[Paper Review] U(1)_B-L: Neutrino Physics and Inflation

V. N. Şenoğuz, Qaisar Shafi|ArXiv.org|Dec 13, 2005

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes a supersymmetric $U(1)_{B-L}$ extension of the MSSM that unifies neutrino mass generation, inflation, and leptogenesis via a gauged $U(1)_{B-L}$ symmetry broken at $\sim10^{16}$ GeV. The seesaw mechanism explains light neutrino masses, while inflation driven by the inflaton field $S$ yields a scalar spectral index $n_s = 0.99 \pm 0.01$ and negligible tensor-to-scalar ratio, consistent with CMB observations.

ABSTRACT

A gauged U(1)_B-L symmetry predicts three right handed handed neutrinos and its spontaneous breaking automatically yields the seesaw mechanism. In a supersymmetric setting this breaking can be nicely linked with inflation to yield deltaT/ T proportional to (M_B-L / M_P)^2, where M_B-L (M_P) denote the B-L breaking (Planck) scale. Thus M_B-L is estimated to be of order 10^16 GeV, and the heaviest right handed neutrino mass is less than or of order 10^14 GeV. A second right handed neutrino turns out to have a mass of order 10-10^2 T_r, where T_r (=0.97. The tensor to scalar ratio r is negligible, and dn_s/dlnk

Motivation & Objective

• To unify neutrino mass generation, inflation, and leptogenesis within a supersymmetric $U(1)_{B-L}$ extension of the MSSM.
• To determine the $B-L$ breaking scale $M_{B-L}$ using inflationary constraints from CMB anisotropy $\delta T/T$.
• To resolve the MSSM $\mu$-problem and suppress dimension-five proton decay via a $U(1)_R$ symmetry.
• To ensure compatibility of reheating temperature $T_r$ with successful leptogenesis and gravitino constraints.

Proposed method

• Implementing supersymmetric hybrid inflation using a gauge singlet superfield $S$ and a pair $\Phi, \overline{\Phi}$ transforming under $U(1)_{B-L}$, with superpotential $W = \kappa S(\Phi\overline{\Phi} - M^2)$.
• Using a $U(1)_R$ R-symmetry to forbid the $\mu$-term at the renormalizable level and allow its dynamical generation via $\langle S \rangle$ after inflation.
• Computing the effective potential with one-loop radiative corrections including logarithmic terms dependent on $\kappa$, $M$, and $S$.
• Deriving the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ from the inflationary potential, including SUGRA corrections.
• Relating the reheating temperature $T_r$ to the inflaton decay width $\Gamma_h \propto \lambda^2 m_\chi$, with $\lambda$ from the $\lambda S h^2$ term.
• Using the $Z_2$ subgroup of $U(1)_R$ as matter parity to suppress dimension-five proton decay and stabilize the LSP.

Experimental results

Research questions

• RQ1 What is the $B-L$ breaking scale $M_{B-L}$ constrained by inflationary CMB anisotropy $\delta T/T$?
• RQ2 How can the MSSM $\mu$-problem be resolved within a supersymmetric $U(1)_{B-L}$ model with dynamical $\mu$-term generation?
• RQ3 What is the role of the $U(1)_R$ symmetry in enabling inflation, suppressing proton decay, and stabilizing the LSP?
• RQ4 What are the viable ranges of reheating temperature $T_r$ and inflaton coupling $\kappa$ consistent with leptogenesis and gravitino constraints?
• RQ5 How do the scalar spectral index $n_s$ and tensor-to-scalar ratio $r$ depend on the model parameters in hybrid and smooth hybrid inflation?

Key findings

• The $B-L$ breaking scale is constrained to $M_{B-L} \sim 10^{16}$ GeV, consistent with the seesaw mechanism and the observed $\delta T/T$ from CMB anisotropy.
• The scalar spectral index is predicted to be $n_s = 0.99 \pm 0.01$ for the simplest models, with $r \ll 1$ and $dn_s/d\ln k \lesssim 10^{-3}$.
• For smooth hybrid inflation, $n_s \geq 0.97$, and the tensor-to-scalar ratio remains negligible.
• The reheating temperature $T_r$ is bounded below by $2 \times 10^7$ GeV (hybrid) to $4 \times 10^9$ GeV (smooth), depending on model details and $\lambda$ coupling.
• The inclusion of $\lambda S h^2$ in the superpotential increases $T_r$ significantly, with $T_r \gtrsim 4 \times 10^8$ GeV for hybrid inflation and $\gtrsim 10^{12}$ GeV for smooth hybrid inflation.
• The heaviest right-handed neutrino mass is estimated to be $\lesssim 10^{14}$ GeV, while a second right-handed neutrino has mass $\sim 10-10^2$ times $T_r$.