Search for Lorentz violations through the sidereal effect at the $\mathrm{NO}\nu \mathrm{A}$ experiment

Long-baseline neutrino oscillation experiments offer a unique laboratory to test the fundamental Lorentz symmetry, which is at the heart of both the standard model of particle and general relativity theory. The sidereal modulation in neutrino events will act as the smoking-gun experimental signature of Lorentz and $CPT$ violation. In this study, we investigate the impact of the sidereal effect on standard neutrino oscillation measurements within the context of the NuMI Off-Axis ${\nu }_e$ Appearance Experiment ($\mathrm{NO}\nu \mathrm{A}$) experiment. Additionally, we assess the sensitivity of the $\mathrm{NO}\nu \mathrm{A}$ experiment to detect Lorentz-violating interactions, taking into account the sidereal effect. Furthermore, we highlight the potential of the $\mathrm{NO}\nu \mathrm{A}$ experiment to set new constraints on anisotropic Lorentz-violating parameters.

Figure 1

The standard neutrino oscillation 1D probability spectrum in terms of energy, as well as the probability distribution in terms of local sidereal time (LST) and energy for the appearance channel (top) and disappearance channel (bottom) without taking LIV parameters into account. The oscillation parameters listed in Table 1 are adopted to calculate the probability distribution.

Figure 2

The probability difference distribution for the appearance channel for $X$-type components ($a_{\alpha \beta }^X$, $c_{\alpha \beta }^{TX}$, $c_{\alpha \beta }^{XX}$, $c_{\alpha \beta }^{XZ}$, $c_{\alpha \beta }^{XY}$, with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$). In each panel, one specific LIV parameter is set to $1\times {10}^{-23}$, while the others are set to 0.

Figure 3

The probability difference distribution for the disappearance channel for $X$-type components ($a_{\alpha \beta }^X$, $c_{\alpha \beta }^{TX}$, $c_{\alpha \beta }^{XX}$, $c_{\alpha \beta }^{XZ}$, $c_{\alpha \beta }^{XY}$, with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$). In each panel, one specific LIV parameter is set to $1\times {10}^{-23}$, while the others are set to 0.

Figure 4

Correlations between the nondiagonal parameters ($a_{\alpha \beta }^X$, $c_{\alpha \beta }^{TX}$, $c_{\alpha \beta }^{XX}$, $c_{\alpha \beta }^{XZ}$, $c_{\alpha \beta }^{XY}$ with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$) and mixing angle ${\theta }_{23}$ at $2\sigma$, $2.5\sigma$, and $3\sigma$ confidence level (CL).

Figure 5

Correlations between the nondiagonal parameters ($a_{\alpha \beta }^X$, $c_{\alpha \beta }^{TX}$, $c_{\alpha \beta }^{XX}$, $c_{\alpha \beta }^{XZ}$, $c_{\alpha \beta }^{XY}$ with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$) and Dirac $CP$ phase ${\delta }_{CP}$ at $2\sigma$, $2.5\sigma$, and $3\sigma$ CL.

Figure 6

Correlations between the nondiagonal parameters ($a_{\alpha \beta }^X$, $c_{\alpha \beta }^{TX}$, $c_{\alpha \beta }^{XX}$, $c_{\alpha \beta }^{XZ}$, $c_{\alpha \beta }^{XY}$ with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$) and ${\mathrm{\Phi }}_{\text{parameter}}$ at $2\sigma$, $2.5\sigma$, and $3\sigma$ CL.

Figure 7

Sensitivity plots of the LIV parameters for $\mu e$, $\mu \mu$, $\overline{\mu }$ $\overline{e}$, $\overline{\mu }$ $\overline{\mu ,}$ and all channels combined with $2\sigma$ and $3\sigma$ cut.

Figure 8

The probability difference distribution for the appearance channel for $Y$-type components ($a_{\alpha \beta }^Y$, $c_{\alpha \beta }^{TY}$, $c_{\alpha \beta }^{YY}$, $c_{\alpha \beta }^{YZ}$ with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$). In each panel, one specific LIV parameter is set to $1\times {10}^{-23}$, while the others are set to 0.

Figure 9

The probability difference distribution for the disappearance channel for $Y$-type components ($a_{\alpha \beta }^Y$, $c_{\alpha \beta }^{TY}$, $c_{\alpha \beta }^{YY}$, $c_{\alpha \beta }^{YZ}$ with $\alpha \beta =e\mu$, $e\tau$, and $\mu \tau$). In each panel, one specific LIV parameter is set to $1\times {10}^{-23}$, while the others are set to 0.