Effects of CPT violation on the neutrino charge radius in the Standard Model Extension

Abstract

CPT-odd effects on the neutrino charge radius are studied within the Standard Model Extension. We consider CPT violation from the electroweak Yang-Mills sector, characterized by Lorentz-violating coefficients $(k_1{)}_{\mu }$ and $(k_2{)}_{\mu }$, which have positive mass units. The $\bar{\nu }\nu \gamma$ vertex arises at tree level via exchange of two $Z$ bosons. Although suppressed by $\frac{1}{m_Z^4}$, this process is notable. The vertex function ${\Gamma }_{\mu }$ includes three independent gauge structures satisfying the Ward identity $q^{\mu }{\Gamma }_{\mu }=0$, characteristic of neutral particles, and induces gauge-independent electromagnetic form factors. Besides charge and anapole, two novel form factors appear. The charge form factor $f_Q(q^2)$ contains an energy-dependent term causing $f_Q(0)\ne 0$, so electromagnetic properties are undefined for real photons with CPT violation. Instead, $f_Q$ and the charge radius are defined in the static limit: $q^0=0$ and $\mathbf{q}\to 0$. Here, $f_Q(0,0)=0$ and a correction to the SM neutrino charge radius is found: \[ \langle r^2_ν\rangle_{CPTV} = \frac{3c_{2W}}{2c_W^4} \left[\frac{k_2^2}{m_Z^2} + \frac{\mathbf{k}_2^2}{m_Z^2}\cos^2θ_γ\right] \frac{1}{m_Z^2}, \] with ${\theta }_{\gamma }$ the angle between $\mathbf{q}$ and ${\mathbf{k}}_2$. Using recent bounds on $(k_i{)}_{\mu }$ and reasonable assumptions, we obtain a small correction $⟨r_{\nu }^2{⟩}_{CPTV}\le 0.83\times 10^{-51}{\mathrm{cm}}^2$.

12 pages, 2 figures