( <102 TeV105 TeV) was excluded by the experiments ofocean water
NLSP stau should be unstable
Bound states of stau and light elements shouldhave been formed

Big-bang nucleosythesis (BBN)

Freezeout of neutron to proton ratio⎡ Q⎤Exp ⎢ − ⎥⎣ T⎦⎛ nn ⎞1≈⎜⎜ ⎟⎟⎝ n p ⎠freezeout 7

He4 mass fraction

4nHepnpn He = nn /24

ρ He 4 × mN × n He2(nn / n p )freezeout≈≈ 0.25
Yp ≡≈ρBmN × (nn + n p ) (nn / n p )freezeout +144cf) 0.1 MeV ~ 109K3) T ~ 0.1 MeV (t ~ 100 sec)p + n → D +γ

TBD = 2.2 MeV4) T < 0.1 MeV (t > 100 sec)nD / nH ∼ 16.3(T / mN )3/ 2η exp[ BD / T ] > 0.01

D + D → T + p, 3 He+n
T + D ( 3 He + D) → 4 He+n ( 4 He+p)
A little D and 3 He are left as cold ashes

There is no stable nuclei for A=5,8. Mass 7 nuclei are produced a little.
4He + T → 7 Li+γ4

He + 3 He → 7 Be+γ74

He + D → 6 Li+γ

Be + e − → 7 Li+ν e

Observational Light Element
Abundances
He4Yp = 0.2516 ± 0.004

Fukugita, Kawasaki (2006)
Peimbert,Lridiana, Peimbert(2007)
Izotov,Thuan, Stasinska (2007)

D

D/H = (2.82 ± 0.26) × 10 −5Li7log10 ( 7Li/H ) = −9.90 ± 0.09 ( +0.35)syst.

Melendez,Ramirez(2004)

Li/ 7Li < 0.046 ± 0.022 ( +0.106)sysAsplund et al(2006)

Li6He3

6He /D < 0.83 + 0.27

3O’Meara et al. (2006)

Geiss and Gloeckler (2003)

SBBN

7Be + e- Æ 7Li + νe(≡ nB / nγ )

CHArged Massive Particle (CHAMP)
Kohri and Takayama, hep-ph/0605243
See also literature, Cahn-Glashow (‘81)

Candidates of long-lived CHAMP in modern cosmology
stau, stop …
N+“CHAMP recombination” with light elemcts
Tc~ E bin/40 ~ 10keV
CHAMP(Ebin ~ α2 mi ~ 100keV )See also the standard recombination between electron and, (T ~ E /40 ~ 0.1eV, E ~ α m ~ 13.6eV ) )protoncbinbin

2e

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

Pospelov’s effectPospelov (2006),hep-ph/0605215• CHAMP bound state with 4He enhances
the rate D + He → Li + γ46

D + ( He,C ) → Li + C
4−6−• Enhancement of cross section~ (λγ / aBohr ) ~ (30) ~ 10557 −8Confirmed by Hamaguchi etal (07), hep-ph/0702274

Stau NLSP and gravitino LSP Scenario
Kawasaki, Kohri, Moroi, Yotsuyanagi (08)Relic abundance(25τ ∼ m3/2
mpl2 / mNLSP∼ 103 s mNLSP /102GeV

Lifetime

τ>103secmτ = 100GeV

Lifetime

τ>103sec) (−5m3/2 /10−1GeV)

2

Lithium Problem
If we adopted smaller systematicerrors for observational data of 6Li
and 7Li , the BBN theory does notagree with observation of Liabundances.

SBBN(4-5)×10-10
5×10-5(≡ nB / nγ )Lithium 7a factor of two or threesmaller
T > !!!
5700 K ( ∝ M ), [Fe/H ] < -2zObserved metal poor halo stars in Pop IIzAbundance does not depend on metalicity for“Spite’s plateau”

effzExpected that there is little depletion in stars.

7−10Li / H = 1.26+−0.32
×10(1σ )0.21log ( 7 Li / H ) = −9.90 ± 0.09 (1σ )Ryan et al.(2000)
Bonifacio et al.(2006)

Lemoine et al., 1997

Degenerate stau NLSP and neutralino
LSP Scenario
Jittoh, Kohri, Koike, Sato, Shimomura, Yamanaka, 2010

δ m = mτ − mχ < 0.1GeV Long-lived and Charged current in BS0DM

Destroyed
NLSP

Effectively Be7, Li7
are destroyed!!!

See also Bird, Koopman and Pospelov (07)Relic abundance and BBN constraint
in degenerate-mass scenario
Jittoh, Kohri, Koike, Sato, Shimomura, Yamanaka, 2010
BBN allowed

Relicabundacefor DM

Large-scale structure (LSS)• Primordial density perturbation created in inflation is a seedof galaxy• The perturbation of Cold Dark Matter (CDM) could evolve
without interacting background plasma of photon, proton andelectron• Acoustic oscillation of CHAMP-radiation fluid could haveerased the density perturbation of galaxy scalek ~ 0.1 Mpc (τ /10 s )
−1

61/ 2

Shigurdson and Kamionkowski (04)
Kohri and Takahashi (09)

Fraction of bound state
Most of CHAMPs areincluded into He4 for
Y < 1012
They are still
positively-charged!

