Gravitino Production from Heavy Scalar Decay M. Yamaguchi (Tohoku Univ.) with T. Asaka & S. Nakamura April 21, SNU, Korea Refs. Nakamura & MY, hep-ph/ Asaka, Nakamura & MY, hep-ph/ See also: Endo, Hamaguchi & Takahashi, hep-ph/ Kawasaki, Takahashi &Yanagida, hep-ph/ Dine, Kitano, Morisse & Shirman, hep-ph/

2 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

3 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

4 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 05 Endo-MY-Yoshioka 05 Choi-Jeong-Okumura 05 Falkowski-Lebedev-Mambrini 05

5 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

6 Talk Plan Motivations Heavy Scalar Decay Cosmology –Unstable Gravitino –Stable Gravitino Implications Conclusions

7 Heavy Scalar Decay

8 Decay into Gauge Bosons/Gauginos interaction through gauge kinetic function –S(X): holomorphic function of X Decay into gauge boson pair Nakamura & MY 06

9 decay rate

10 Decay into Gaugino Pair most important contribution: Decay rate same as the decay into gauge bosons: no suppression The result is different from Moroi& Randall. Nakamura-MY 06 Endo-Hamaguchi -Takahashi 06 Dine et al 06

11 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 integral

12 Decay into Gravitino Pair Lagrangian (in Planck unit) chiral tr. total Kaehler pot. Note gravitino mass

13 Interaction of X to gravitino bi-linear Auxiliary field (SUSY breaking) expectation for moduli:

14 Decay amplitude helicity ½ component decay amplitude into gravitino with helicity ½ component

15 For moduli, we expect d 3/2 of order unity. Decay amplitude into helicity ½ is enhanced ~1/m 3/2 no such enhancement for helicity 3/2 Decay Rate Nakamura-MY 06 Endo,Hamaguchi,Takahashi 06

16 Total decay rate: Branching ratio to gravitino pair - expect d 3/2 of order unity for moduli

17 Evaluation of d 3/2 for general scalar field X scalar potential derivative of scalar potential F auxiliary field Asaka-Nakamura-MY ‘06

18 1. Case of spontaneous SUSY breaking stationary point conditons Using we find

19 estimation of each term Note: The above is achieved if, e.g. For moduli,

20 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 d 3/2 to some degree

21 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 05 Asaka-Nakamura-MY 06

22 Cosmology

23 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 82 Khlopov-Linde 84 Ellis-Kim-Nanopoulos 84 Kawasaki-Moroi 95 …..

24 Constraints from BBN on abundance of unstable graivitinos Kawasaki-Kohri-Moroi

25 stable gravitino –constraint from overclosure of gravitino dark matter –graviitno abundance  upperbound of TR Pagels-Primack 82 Moroi-Murayama-MY

26 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

27 Constraints we consider: Unstable gravitino –BBN constraint on the decay of graviitnos, producing hadronic &EM showers –Constraint on abundance of LSPs produced at gravitino 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 06 Asaka-Nakamura-MY 06

28 Gravitino Decay total decay rate  reheat temperature decay rate into gravitino pair  branching ratio into gravitino

29 Moduli-like field: d tot ~O(1), d 3/2 ~O(1) B 3/2 ~O(0.01) A general case is discussed in Asaka et al Here we mainly describe the case of moduli-like field

30 Case of Unstable Gravitino BBN constraint on graviitno yield: –thermal gravitinos –non-thermal gravitinos produced at X decay:

Y 3/2 BBN constraint: Case with d 3/2 ~O(1) is excluded if M 3/2 <10-100TeV Asaka-Nakamura-MY 06

32 case of heavy gravitino Constraint: –Gravitino  LSP –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 (later epoch)  lower bound on the graviitno mass

33 case study: LSP=neutral Wino (largest annihilation cross section) Gravitino mass must be heavier than ~10 6 GeV to escape overclosure constraint. (wino case) Even severer constraint on graviitno mass for other neutralino case Low energy SUSY may be disfavored in the presence of moduli. (unstable gravitino) Nakamura-MY 06

34 more general case Asaka-Nakamura-MY We obtain lower-bound as well as upper-bound on reheat temperature. Y 3/2

35 Case of Stable Gravitino Overclosure constraint This constraint is less severe than the unstable case.

36 Upper Bound on M X (T R ) Asaka-Nakamura-MY 06

37 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 becomes non-relativistic Free-streaming of gravitinos: suppresses small scale structure  constraint from observation

38 For gravitinos produced by X decay Note: No constraint on free-streeming if

39 Free-streaming constraint (gravitino DM) Allowed Region exists for moduli-like field!! (a solution to moduli problem) Asaka-Nakamura-MY 06

40 Gravitino WDM region (general case) BBN constraint on decay of NLSP (stau) Asaka-Nakamura-MY 06

41 Implications

42 Implications Case of Moduli fields (Planck suppressed int./ no particular suppression to decay into gravitinos) 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

43 Implications to inflation model building modular inflation: (inflaton=moduli) severely constrained other inflation scenarios –chaotic inflation Z 2 symmetry  F X =0: no dangerous gravitino production –new inflation/hybrid inflation Gravitino production may be suppressed  Model dependent analysis is required Kawasaki-Takahashi-Yanagida 06

44 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 problems in heavy moduli case. –Unstable gravitino: serious difficulty –Stable graviitno: some allowed region if gravitino is light and stable.

45 Implications to inflation model building –modular inflation: seems problematic if gravitino is unstable –chaotic/new/hybrid inflations chance to escape constraints (smaller coupling of inflaton to gravitino pair)