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

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 $S{U}_{L}(2)$-invariant Lorentz tensor structure of nonrenormalizable type for the $WW\ensuremath{\gamma}$ 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 ${f}_{Q}^{\mathrm{eff}}({q}^{2})={q}^{2}{f}_{A}^{\mathrm{eff}}({q}^{2})$ (${f}_{Q}^{\mathrm{eff}}({q}^{2})={f}_{Q}^{\mathrm{SM}}({q}^{2})+{f}_{Q}^{{O}_{W}}({q}^{2})$, ${f}_{A}^{\mathrm{eff}}({q}^{2})={f}_{A}^{\mathrm{SM}}({q}^{2})+{f}_{A}^{{O}_{W}}({q}^{2})$) is still fulfilled and hence the relation ${a}_{\ensuremath{\nu}}^{\mathrm{eff}}=⟨{r}_{\ensuremath{\nu}}^{2}{⟩}^{\mathrm{eff}}/6$ (${a}_{\ensuremath{\nu}}^{\mathrm{eff}}={a}_{\ensuremath{\nu}}^{\mathrm{SM}}+{a}_{\ensuremath{\nu}}^{{O}_{W}}$, $⟨{r}_{\ensuremath{\nu}}^{2}{⟩}^{\mathrm{eff}}=⟨{r}_{\ensuremath{\nu}}^{2}{⟩}^{\mathrm{SM}}+⟨{r}_{\ensuremath{\nu}}^{2}{⟩}^{{O}_{W}}$) is gotten, just as in the standard model (SM). Using the experimental constraint on the anomalous $WW\ensuremath{\gamma}$ vertex, a value for the additional contribution to the charge radius of $|⟨{r}_{\ensuremath{\nu}}^{2}{⟩}^{{O}_{W}}|\ensuremath{\lesssim}{10}^{\ensuremath{-}34}\text{ }\text{ }{\mathrm{cm}}^{2}$ is obtained, which is 1 order of magnitude lower than the SM value.