Neutrino Lorentz invariance violation from the 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 CPT-even dimension-4 operators of the Standard Model Extension (SME). Moreover, in this paper, we have mostly analyzed the projected sensitivities to the CPT-even isotropic $c_{\alpha \beta}$ and $Z-$spatial $c_{\alpha \beta}^{ZZ}$ SME coefficients, in the context of a long-baseline experimental configuration. We study the particular case of DUNE and show its sensitivity to this type of new physics. The current IceCube experiment and upcoming neutrino experiments such as KM3NeT, IceCube-Gen2, and GRAND proposals may clarify these classes of neutrino non-standard interactions.