Search for Lorentz-invariance violation with the first KATRIN data

M. Aker et al. (KATRIN Collaboration)

Phys. Rev. D 107, 082005 – Published 26 April 2023

Abstract

Some extensions of the Standard Model of particle physics allow for Lorentz invariance and charge-parity-time invariance violations. In the neutrino sector strong constraints have been set by neutrino-oscillation and time-of-flight experiments. However, some Lorentz-invariance-violating parameters are not accessible via these probes. In this work, we focus on the parameters $(a_{of}^{(3)})_{00}$ , $(a_{of}^{(3)})_{10}$ , and $(a_{of}^{(3)})_{11}$ which would manifest themselves in a nonisotropic $β$ -decaying source as a sidereal oscillation and an overall shift of the spectral endpoint. Based on the data of the first scientific run of the KATRIN experiment, we set the first 90% confidence-level limit on $| (a_{of}^{(3)})_{11} |$ of $< 0.9 \times 10^{- 6} GeV$ to $3.7 \times 10^{- 6} GeV$ , depending on the phase. Moreover, we derive new constraints on $(a_{of}^{(3)})_{00}$ and $(a_{of}^{(3)})_{10}$ .

Received 2 October 2022
Revised 8 February 2023
Accepted 14 March 2023

DOI:https://doi.org/10.1103/PhysRevD.107.082005

Physics Subject Headings (PhySH)

Particle astrophysics

Neutrinos

Lorentz symmetry Particle properties

Spectroscopy

Particles & FieldsGeneral PhysicsNuclear Physics

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Issue

Vol. 107, Iss. 8 — 15 April 2023

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Images

Figure 1
Sketch of the equatorial coordinate system. The Earth is rotating with $ω_{\oplus}$ within the Lorentz-invariance-violating vector field $a^{μ}$ , defined to be perpendicular to the $z$ axis. Therefore, the KATRIN experiment, which is located at the colatitude $χ \approx 41 °$ , is moving with velocity $β_{rot}$ (rotation velocity of the Earth at the position of KATRIN). The beam axis of the KATRIN experiment is tilted with respect to the local north by $ξ \approx 17 °$ (this angle is enlarged in the figure for illustration purposes). The angle $θ_{0} \approx 50.4 °$ depicts the experimental acceptance angle with respect to the KATRIN beam axis.
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Figure 2
Main components of the KATRIN experiment: (a) Tritium source, (b) transport and pumping sections, (c) main spectrometer, (d) focal plane detector. The dashed line below illustrates the KATRIN beamline. The experiment has an orientation of $ξ \approx 16 °$ east to the local north N. The acceptance angle $θ_{0} = 50.4 °$ defines the acceptance cone of the $β$ electrons. The black arrows below the spectrometer indicate the electron momentum (without electric field). When propagating from $B_{s}$ to $B_{\min}$ , the pitch angle $θ$ (angle between the electron momentum and the magnetic field lines) is reduced; while when moving from $B_{s}$ to $B_{\max}$ , the pitch angle is increased. An electron starting with $θ > θ_{0}$ will be reflected at $B_{\max}$ .
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Figure 3
(a) Electron spectrum $R (q U)$ of a single scan where all pixels are combined (uniform fit). The spectrum of the best fit $R_{calc} (q U)$ extends to the endpoint $E_{0}$ and lies on top of an energy-independent background $R_{bg}$ . (b) Residuals of $R (q U)$ relative to the $1 σ$ -uncertainty band of the best fit model. (c) Measurement-time distribution.
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Figure 4
Illustration of the effective-time concept. Here we assume a certain Lorenz-invariance-violation scenario, illustrated by the red line. The corresponding individual endpoint measurements (blue dots) are shown at the time of the start of each 2-hour scan. Shifting the data points by a fixed time (here: 87 minutes) reproduces the true variation of the endpoint. An individual time shift is evaluated for up scans and down scans (see main text). To good approximation the time shift is independent of the size of the Lorentz invariance violation.
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Figure 5
Illustration of the fitted endpoints (blue dots) at their effective times $t_{e}$ . The red line shows the best fit of an oscillation with sidereal frequency and free amplitude and free phase. The best fit corresponds to $A_{best} \approx 0.03 eV$ and $ϕ_{best} \approx 0.78 π$ and has a reduced $χ_{R}^{2} = 0.98$ . The bottom panel displays the normalized residuals of the data fit (black).
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Figure 6
90% CL exclusion limit for the Lorentz-invariance-violating parameter $| (a_{of}^{(3)})_{11} |$ and the phase $ϕ$ . The right $y$ axis displays the corresponding amplitude of the endpoint oscillation, according to Eq. (3). Using a $χ^{2}$ -grid search and Wilks’ theorem, the exclusion limit for the total uncertainties (blue solid line) are calculated. The green dashed-dotted line shows the exclusion limit, including only the statistical uncertainty. The orange dashed line includes an enlarged statistical uncertainty due to the non-Poissonian (NP) distribution of the background rate, as explained in the main text. The best fit is shown by the black cross.
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