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

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 $WW\gamma$ 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 $f_Q^{eff}(q^2)=q^2{f}_A^{eff}(q^2)$ ($f_Q^{eff}(q^2)=f_Q^{SM}(q^2)+f_Q^{O_W}(q^2)$, $f_A^{eff}(q^2)=f_A^{SM}(q^2)+f_A^{O_W}(q^2)$) is still fulfilled and hence the relation $a_{\nu }^{eff}=<r_{\nu }^2{>}^{eff}\mathrm{/}6$ ($a_{\nu}^{eff} = a_{\nu}^{SM}+ a_{\nu}^{O_W}$,$<r^2_{\nu} > ^{eff} = < r^2_{\nu} > ^{SM}+< r^2_{\nu} > ^{O_W}$)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.