Neutrino Lorentz invariance violation from the \(\textit{CPT}\)-even SME coefficients through a tensor interaction with cosmological scalar fields

Numerous non-standard interactions between neutrinos and scalar fields have been suggested in the literature. In this work, we have outlined the case of tensorial neutrino non-standard interactions with scalar fields, which can be related to the effective \(\textit{CPT}\)-even dimension-4 operators of the Standard Model Extension (SME). We illustrate how bounds placed on these parameters can be associated with limits on the energy scale of the proposed neutrino interactions with cosmic scalars. Besides, as a case study, we employ a DUNE-like experimental configuration to assess the projected sensitivities to the \(\textit{CPT}\)-even isotropic \(c_{\alpha \beta }\) and Z-spatial \(c_{\alpha \beta }^{ZZ}\) SME coefficients. For the case of the isotropic SME coefficients, an upper limit on the energy scale of the interaction can be placed. The current IceCube experiment and upcoming neutrino experiments such as DUNE, KM3NeT, IceCube-Gen2, and GRAND proposals, may clarify these classes of neutrino non-standard interactions.