Gravitino Production from HeaGravitino Production from Heavy Scalar Decayvy Scalar Decay

M. Yamaguchi (Tohoku Univ.)with T. Asaka & S. Nakamura

April 21, 2006 @ SNU, Korea

Refs. Nakamura & MY, hep-ph/0602081 Asaka, Nakamura & MY, hep-ph/0604132See also: Endo, Hamaguchi & Takahashi, hep-ph/0602061 Kawasaki, Takahashi &Yanagida, hep-ph/0603265 Dine, Kitano, Morisse & Shirman, hep-ph/0604140

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Motivations Scalar Decay: important role in cosmology e.g. inflaton, moduli fields

Decay of Scalar reheating of the universe

Unwanted particles may be produced at the same time.

“Gravitino”– Gravitinos produced in thermal bath during reheating– Gravitinos produced directly by scalar decay

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Cosmological Moduli Problem

• Coherent oscillation of moduli fields would dominate the energy density of the universe.

• Late decay reheating of the universe– If mass is TeV, the reheat temperature is too low << 1

MeV !

disaster for big-bang nucleosynthesis (BBN)

Hope: may be OK if moduli is heavy

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heavy moduli?

Heavy moduli seem to be naturally realized in some supersymmetric models,

such as KKLT-type model.

This observation motivates us to investigate moduli decay (and heavy scalar decay in general) very carefully.

Choi-Falkowski-NiIlles-Olechowski 05Endo-MY-Yoshioka 05Choi-Jeong-Okumura 05Falkowski-Lebedev-Mambrini 05

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We realized that some essential properties of the decay have been overlooked (or understood incorrectly) for long time,

including

Decay into gaugino pair

Decay into gravitino pair

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Talk PlanTalk Plan

• Motivations

• Heavy Scalar Decay

• Cosmology– Unstable Gravitino– Stable Gravitino

• Implications

• Conclusions

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Heavy Scalar DecayHeavy Scalar Decay

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Heavy Scalar DecayHeavy Scalar Decay

• Decay into Gauge Bosons/Gauginos

• interaction through gauge kinetic function – S(X): holomorphic function of X

• Decay into gauge boson pair

Nakamura & MY 06

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decay rate

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Decay into Gaugino Pair

most important contribution:

Decay rate

same as the decay into gauge bosons: no suppressionThe result is different from Moroi& Randall.

Nakamura-MY 06Endo-Hamaguchi-Takahashi 06Dine et al 06

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Decay into fermion pair/sfermion pair

• two body decay:– use of eqs. of motion:suppressed by small fermion/sfermion masses

• three body decay e.g.– no mass suppression – suppression from gauge couplings & phase space int

egral

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Decay into Gravitino Pair

Lagrangian (in Planck unit)

chiral tr.

total Kaehler pot.

Note gravitino mass

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Interaction of X to gravitino bi-linear

Auxiliary field (SUSY breaking)

expectation for moduli:

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Decay amplitude

helicity ½ component

decay amplitude into gravitino with helicity ½ component

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For moduli, we expect d3/2 of order unity.

Decay amplitude into helicity ½ is enhanced ~1/m3/2

no such enhancement for helicity 3/2

Decay Rate

Nakamura-MY 06Endo,Hamaguchi,Takahashi 06

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Total decay rate:

Branching ratio to gravitino pair

- expect d3/2 of order unity for moduli

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Evaluation of d3/2　 for general scalar field　 X

scalar potential

derivative of scalar potential

F auxiliary field

Asaka-Nakamura-MY ‘06

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1. Case of spontaneous SUSY breaking

stationary point conditons

Using

we find

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estimation of each term

Note: The above is achieved if, e.g.

For moduli,

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To summarize, we find

The above can apply to moduli inflaton etc.

Remark: Dine et al mass diagonalization between X and Z chance to suppress d3/2 to some degree

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2. Case of Explicit SUSY Breaking

KKLT: SUSY AdS vacuum is uplifted by anti-D3 brane explicit SUSY breaking

Stationary point condition

Vanishing vacuum energy

Choi-Falkowski -Nilles-Olechowski 05Asaka-Nakamura-MY 06

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CosmologyCosmology

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Gravitino Cosmology

• thermal gravitinos– produced in the thermal bath after reheating

cosmological embarassment

unstable gravitino– constraint from big-bang nucleosynthesis– gravitino abundance upperbound on reheat

temperature

Weinberg 82Khlopov-Linde 84Ellis-Kim-Nanopoulos 84Kawasaki-Moroi 95…..