Time-evolution of fluctuation
Horizon reentry before matter-radiation equality epoch-6-5-4-3aEQ-2-1

∝aDM

∝a２
BaryonLog aMa and Bertschinger (95)
See also 松原隆彦 「シリーズ 現代の天文学3 宇宙論 ＩＩ宇宙の進化」

Constraint from Large-Scale Structure
Kohri and Takahashi (09)

Detectability of long-lived stau in LHC
See also Takumi Ito’s talkPlace additional stoppers near ATLAS orCMS to stop long-lived charged SUSY
particles (even for cτ > 10 m)• 5 m Iron wall Hamaguchi, Kuno, Nakaya, and Nojiri (04)
• Water tankFeng and Smith (04)• Surrounded rock
De Roek, Ellis, Gianotti, Mootgat, Olive and Pape (05)See also Asai-Hamaguchi-Shirai (09) for a possibility of the detection
without those additional stoppers

Summary•The gravitino LSP with thermally produced stau
NLSP scenario is severely constrained•Long-lived CHAMPs should be also constrained bystructure formation of galaxy•Stau NLSP can be detected by LHC (See alsoTakumi Ito’s talk)Introduction to SUSY
Supersymmetry (SUSY)
Solving “Hierarchy Problem”
Realizing “Coupling constant unification in GUT”

neutralinoFermion

Boson

quark

squarkleptonsleptonphotinophotongravitino

graviton

Lightest SUSY particle (LSP) is a good candidate fordark matter

Supergravity• Local theory of Supersymmetry and a good candidate forquantum gravity• Predicting a massive super partner of graviton, gravititno• Predicting a long-lived particle, e.g., decaying NLSP
gravitino into LSP neutralino, or decaying NLSP neutralino orstau into gravitino LSP• Typically the lifetime can be longer than one second! This isdangerous for cosmology.

τ ∼ m pl / m233/2

62∼ 10 sec(m3 / 2 /10 GeV)

-3

Lithium 6Asplund et al.(2006)

zObserved in metal poor halo stars in Pop II
z6Li plateau?
6Li / Li = 0.022 − 0.090

77Li / H ≈ (1.1 − 1.5) × 10−10

still disagrees with SBBN
Astrophysically, factor-of-two depletion of Li7 needs afactor of O(10) Li6 depletion (Pinsonneault et al ’02)
We need more primordial Li6?

Doppler broadening
Cold ISM

7Li

6Li

Knauth, Federman,Lambert (2006)

LP815-43
Asplund et al.(2006)

7Li+6LiScenario of BBNcf) 1 MeV ~ 1010K1) T > 1 MeV (t < 1sec)
Radiation

γ , e ,νMattern, p±

Weak interaction is in equilibriumn + e ↔ p +ν e+nn
⎡ Q⎤
= Exp ⎢ − ⎥np⎣ T⎦(Q ≡ mn − m p ∼ 1.29 MeV)

2) T ~ 1 MeV (t ~ 1 sec) cf) 1 MeV ~ 10 K
10Feezeout of weak interaction•Weak interaction rate
•Hubble expansion rate

Γ n ↔ p ~ σ n ↔ p ne ~ GF2 T 5
H=Γ ⎛T⎞≈⎜⎟H ⎝ 0.8 MeV ⎠Γ < H (T < 0.8 MeV ≡ T f )a (t )~ T 2 / M pla (t )3( n /n ) is fixed⎛ nn ⎞⎡ Q⎤≈ Exp ⎢ − ⎥⎜⎜ ⎟⎟⎝ n p ⎠freezeout⎣⎢ T f ⎦⎥np

Time evolution of light elements

Radiative decay modex

D+p+nHe3/D >~ O(1)

Hadronic decay modex

Reno, Seckel (1988)
S. Dimopoulos et al.(1989)

Two hadron jets with

E jet = mX /3

Bh ≈ α / 4π ≈ 10−3x

One hadron jet with

E jet = mX /2

Bh = 1

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

Extraordinary inter-conversion reactions between n and pcf)

n +π + → p +π 0p +π − → n +π 0weakstrongΓn ↔ p = Γ n ↔ p + Γ n ↔ p

Hadron inducedexchangeΓn ↔ p ↑ ⇒ n / p ↑Even after freeze-out of n/p in SBBN

More He4, D, Li7 …

(II) Late stage of BBN (T < 0.1MeV)
Hadronic showers and “Hadro-dissociation”

En= Ef(p)S. Dimopoulos et al. (1988)
Kawasaki, Kohri, Moroi (2004)

Non-thermal Li, Be Production byenergetic nucleons or photons
Dimopoulos et al (1989)
Jedamzik (2000)
3
⎧He+X
4
3N (or γ ) + He → ⎨T,He+X
T⎩He

4N (or γ ) + He → He +X
44*He

4Energy loss

① T(He3) – He4 collision
T + 4He → 6Li + n[8.4 MeV]

He + 4He → 6Li + p[7.0 MeV]

3② He4 – He4 collision
He + 4He → 6Li, 7Li, 7Be + ...

4

Massive particle X
Upper bounds on mx Yx in both photodissociationand "hadrodissociation" scenario

Yx ≡ nx / s

Kawasaki, Kohri, Moroi (04)Mildobservational
upper boundMildobservational
upper boundNeutralino (bino) LSP and gravitino“NLSP”

Upper bound on reheating temperature
in case of gravitino NLSP and neutralino
Kawasaki, Kohri, Moroi, Yotsuyanagi (08)
LSP scenario
TR ≈ 109 GeV (Y3/ 2 /10 −12 )τ ∼ 106 sec(m3 / 2 /102 GeV)-3Yx ≡ nx / s

Neutralino (bino) NLSP and gravitino LSPGravitino LSP and thermally porduced
neutralino (Bino) “NLSP” scenario
Feng, Su, and Takayama (03)Lifetimeτ ∼ m m pl / mNLSP
23/2

2Relic abundancemB = 100GeV

5Steffen (06)Kawasaki, Kohri, Moroi, Yotsuyanagi (08)No allowed region forDM density