We show that discovery of baryon number violation in two processes with at least one obeying the selection rule Delta (B-L) = pm 2 can determine the Majorana character of neutrinos. Thus observing p to e^+ pi^0 and n to e^- pi^0 decays, or p to e^+ p
i^0 and n-nbar oscillations, or n to e^- pi^+ and n-nbar oscillations would establish that neutrinos are Majorana particles. We discuss this in a model-independent effective operator approach.
This report, prepared for the Community Planning Study - Snowmass 2013 - summarizes the theoretical motivations and the experimental efforts to search for baryon number violation, focussing on nucleon decay and neutron-antineutron oscillations. Prese
nt and future nucleon decay search experiments using large underground detectors, as well as planned neutron-antineutron oscillation search experiments with free neutron beams are highlighted.
We investigate the effects of messenger-matter mixing on the lightest CP-even Higgs boson mass m_h in gauge-mediated supersymmetry breaking models. It is shown that with such mixings m_h can be raised to about 125 GeV, even when the superparticles ha
ve sub-TeV masses, and when the gravitino has a cosmologically preferred sub-keV mass. In minimal gauge mediation without messenger-matter mixing, realizing m_h = 125 GeV would require multi-TeV SUSY spectrum. The increase in $m_h$ due to messenger-matter mixing is maximal in the case of messengers belonging to 10+bar{10} of SU(5) unification, while it is still significant when they belong to $5+bar{5}$ of SU(5). Our results are compatible with gauge coupling unification, perturbativity, and the unification of messenger Yukawa couplings. We embed these models into a grand unification framework with a U(1) flavor symmetry that addresses the fermion mass hierarchy and generates naturally large neutrino mixing angles. While SUSY mediated flavor changing processes are sufficiently suppressed in such an embedding, small new contributions to K^0-bar{K^0} mixing can resolve the apparent discrepancy in the CP asymmetry parameters sin2beta and epsilon_K.
