Gravitino Dark Matter Gravitino Dark Matter & R-Parity Violation& R-Parity Violation

M. Lola MEXT-CT-2004-014297

(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 CandidatesSUSY (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 supersymmetryR-violating supersymmetry

R-violating couplings & LSP decaysR-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?Gravitino LSP in R-violating supersymmetry?

3-body trilinear R-violating decays3-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 2-body bi-linear R-violating decays

Takayama, YamaguchiBuchmuler et al.

Suppressed by:

- Gravitino vertex (~1/Mp)

-Neutralino-neutrino mixing

(model dependent)

Radiative 2-body trilinear R-violating decaysRadiative 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 3rd 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 decaysRadiative versus 3-body decays

Lifetime versus SUSY massesLifetime versus SUSY masses

Max allowed couplings Max allowed couplings (photon spectra & DM considerations)(photon spectra & DM considerations)

Photon Spectra Photon Spectra (bilinear R-violation)(bilinear R-violation)

- Non-shaded area compatible with photon spectra

- Possible solution to EGRET data for gravitinos ≥ 5 GeV

(Takayama, Yamaguchi)

NLSP decaysNLSP 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 effectsFlavour 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 Link to Flavour Effects in Fermion Masses 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 3rd generation

(leading to large radiative decays) naturally higher

Mixing effects important & can affect decays

ConclusionsConclusions

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