Neutrino oscillation in a minimal length spacetime

Abstract

We investigate how neutrino oscillations are modified in a non-commutative spacetime characterized by a minimal length scale, described by the Quesne-Tkachuk algebra. By incorporating the algebra's deformation parameter $\beta$ into the effective neutrino mass, we derive the 2-flavor oscillation probability in this non-commutative setting. The resulting probability depends not only on the usual mass-squared difference but also on a fourth-order mass difference scaled by $\beta$. A comparison between the standard and non-commutative oscillation probabilities reveals a beat pattern arising from the additional non-commutative phase, which induces a small shift in the oscillation profiles. Finally, we extend our analysis to include the effects of a magnetic field on neutrino propagation.