Lorentz violation in neutron decay and allowed nuclear<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>β</mml:mi></mml:math>decay

Abstract

Background: The search for violations of Lorentz invariance is nowadays motivated by attempts to unify the standard model of particle physics with general relativity. Such theories of ``quantum gravity'' predict Lorentz-violating signals that could be detected in low-energy precision experiments. In this context, Lorentz invariance has been tested poorly in the weak interaction.Purpose: We explore the possibility that the weak interaction violates Lorentz, and in particular rotational, invariance in neutron and allowed nuclear $\ensuremath{\beta}$ decay.Method: A broad class of Lorentz-violating effects is considered in an effective field theory approach, wherein the standard propagator of the $W$ boson acquires an additional Lorentz-violating tensor.Results: The general decay rate for allowed $\ensuremath{\beta}$ decay that incorporates the modified $W$-boson propagator is derived. The resulting Lorentz-violating signals are discussed for the different types of $\ensuremath{\beta}$-decay transitions: Fermi, Gamow-Teller, and mixed. We study the implications of our formalism for dedicated $\ensuremath{\beta}$-decay experiments. We give a short overview of the few relevant experiments that have been performed in the past or are ongoing.Conclusions: Our work provides a general theoretical framework that should be used for designing and interpreting $\ensuremath{\beta}$-decay experiments that search for Lorentz violation. In particular, it determines the kind of experiments that are necessary to probe different parameters that quantify Lorentz violation, and it establishes their sensitivity.