Gravitino Dark Matter & R-Parity Violation M. Lola MEXT-CT (work with P. Osland and A. Raklev) Prospects for the detection of Dark Matter Spain, September 2007 (ENTAPP)

 Neutralinos  Gravitinos  Sneutrinos  Axinos Severe constraints to allowed parameter space by combined studies of  BBN and NLSP decays  LEP data  Direct Searches SUSY (MSSM) Dark Matter Candidates

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

R-violating couplings & LSP decays R-violating couplings & LSP decays

- 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 LSP 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 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

Lifetime versus SUSY masses

Max allowed couplings (photon spectra & DM considerations)

Photon Spectra (bilinear R-violation) - Non-shaded area compatible with photon spectra - Possible solution to EGRET data for gravitinos ≥ 5 GeV (Takayama, Yamaguchi)

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

-SM symmetries allow 45 R-violating operators - Lepton & Baryon Parities forbid subsets of them Lepton Parity: only Baryon Parity: only Flavour effects If Z3 not flavour-blind, could chose even subsets within

(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

An example (King, Ross)  R-violating couplings of 3 rd generation (leading to large radiative decays) naturally higher  Mixing effects important & can affect decays

Conclusions Significant parameter space where radiative decays dominate over tree-body ones Lifetime long enough for gravitino DM AND observable R-violation in colliders NLSP decays easily compatible with BBN Photon spectrum consistent with measurements Results sensitive to flavour effects Probe Flavour Structure of Fundamental Theory