Tests of Lorentz violation in ${\overline{\nu }}_{\mu }\to {\overline{\nu }}_e$ oscillations

A recently developed standard-model extension (SME) formalism for neutrino oscillations that includes Lorentz and $CPT$ violation is used to analyze the sidereal time variation of the neutrino event excess measured by the liquid scintillator neutrino detector (LSND) experiment. The LSND experiment, performed at Los Alamos National Laboratory, observed an excess, consistent with neutrino oscillations, of ${\overline{\nu }}_e$ in a beam of ${\overline{\nu }}_{\mu }$. It is determined that the LSND oscillation signal is consistent with no sidereal variation. However, there are several combinations of SME coefficients that describe the LSND data; both with and without sidereal variations. The scale of Lorentz and $CPT$ violation extracted from the LSND data is of order ${10}^{-19}\mathrm{GeV}$ for the SME coefficients $a_L$ and $E\times c_L$. This solution for Lorentz and $CPT$ violating neutrino oscillations may be tested by other short baseline neutrino oscillation experiments, such as the MiniBooNE experiment.

Figure 1

Coordinate systems for the sidereal time variation analysis: a) the Sun-centered system, b) the Earth-centered system, c) the LANL local coordinate system, and d) the definition of $T_{\oplus }=0$.

Figure 2

Distribution of beam-on neutrino candidate events in a) run number vs solar day (day $1=\mathrm{\text{January}}1$) and b) GM time vs sidereal time. The year of each set of runs is indicated in a).

Figure 3

Sidereal a) and GM b) time distributions of beam-off data using 37 time bins. The solid lines indicate the expected underlying distribution with no sidereal time variation. The error bars displayed in this plot (and subsequent) are the square root of the number in each bin.

Figure 4

Sidereal a) and GM b) time distributions of the 186 beam-on oscillation candidate events in 37 bins. The solid lines indicate the expected underlying distribution with no sidereal time variation.

Figure 5

Sidereal time distribution of beam-on data with ${}^{12}C({\nu }_e,e^{-}{)}^{12}{N}_{\mathrm{g}.\mathrm{s}.}$ cuts. The line indicates the average value.

Figure 6

Sidereal time distribution of the LSND oscillation data in 24 time bins together with the maximum-$\ell$ solutions for the 1-parameter (solid line), 3-parameter (dotted line), and 5-parameter (dot-dashed line) combinations. The dashed line indicates the estimated background contribution.

Figure 7

Log likelihood values for the 3-parameter description of the LSND sidereal time distribution: a) $({\mathcal{A}}_s{)}_{\overline{e}\overline{\mu }}$ vs $(\mathcal{C}{)}_{\overline{e}\overline{\mu }}$, b) $({\mathcal{A}}_c{)}_{\overline{e}\overline{\mu }}$ vs $(\mathcal{C}{)}_{\overline{e}\overline{\mu }}$, and c) $({\mathcal{A}}_c{)}_{\overline{e}\overline{\mu }}$ vs $({\mathcal{A}}_s{)}_{\overline{e}\overline{\mu }}$. The contours in a)–c) indicate the $1\mathrm{\text{−}}\sigma$ (total error) allowed regions ($\ell >{\ell }_{\max }-1.77$) and the stars indicate the maximum-$\ell$ parameter values.

Figure 8

Sidereal a) and GM b) time distributions of the high-energy, beam-off data in 14 bins. The solid lines indicate the expected underlying distribution with no sidereal time variation.

Figure 9

Sidereal a) and GM b) time distributions of the 73 LSND high-energy, beam-on oscillation candidate events in 14 bins. The solid lines indicate the expected underlying distribution with no sidereal time variation.

Figure 10

Sidereal time distribution of the high-energy LSND oscillation data in 9 time bins together with the maximum-$\ell$ solutions for the 1-parameter (solid line) and 3-parameter (dotted line) combinations. The dashed line indicates the estimated background contribution.

Figure 11

Log likelihood values for the 3-parameter description of the high-energy LSND sidereal time distribution: a) $({\mathcal{A}}_s{)}_{\overline{e}\overline{\mu }}$ vs $(\mathcal{C}{)}_{\overline{e}\overline{\mu }}$, b) $({\mathcal{A}}_c{)}_{\overline{e}\overline{\mu }}$ vs $(\mathcal{C}{)}_{\overline{e}\overline{\mu }}$, and c) $({\mathcal{A}}_c{)}_{\overline{e}\overline{\mu }}$ vs $({\mathcal{A}}_s{)}_{\overline{e}\overline{\mu }}$. The contours in a)–c) indicate the $1\mathrm{\text{−}}\sigma$ (total error) allowed regions ($\ell >{\ell }_{\max }-1.77$) and the stars indicate the maximum-$\ell$ parameter values.