Quantum effects on neutrino parameters from a flavored gauge boson

Abstract

We calculate the one-loop renormalization group equations of the neutrino mass matrix when the Standard Model particle content is extended with a massive gauge boson which has family-dependent couplings to the left-handed leptons. We show that quantum effects induced by the extra gauge boson increase the rank of the neutrino mass matrix at the one-loop level, in contrast to the well-known result that Standard Model fields can only increase the rank at the two-loop level. We also discuss the possibility of generating dynamically the measured mass differences and mixing angles between the active neutrinos in scenarios with normal and inverted mass ordering.

Figures (7)

• Figure 1: Scatter plot of the absolute value of the smallest right-handed neutrino mass $|M_1|$ vs. $Z'$ gauge boson mass $M_{Z'}$ from random, uniform scans of $\lambda, \langle S_1 \rangle/\langle S_0 \rangle, \langle S_2 \rangle/\langle S_0 \rangle,$ and $g'$. The values admitting the RGE effect discussed here are below the diagonal with $M_{Z'} = |M_1|$.
• Figure 2: One-loop diagram of $Z'$ giving rise to the $G^T \kappa G$ term in the RGE. The light gray arrow denotes fermion flow used for the calculation, following Denner:1992vza.
• Figure 3: Running of the eigenvalues (left panel) and the mixing angles (right panel) for a scenario where at the cut-off scale $\kappa_3=1$ (in arbitrary units), $\kappa_1=\kappa_2=\kappa_3/100$, $\theta_{12}=15^\circ$, $|\theta_{13}|=10^\circ$, $\theta_{23} = 50^\circ$, and when an $L_\mu-L_\tau$ gauge boson has a mass $M_{Z'}=10^{9}$ GeV and the gauge coupling is $g'=1$.
• Figure 4: Running of the eigenvalues (left panel) and the mixing angles (right panel) for a scenario where at the cut-off scale $\kappa_3=1$ (in arbitrary units), $\kappa_1=\kappa_2=0$, $\theta_{12}= 15^\circ$, $|\theta_{13}|=10^\circ$, $\theta_{23} = 50^\circ$, and when an $L_\mu-L_\tau$ gauge boson has a mass $M_{Z'}=10^{9}$ GeV and the gauge coupling is $g'=1$.
• Figure 5: Same as Fig. \ref{['fig:k1eqk2eqk3_100']}, but for $\kappa_1=-\kappa_2$.