Type III seesaw with R-parity violation in light of mW (CDF)

Motivated by the recently reported measurement of the W boson mass MW=80.4335±0.0094 GeV by the CDF collaboration, we propose a type III seesaw extension of the minimal supersymmetric standard model (MSSM) which also includes an R-parity violating term. Without taking potential SUSY radiative corrections into account, we show that the CDF measurement of MW and the LEP measurement of the ρ parameter can be simultaneously accommodated at the 2σ level. A long-lived gravitino in a few GeV mass range is a unique viable dark matter candidate in this framework.