New constraints on R-parity violation from \mu-e conversion in nuclei

We derive new constraints on the products of explicitly R-parity violating couplings $\lambda$ and $\lambda'$ in MSSM from searches for \mu-e conversion in nuclei. We concentrate on the loop induced photonic coherent conversion mode. For the combinations $|\lambda\lambda|$ which in \mu-e conversion can be probed only at loop level our constraints are in many cases more stringent than the previous ones due to the enhancement of the process by large $\ln(m^2_f/m^2_{\tilde f}).$ For the combinations of $|\lambda'\lambda'|$ the tree-level \mu-e conversion constraints are usually more restrictive than the loop ones except for two cases which involve the third generation. With the expected improvements in the experimental sensitivity, the \mu-e conversion will become the most stringent test for all the involved combinations of couplings.