Upper bound on all products of R-parity violating couplings ${\lambda }^{\prime }$ and ${\lambda }^{\prime \prime }$ from proton decay

Abstract

We prove that {\em any} product of R-parity violating couplings ${\lambda }^{\prime }$ (L-violating) and ${\lambda }^{\prime \prime }$ (B-violating) can be strongly restricted by proton decay data. For any pair ${\lambda }^{\prime }$ and ${\lambda }^{\prime \prime }$ the decay exists at least at one loop level. For squark masses below 1 TeV we find the conservative bounds $|{\lambda }^{\prime }\cdot {\lambda }^{\prime \prime }|<10^{-9}$ in absence of squark flavor mixing, and $|{\lambda }^{\prime }\cdot {\lambda }^{\prime \prime }|<10^{-11}$ when this mixing is taken into account. We study the dependence of the bounds on the flavor basis in which R-parity breaking couplings are determined.

Comments: LaTeX, 13 pages, 2 LaTeX figures