Effects of physics beyond the standard model on the neutrino charge radius: an effective Lagrangian approach

TL;DR

This paper investigates how physics beyond the Standard Model, through an effective Lagrangian approach, affects the neutrino charge radius and electromagnetic form factors, finding that new contributions are finite, gauge independent, and smaller than Standard Model predictions.

Contribution

It introduces a gauge-invariant, finite one-loop level correction to neutrino electromagnetic form factors from nonrenormalizable effective operators, extending the Standard Model analysis.

Findings

Additional contributions to neutrino charge radius are gauge independent and finite.

New physics effects reduce the neutrino charge radius by an order of magnitude.

The relation between charge radius and anapole moment remains valid with new physics.

Abstract

In this work, we look for possible new physics effects on the electromagnetic charge and anapole form factors, $f_Q(q^2)$ and $f_A(q^2)$, for a massless Dirac neutrino, when these quantities are calculated in the context of an effective electroweak Yang-Mills theory, which induces the most general $SU_L(2)$--invariant Lorentz tensor structure of nonrenormalizable type for the $WW\gamma$ vertex. It is found that in this context, besides the standard model contribution, the additional contribution to $f_{Q}(q^2)$ and $f_{A}(q^2)$ ($f_{Q}^{O_W}(q^2)$ and $f_{A}^{O_W}(q^2)$, respectively) are gauge independent and finite functions of $q^2$ after adopting a renormalization scheme. These form factors, $f_{Q}^{O_W}(q^2)$ and $f_{A}^{O_W}(q^2)$, get contribution at the one loop level only from the proper neutrino electromagnetic vertex. Besides, the relation $f_{Q}^{eff}(q^2)=q^2f_{A}^{eff}(q^2)$ ($f_{Q}^{eff}(q^2)=f_{Q}^{SM}(q^2)+f_{Q}^{O_W}(q^2)$, $f_{A}^{eff}(q^2)=f_{A}^{SM}(q^2)+f_{A}^{O_W}(q^2)$) is still fulfilled and hence the relation $a_{\nu}^{eff} = < r^2_{\nu} > ^{eff} /6$ ($a_{\nu}^{eff} = a_{\nu}^{SM}+ a_{\nu}^{O_W}$, $<r^2_{\nu} > ^{eff} = < r^2_{\nu} > ^{SM}+< r^2_{\nu} > ^{O_W}$)is gotten, just as in the SM. Using the experimental constraint on the anomalous $WW\gamma$ vertex, a value for the additional contribution to the charge radius of $|< r^2_{\nu} >^{O_W}| \lsim 10^{-34} cm^2$ is obtained, which is one order of magnitude lower than the SM value.