Tests of Lorentz invariance using beta decays

Single beta decay
Double beta decay

Given the succesful program of searches for Lorentz violation using neutrino-oscillation experiments, in this paper we explore potential effects of deviations from Lorentz invariance that could arise in beta-decay experiments. Neutrino oscillations are insensitive to many effects that are only observable in decay processes. In fact, we describe a set of operators whose observable effects are absent in neutrino oscillations and neutrino time-of-flight measurements. These operators, that we call countershaded, could produce large relativity violations that have escaped observation to date. Their effects appear only for processes involving the phase space of the neutrino, which motivated the study of beta decay. Furthermore, current efforts for direct measurements of neutrino mass as well as for unraveling the nature of the neutrino (Dirac vs. Majorana) have led to the development of many experiments studying single- and double-beta decays. Precision measurements of weak-interaction parameters using neutron decay are also a worldwide effort these days. These works describe how different beta-decay experiments can be used to search for relativity violations.

Single beta decay

• Tritium decay: the absolute mass scale of the neutrino can be determined by studying the spectrum of tritium decay. The distortion of this spectrum near the endpoint energy constitutes a direct measurement of neutrino mass. In the presence of Lorentz violation, different novel effects appear. For instance, effective-dimension-three operators in the SME can shift the endpoint energy. This shift in the experimental data can be constant and equal for all experiments (isotropic Lorentz violation), constant and orientation dependent, or time dependent (shift changes with sidereal time). Effective-dimension-two operators in the SME produce a modification to the mass parameter determined by the distortion near the endpoint. This means that the mass-squared parameter can depend on the location and orientation of the experiment, can change with sidereal time, and it can even be negative without the neutrino being a tachyon. These effects can be studied using data of completed experiments such as Mainz and Troitsk. In particular, estimations indicate that the KATRIN experiment will have high sensitivity to the unconventional features sumarized above.

• Neutron decay: precision measurement of weak-interaction parameters is an active experimental program. These studies involve the decay of polarized and unpolarized neutrons, which also can be used to search for Lorentz violation. Deviations from exact Lorentz invariance appear as modifications of the spectrum of the beta electrons (which could alter the neutron lifetime) and corrections to the conventional experimental asymmetries used to determine the correlations involving the emitted antineutrino (electron-antineutrino asymmetry ${\color{blue}a}$ and spin-antineutrino asymmetry ${\color{red}B}$). The corrections to these asymmetries include constant shifts and sidereal variations. These effects can be studied by a variety of experiments including aCORN, emiT, nTRV, PERKEO, and UCNA.

Relativity violations and beta decay.
J. S. Díaz, V. A. Kostelecký, and R. Lehnert, Phys. Rev. D 88, 071902 (2013). [arXiv:1305.4636]

Tests of Lorentz symmetry in single beta decay.
J. S. Díaz, Adv. High Energy Phys. 2014, 305298 (2014). [arXiv:1408.5880]


Double beta decay

In 1935, Maria Goeppert-Mayer [Phys. Rev. 48, 512] proposed the possibility of a simultaneous beta decay of two neutrons in a nucleus into pairs of protons, electrons, and antineutrinos $(A,Z)\to(A,Z+2)+2\color{blue}{e^-}+2\color{red}{\bar\nu_e}$. This rare process known as two-neutrino double beta decay ($\color{Brown}{2\nu\beta\beta}$) has been observed in many elements.
If neutrinos are their own antiparticles, the antineutrino emitted by the virtual intermediate nuclear state could appear as a virtual particle connecting the two beta decays $(A,Z)\to(A,Z+2)+2\color{blue}{e^-}$. This process is known as neutrinoless double beta decay ($\color{Brown}{0\nu\beta\beta}$) and remains unobserved to date.
A new generation of experiments are searching for the neutrinoless mode because its observation would prove that neutrinos are Majorana particles and the violation of lepton number.
This paper describes how these experiments can also search for relativity violations. The experimental
signatures of deviations from Lorentz and CPT invariance in double beta decay are presented.

• Two-neutrino double beta decay: although $\color{Brown}{2\nu\beta\beta}$ constitutes a background for searches of neutrinoless double beta decay, the large amount of data from the two-neutrino mode can be used to investigate deformations of the electron sum spectrum produced by isotropic Lorentz violation in the neutrino sector. The spectrum receives a correction that is maximized at a well-defined energy (presented in the paper for different isotopes). An experimental investigation of this feature requires the search for deviations from the conventional spectrum. The operator responsible for this effect is also a new source of CP violation in neutrinos.

• Neutrinoless double beta decay
: Lorentz-violating Majorana couplings modify the neutrino propagator, introducing novel effects in $\color{Brown}{0\nu\beta\beta}$. There is a charge-conjugation-preserving operator that can trigger neutrinoless double beta decay even if the Majorana neutrino mass is negligible. Since this decay mode remains unobserved, lower bounds on the half life $T^{0\nu}_{1/2}$ of a particular isotope can also be used to constrain the relevant coefficients for Lorentz violation. Modified electron angular correlation are also obtained for experiments with tracking systems that can reconstruct the direction of the two emitted electrons.

Limits on Lorentz and CPT violation from double beta decay.
J. S. Díaz, Phys. Rev. D 89, 036002 (2014). [arXiv:1311.0930]

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