[Paper Review] R-parity Conserving Minimal SUSY $B-L$ Model

Nobuchika Okada, Nathan Papapietro|arXiv (Cornell University)|Mar 6, 2016

Particle physics theoretical and experimental studies32 references3 citations

TL;DR

This paper proposes a minimal R-parity-conserving supersymmetric U(1)$_{B-L}$ extension of the MSSM, where one right-handed neutrino superfield (Φ) has even R-parity and its scalar component drives radiative U(1)$_{B-L}$ symmetry breaking via a negative mass squared generated by renormalization group running. The model yields Dirac neutrinos with one massless state and introduces a new dark matter candidate from the mixing of the B-L gaugino and the fermionic component of Φ, while the Z′ boson's invisible decay width can distinguish Dirac from Majorana right-handed neutrinos at the LHC.

ABSTRACT

We propose a simple gauged U(1)$_{B-L}$ extension of the minimal supersymmetric Standard Model (MSSM), where R-parity is conserved as usual in the MSSM. The global $B-L$ (baryon number minus lepton number) symmetry in the MSSM is gauged and three MSSM gauge-singlet chiral multiplets with a unit $B-L$ charge are introduced, ensuring the model free from gauge and gravitational anomalies. We assign an odd R-parity for two of the new chiral multiplets and hence they are identified with the right-handed neutrino superfields, while an even R-parity is assigned to the other one ($Φ$). The scalar component of $Φ$ plays the role of a Higgs field to break the U(1)$_{B-L}$ symmetry through its negative mass squared, which is radiatively generated by the renormalization group running of soft supersymmetry (SUSY) breaking parameters from a high energy. This radiative U(1)$_{B-L}$ symmetry breaking leads to its breaking scale being at the TeV naturally. Because of our novel R-parity assignment, three light neutrinos are Dirac particles with one massless state. Since R-parity is conserved, the lightest neutralino is a prime candidate of the dark matter as usual. In our model, the lightest eigenstate of the mixture of the $B-L$ gaugino and the fermionic component of $Φ$ appears as a new dark matter candidate. We investigate phenomenology of this dark matter particle. We also discuss collider phenomenology of our model. In particular, the $B-L$ gauge boson ($Z'$), once discovered at the Large Hadron Collider, can be a probe to determine the number of (right-handed) Dirac neutrinos with its invisible decay width, in sharp contrast with the conventional $B-L$ extension of the SM or MSSM where the right-handed neutrinos are heavy Majorana particles and decay to the SM leptons.

Motivation & Objective

• To construct a minimal, anomaly-free SUSY extension of the MSSM with gauged U(1)$_{B-L}$ symmetry and R-parity conservation.
• To achieve natural TeV-scale U(1)$_{B-L}$ symmetry breaking via radiative generation of a negative soft mass squared for the R-parity even right-handed sneutrino (Φ).
• To realize Dirac neutrinos with one massless state by assigning odd R-parity to only two of the three right-handed neutrino superfields.
• To identify a new dark matter candidate from the mixing of the B-L gaugino and the fermionic component of Φ, distinct from the lightest neutralino.
• To explore collider phenomenology, particularly the Z′ boson's invisible decay width as a probe of the Dirac nature of light neutrinos.

Proposed method

• Introduce three right-handed neutrino chiral superfields to the MSSM, assigning even R-parity to one (Φ) and odd R-parity to the other two.
• Use the scalar component of Φ as the Higgs field for U(1)$_{B-L}$ symmetry breaking, with its mass squared driven negative by renormalization group evolution of soft SUSY breaking parameters.
• Ensure anomaly freedom by including exactly three chiral multiplets with unit B-L charge, preserving gauge and gravitational anomaly cancellation.
• Construct the superpotential such that Φ does not couple via Dirac Yukawa terms to lepton doublets, preventing Majorana mass terms and ensuring Dirac neutrino masses.
• Perform renormalization group analysis to show that the negative mass squared for Φ's scalar component arises naturally from high-scale soft parameters.
• Compute the relic abundance of the lightest R-parity odd state (χℓ), a mixture of the B-L gaugino and the fermionic component of Φ, and identify a Z′ resonance enhancement for correct dark matter relic density.

Experimental results

Research questions

• RQ1 Can a minimal R-parity-conserving SUSY B-L model be constructed without introducing a separate B-L Higgs field, while ensuring anomaly freedom and natural TeV-scale symmetry breaking?
• RQ2 How does assigning even R-parity to one right-handed neutrino superfield affect the neutrino mass spectrum and the resulting Dirac nature of light neutrinos?
• RQ3 What is the phenomenological signature of the new dark matter candidate formed by mixing the B-L gaugino and the fermionic component of the R-parity even right-handed neutrino?
• RQ4 Can the invisible decay width of the Z′ boson at the LHC distinguish between Dirac and Majorana right-handed neutrinos in this model?
• RQ5 How does the radiative U(1)$_{B-L}$ symmetry breaking mechanism depend on the soft SUSY breaking parameters and their running?

Key findings

• The scalar component of the R-parity even right-handed neutrino superfield (Φ) generates a negative mass squared via renormalization group running, leading to natural U(1)$_{B-L}$ symmetry breaking at the TeV scale.
• The model produces three light neutrinos as Dirac particles, with one massless state, due to the absence of Majorana mass terms and only two Dirac Yukawa couplings.
• A new dark matter candidate emerges as the lightest R-parity odd state, composed of a mixture of the B-L gaugino and the fermionic component of Φ, with its relic abundance naturally reproduced via Z′ boson s-channel resonance when its mass is near half the Z′ mass.
• The invisible decay width of the Z′ boson is sensitive to the number of light right-handed neutrinos: for N(νR)=2, the total width is 12% larger than for N(νR)=0, making it distinguishable at the High-Luminosity LHC with 1000 fb⁻¹ luminosity.
• With mZ′=3.5 TeV and gBL=0.25, the LHC could observe 892 signal events for N(νR)=2 versus 1049 for N(νR)=0 in the invariant mass window MZ′±100 GeV, with a 4–5σ significance difference.
• The model provides a novel probe of Dirac neutrinos at the LHC via precise measurement of the Z′ boson’s invisible decay width, contrasting sharply with conventional B-L models where right-handed neutrinos are heavy Majorana particles.