Gravitino Dark Matter in R-violating SUSY M. Lola MEXT-CT Work with N.E.Bomark, P.Osland and A.Raklev

Content  Dark Matter: Is observable R-violation compatible with SUSY DM?  Gravitino decays in R-violating SUSY  Couplings & Flavour Effects  Link to Lepton flavour violation: R-violation versus MSSM  Conclusions

In addition to couplings generating fermion masses, also - These violate lepton and baryon number - If simultaneously present, unacceptable p decay Motivation for R-violating supersymmetry

X Either kill all couplings via R-parity (SM: +1, SUSY: -1) LSP: stable, dark matter candidate Colliders: Missing energy Or allow subsets by baryon / lepton parities LSP: unstable – lose (?) a dark matter candidate Colliders: Multi-lepton/jet events Ways out:

- If LSP a gravitino, its decays very suppressed by Mp - The lighter the gravitino, the longer the lifetime Questions: can gravitinos be DM even with broken R-parity? Can we hope for BOTH DM AND R-violation in colliders? Answer: depends on how gravitinos decay under R-violation Gravitino DM in R-violating supersymmetry?

3-body trilinear R-violating decays Chemtob, Moreau Suppressed by: - Gravitino vertex (~1/Mp) -Phase space / fermion masses (for light gravitino and heavy fermions)

2-body bi-linear R-violating decays Takayama, Yamaguchi Buchmuler et al. Suppressed by: - Gravitino vertex (~1/Mp) -Neutralino-neutrino mixing (model dependent)

Radiative 2-body trilinear R-violating decays SL, P. Osland, A. Raklev Suppressed by: - Gravitino vertex (~1/Mp) - Loop factors (~ fermion mass)

Radiative decays dominate for:  Smaller gravitino masses  R and L violation via operators of the 3 rd generation  Small neutrino-neutralino mixing Large gravitino lifetime (can be DM), due to:  Gravitational suppression of its couplings  Smallness of R-violating vertices  Loop, phase space, or mixing effects Maximum stability (neither radiative nor tree-level decays)!

Radiative versus 3-body decays Couplings ~10^(-4) for consistency with the photon spectrum

NLSP decays - No source of suppression other than R-violating couplings - Decay well before BBN compatible with gravitino DM

R-violating signals: couplings & LSP decays Ordinary MSSM neutralino coupling Neutr. Decays to 3 SM particles R-parity violating coupling

(i.e. Why the top mass so much larger than all others?)  Invariance under symmetry determines mass hierarchies Link to Flavour Effects in Fermion Masses Charges such that only Top-coupling 0 flavour charge X All others forbidden, only appear in higher orders Higher charge (lower generation) implies larger suppression

Flavour effects If Z 3 not flavour-blind, could chose even subsets within - SM symmetries allow 45 R-violating operators - Lepton & Baryon Parities forbid subsets of them Baryon Parity: only Lepton Parity: only Bilinear R-violation allowed -Bilinear R-violation forbidden -μ term i.e. by Giudice-Masiero mech. -or Hall, Lykken, Weinberg mech.

An example (King, Ross)  R-violating couplings of 3 rd generation (leading to large radiative decays) naturally higher

Neutrinos in R-violating SUSY 1-loop neutrino mass contributions:

R-violation: Correlated Rates depending on coupling combinations (A. de Gouvea, S.L, K. Tobe) To be compared with 160 and 0.92 in MSSM (where on shell photon penguin dominates)

Different picture in SUSY!

For all processes at loop level:

For:

Conclusions R-violating SUSY equally motivated with MSSM Interesting signals but also strong bounds Possible to have both gravitino DM AND observable R-violation in colliders Results sensitive to flavour effects Probe Flavour Structure of Fundamental Theory