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We calculate the neutrino mass matrix up to one loop order in the MSSMwithout R-parity, including the bilinears in the mass insertion approximation.This introduces additional diagrams usually neglected in the literature. Wesystematically consider the possible new diagrams, and find a few missing fromour previous work. We provide analytic expressions for the mass matrix elementsin the neutrino flavour basis, which are independent of the $H_d - L_i$ basischoice in the Lagrangian. We compare the contributions from different diagrams,and make ``Lagrangian-basis-independent'' estimates of when the new diagramsneed to be included. We briefly discuss the phenomenology of a toy model ofbilinear R-parity violation.Comment: appendix added about avoiding scale dependent loops; a few sign  change

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Basis independent neutrino masses in the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow><mml:mrow><mml:mi>p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>violating minimal supersymmetric standard model

Basis independent neutrino masses in theRpviolating minimal supersymmetric standard model