A Theoretical Framework for R-parity Violation

TL;DR

The paper proposes a UV-complete mechanism within heterotic Calabi–Yau compactifications that removes renormalizable trilinear R-parity violation via a spontaneously broken U(1) with a SUSY-zero selection rule, avoiding the need for an unbroken discrete symmetry. It finds bilinear RPV terms generically arise at loop level and all dimension-5 RPV operators can appear, with dimension-5 proton decay operators present in the 4+1 model but absent in the 3+2 model; a precise analysis of two illustrative vacua shows how U(1) charges and holomorphy constrain low-energy operators and mixing. The phenomenology focuses on neutrino masses, LSP decays, BBN constraints, and nucleon decay, revealing distinctive bilinear–dimension-5 RPV signatures such as B-L violating neutron decays that can distinguish this framework from conventional SUSY GUTs. This work connects string-theoretic constructions to testable low-energy signatures, offering predictive correlations between neutrino physics, collider signals, and nucleon decay channels that can guide future experiments.

Abstract

We propose a theoretical framework for R-parity violation. It is realized by a class of Calabi--Yau compactification of Heterotic string theory. Trilinear R-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to non-renormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear R-parity violation is generated, but there are good reasons why they are small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All R-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear R-parity violating operators. B-L breaking neutron decay is predicted.

Figures (20)

• Figure 1: Super Feynman diagrams that generate $\mu$-term in the 4+1 model. There are three different kinds of graphs; a pair of multiplets in the 10 and 10 representations of $\mathop{\rm SU}(5)_{\rm GUT}$ are running in the loop (a), those in the $\overline{\bf 10}$ and 5 representations of the $\mathop{\rm SU}(5)_{\rm GUT}$ in the loop (b) (c), and finally, singlets and $\bar{\bf 5}$'s in the loop (d) (e).
• Figure 2: Diagrams which generate $W \ni H({\bf 5})\space H({\bf 5})\space\bar{\bf 5}\space\bar{\bf 5}$ for the 4+1 model (a) and for the 3+2 model (b).
• Figure 3: Dimension-5 proton decay operators in $W \ni {\bf 10}\space{\bf 10}\space{\bf 10}\space\bar{\bf 5}$ are generated by a diagram (a) in the 4+1 model. Although they appear to be generated in the 3+2 model as well through the diagram in (b), it turns out that they are actually not. See the text for explanation.
• Figure 4: Diagrams which produce $K \ni \bar{\bf 5}^\dag\space \bar{H}$ for the 4+1 model (a) and for the 3+2 model (b).
• Figure 5: (a) is a typical diagram for \ref{['eq:5HKahler-41']} in 4+1 model. (b) is a typical diagram for \ref{['eq:5HKahler-32']} in 3+2 model.