Effect of minimal length uncertainty on neutrino oscillation

Abstract

In this paper, we study the effect of the minimal length on neutrino oscillation in a static magnetic field. In the framework of the generalized uncertainty principle, we reformulate the Hamiltonian for a relativistic neutrino moving in a magnetic field oriented along the z-direction of Cartesian coordinates. Using the modified energy spectrum, we obtain the oscillation probability for different neutrino flavors. In addition, we obtain the energy differences for the neutrino-mass eigenstates. We find that the energy and energy difference depend on the minimal length parameter {\alpha}, and the energy difference becomes independent of {\alpha} when the magnetic field is not present. In addition, we find that the modified probability of oscillation differs from the usual probability of oscillation if a magnetic field is present. Using the current experimental result, we estimate the upper bound on the deformation parameter and the minimal length, and find that the upper bound on the minimal length scale is less than the electroweak scale. If the minimal length is at Planck scale, the minimal length formalism leads to the same result as a quantum theory of gravity with an $SU(2)_{L} \times U(1)$ effective invariant dimension-5 Lagrangian including neutrino and Higgs fields.