No abstract

We present the minimal supersymmetric standard model with general broken R-parity, focusing on minimal supergravity (mSUGRA). We discuss the origins of lepton number violation in supersymmetry. We have computed the full set of coupled one-loop renormalization group equations for the gauge couplings, the superpotential parameters and for all the soft supersymmetry breaking parameters. We provide analytic formulae for the scalar potential minimization conditions which may be iterated to arbitrary precision. We compute the low-energy spectrum of the superparticles and the neutrinos as a function of the small set of parameters at the unification scale in the general basis. Specializing to mSUGRA, we use the neutrino masses to set new bounds on the R-parity violating couplings. These bounds are up-to five orders of magnitude stricter than the previously existing ones. In addition, new bounds on the R-parity violating couplings are also derived demanding a non-tachyonic sneutrino spectrum. We investigate the nature of the lightest supersymmetric particle and find extensive regions in parameter space, where it is not the neutralino. This leads to a novel set of supersymmetric signatures, which we classify.

We analyse bounds on trilinear R-parity violating couplings at the unification scale by renormalising the weak scale bounds. We derive unification scale upper bounds upon the couplings which are broadly independent of the fermion mass texture assumed. The R-parity violating couplings are factors of two to five more severely bounded at the unification scale than at the electroweak scale. In the presence of quark mixing, a few of the bounds are orders of magnitude stronger than their weak scale counterparts due to new R-parity violating operators being induced in the renormalisation between high and low scales. These induced bounds are fermion mass texture dependent. New bounds upon the weak scale couplings are obtained by the requirement of perturbativity between the weak and unification scales. A comprehensive set of the latest limits is included.

We complete the effective potential calculation of the two-loop, top/bottom Yukawa corrections to the Higgs boson masses in the Minimal Supersymmetric Standard Model, by computing the O(α 2 t + α t α b + α 2 b ) contributions for arbitrary values of the bottom Yukawa coupling. We also compute the corrections to the minimization conditions of the effective potential at the same perturbative order. Our results extend the existing O(α 2 t ) calculation, and are relevant in regions of the parameter space corresponding to tan β ≫ 1. We extend to the Yukawa corrections a convenient renormalization scheme, previously proposed for the O(α b α s ) corrections, that avoids unphysically large threshold effects associated with the bottom mass and absorbs the bulk of the corrections into the one-loop expression. For large values of tan β, the new contributions can account for a variation of several GeV in the lightest Higgs boson mass.

We study the O(α t α s +α 2 t ) two-loop corrections to the minimization conditions of the MSSM effective potential, providing compact analytical formulae for the Higgs tadpoles. We connect these results with the renormalization group running of the MSSM parameters from the grand unification scale down to the weak scale, and discuss the corrections to the Higgs mixing parameter µ and to the running CP-odd Higgs mass m A in various scenarios of gravitymediated SUSY breaking. We find that the O(α t α s ) and O(α 2 t ) contributions partially cancel each other in the minimization conditions. In comparison with the full one-loop corrections, the O(α t α s + α 2 t ) two-loop corrections significantly weaken the dependence of the parameters µ and m A on the renormalization scale at which the effective potential is minimized. The residual two-loop and higher-order corrections to µ and m A are estimated to be at most 1% in the considered scenarios.