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Constraints from BBN on abundance of unstable graivitinos

Kawasaki-Kohri-Moroi

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stable gravitino– constraint from overclosure of gravitino dark

matter– graviitno abundance upperbound of TR

Pagels-Primack 82Moroi-Murayama-MY 93........

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The case we consider…

• The heavy scalar X once dominates the universe in the form of coherent oscillation.

• X decay reheats the universe

• Gravitino production– thermal: produced in thermal bath at reheating– non-thermal: produced at X decay

• We will show that the non-thermal gravitino production suffers from very severe cosmological constraints

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Constraints we consider:

• Unstable gravitino– BBN constraint on the decay of graviitnos, producing

hadronic &EM showers– Constraint on abundance of LSPs produced at graviti

no decay– Constraint on abundance of LSPs produced directly at

X decay

• Stable gravitino– Constraint on gravitino abundance from overclosure– Constraint on free-streaming of graviitno WDM– BBN constraint on decay of NLSPs into graviitnos

Nakamura-MY 06Asaka-Nakamura-MY 06

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Gravitino Decaytotal decay rate

reheat temperature

decay rate into gravitino pair

branching ratio into gravitino

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• Moduli-like field: dtot ~O(1), d3/2~O(1)

B3/2~O(0.01)

• A general case is discussed in Asaka et al

• Here we mainly describe the case of moduli-like field

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Case of Unstable Gravitino• BBN constraint on graviitno yield:

– thermal gravitinos

– non-thermal gravitinos produced at X decay:

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10-16

10-13

10-1510-14

Y3/2

BBN constraint:

Case with d3/2~O(1) isexcluded if M3/2 <10-100TeV

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case of heavy gravitino• Constraint:

– GravitinoLSP – Overabundance of the LSPs

• Relic abundance of the LSPs– LSPs are produced by gravitino decay– Annihilation of LSPs– Annihilation is not very efficient at low temperature (lat

er epoch) lower bound on the graviitno mass

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case study: LSP=neutral Wino (largest annihilation cross section)

Gravitino mass must beheavier than ~106 GeVto escape overclosureconstraint. (wino case)

Even severer constrainton graviitno mass for other neutralino case

Low energy SUSY maybe disfavored in the presenceof moduli. (unstable gravitino)

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more general caseAsaka-Nakamura-MY 06

10-16

10-13

10-15

10-14 We obtain lower-bound as well as upper-boundon reheat temperature.

Y3/2

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Case of Stable Gravitino

Overclosure constraint

This constraint is less severe than the unstable case.

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Upper Bound on MX (TR)Asaka-Nakamura-MY 06

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Free-streaming of Gravitino Warm Dark Matter

• gravitino: can be warm dark matter– X decay gravitino very energetic– gravitinos loses energy by red-shift, and beco

mes non-relativistic

• Free-streaming of gravitinos: suppresses small scale structure

constraint from observation

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For gravitinos produced by X decay

Note: No constraint on free-streeming if

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Free-streaming constraint(gravitino DM)

Allowed Region exists for moduli-like field!! 　　　　　　　 (a solution to moduli problem)

Asaka-Nakamura-MY 06

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Gravitino WDM region (general case)

BBN constrainton decay ofNLSP (stau)

Asaka-Nakamura-MY 06

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Implications

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ImplicationsCase of Moduli fields (Planck suppressed int./ no particular suppression to decay into gra

vitinos)

Unstable Gravitino Case: almost ruled out by BBN constraint on gravitino decay

Stable Gravitino Case: constraint from overclosure of gravitino dark matter. less stringent some allowed region with

A solution to cosmological moduli problem

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Implications to inflation model building

• modular inflation: (inflaton=moduli) severely constrained

• other inflation scenarios– chaotic inflation

Z2 symmetry FX=0: no dangerous gravitino production– new inflation/hybrid inflation

Gravitino production may be suppressed Model dependent analysis is required

Kawasaki-Takahashi-Yanagida 06

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Conclusions

• Decay of heavy scalar fields was re-examined.– decay into gauginos– decay into gravitinos

• In general, moduli decay into gravitinos is not suppressed. – Recurrence of cosmological moduli/gravitino problem

s in heavy moduli case.

– Unstable gravitino: serious difficulty– Stable graviitno: some allowed region if gravitino is lig

ht and stable.

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• Implications to inflation model building– modular inflation: seems problematic if graviti

no is unstable

– chaotic/new/hybrid inflations • chance to escape constraints (smaller coupling of i

nflaton to gravitino pair)