Testing the scalar sector of the Standard-Model Extension with neutron gravity experiments

TL;DR

This paper investigates how spontaneous Lorentz symmetry breaking in the scalar sector of the Standard-Model Extension affects gravitational quantum states of ultracold neutrons, using experimental data to set bounds on symmetry-breaking parameters.

Contribution

It derives an effective Hamiltonian for neutrons under Lorentz violation and uses experimental results to constrain the symmetry-breaking parameters.

Findings

Established upper bounds on Lorentz-violating parameters from neutron gravity experiments.

Derived the effective Hamiltonian describing neutrons in a Lorentz-violating gravitational field.

Analyzed gravity-induced interference patterns to test Lorentz invariance.

Abstract

In the present study we analyse, within the scalar sector of the Standard-Model Extension (SME) framework, the influence of a spontaneous Lorentz symmetry breaking on gravitational quantum states of ultracold neutrons. The model is framed according to the laboratory conditions of the recent high-sensitivity GRANIT and $q$Bounce experiments. The high-precision data achieved in such experiments allow us to set bounds on the symmetry breaking parameters of the model. The effective Hamiltonian governing the neutron's motion along the axis of free fall is derived explicitly. It describes a particle in a gravitational field with an effective gravitational constant controlled non-trivially by the Lorentz-violating parameters. In particular, using the exact wave functions and the energy spectrum, we evaluate both the heights associated with the quantum states and the transition frequencies between neighborhoring quantum states. By comparing our theoretical results with those reported in the GRANIT and the $q$Bounce experiments, upper bounds on the Lorentz-violating parameters are determined. We also consider for the first time the gravity-induced interference pattern in a COW-type experiment to test Lorenz-invariance. In this case, an upper bound for the parameters is established as well.