The R-Parity Violating Minimal Supergravity Model

TL;DR

This work extends the mSUGRA framework to include general R-parity violation, focusing on lepton-number violating interactions and their implications. It provides a complete one-loop RGE treatment for RpV-MSSM, a robust iterative approach to radiative EWSB with a multi-doublet scalar potential, and a full mass spectrum including neutrino-neutralino and sneutrino mixing. By linking neutrino masses to RpV couplings, the paper derives stringent bounds on λ, λ', and λ'' that can exceed previous limits by several orders of magnitude for specific SPS points, notably SPS1a. A key finding is that the LSP need not be the neutralino; scenarios with a stau or tau-sneutrino LSP yield distinct collider signatures, including potential detached vertices and multilepton/tau-rich events. Overall, RpV-mSUGRA is shown to be a viable, testable alternative to RPC SUSY with deep connections to neutrino physics and collider phenomenology.

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 formule 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.

Figures (8)

• Figure 1: Upper bound upon ${\bf \lambda}'_{333}(M_{GUT})$ as a function of no-scale mSUGRA parameter point, assuming all quark mixing resides in the down sector at the weak scale. The background colour displays the bound as measured by the bar on the right hand side. Contours of iso-bound are also shown. In the top left-hand white region there is no tachyon-free model for any value of the coupling.
• Figure 2: Upper bound upon ${\bf \lambda}_{231}(M_{GUT})$ as a function of no-scale mSUGRA parameter point. The background colour displays the bound as measured by the bar on the right hand side. Contours of iso-bound are also shown. In the top left-hand white region there is no tachyon-free model for any value of the coupling.
• Figure 3: No-scale supergravity in the R-parity conserved limit. Labeled constraints coming from tachyons are shown. The background colour displays the LSP mass, which can be read off from the bar on the right hand side. Dashed contours are contours of lightest Higgs mass. The white line delineates the labeled regions of $\tilde{\tau}$ LSP and $\chi_1^0$ LSP.
• Figure 4: LSP content of no-scale mSUGRA for $M_{1/2}=500$ GeV, ${\bf \lambda}_{231}$ non-zero at $M_{GUT}$ and weak-scale mixing entirely in the down quarks. The mass of the LSP is displayed in the background and corresponds to the bar on the right hand side. Regions ruled out by the presence of tachyons are in black. The white line delineates labeled regions of different LSP content (e for selectrons and $\tau$ for staus). The dashed lines display contours of equal lightest Higgs mass.
• Figure 5: LSP content of no-scale mSUGRA for $M_{1/2}=500$ GeV, ${\bf \lambda}'_{231}$ non-zero at $M_{GUT}$ and weak-scale mixing entirely in the up quarks. The logarithm of the mass of the heaviest neutrino is displayed in the background and corresponds to the bar on the right-hand side. Regions ruled out by the presence of tachyons are in black. The white line delineates labeled regions of different LSP content. The dashed lines display contours of equal lightest Higgs mass.