Constraints on a noncommutative physics scale with neutrino-electron scattering

Neutrino-electron scatterings ($\nu -e$) are purely leptonic processes with robust standard model predictions. Their measurements can therefore provide constraints to physics beyond the standard model. Noncommutative (NC) field theories modify space-time commutation relations, and allow neutrino electromagnetic couplings at the tree level. Their contribution to the neutrino-electron scattering cross section was derived. Constraints were placed on the NC scale parameter ${\Lambda }_{\mathrm{NC}}$ from $\nu -e$ experiments with reactor and accelerator neutrinos. The most stringent limit of ${\Lambda }_{\mathrm{NC}}>3.3\mathrm{TeV}$ at 95% confidence level improves over the direct bounds from collider experiments.

Figure 1

Schematic diagram of $\nu -e$ scattering via virtual photon exchange in noncommutative space-time, where $\alpha =e$, $\mu$, $\tau$ denotes the flavor state, while $k$ and $p$ ($k^{\prime }$ and $p^{\prime }$) are the initial (final) four-momenta of the neutrino probe and electron target, respectively. The NC coupling is given in Eq. (6) while ${\theta }^{\mu \nu \rho }$ is defined in Eq. (7).

Figure 2

Differential cross sections averaged over the neutrino spectra as a function of the recoil energy for (a) Top: TEXONO experiment with reactor ${\overline{\nu }}_{\mathrm{e}}$ [5, 42], (b) Middle: LSND experiment with ${\nu }_{\mathrm{e}}$ from stopped-pion [43], and (c) Bottom: CHARM-II experiment with accelerator ${\nu }_{\mu }({\overline{\nu }}_{\mu })$ [44]. Both SM and NC contributions are displayed.