Anisotropic Lorentz invariance violation in reactor neutrino experiments

Recent reactor neutrino oscillation experiments reported precision measurements of <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961753.png" baseline="-3.5" display="inline" id="mathml_M1" overflow="scroll"><mml:mrow class="MJX-TeXAtom-ORD"> <mml:msup><mml:mi>sin</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:mo>⁡</mml:mo><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:msub><mml:mi>&#x03B8;</mml:mi> <mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>13</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:mrow></math></inline-formula> and <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961754.png" baseline="-3.5" display="inline" id="mathml_M2" overflow="scroll"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi mathvariant="normal">&#x0394;</mml:mi><mml:msubsup><mml:mi>m</mml:mi><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>e</mml:mi><mml:mi>e</mml:mi></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:mrow></math></inline-formula> under the standard <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961755.png" baseline="-0.5" display="inline" id="mathml_M3" overflow="scroll"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>3</mml:mn><mml:mi>&#x03BD;</mml:mi></mml:mrow></math></inline-formula> oscillation framework. However, inter-experiment consistency checks through the parameter goodness-of-fit test reveal proximity to tension boundary, with the Double Chooz, RENO, and Daya Bay ensemble yielding <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961756.png" baseline="-3.5" display="inline" id="mathml_M4" overflow="scroll"> <mml:mrow class="MJX-TeXAtom-ORD"><mml:msub><mml:mi>p</mml:mi><mml:mtext>PG</mml:mtext></mml:msub><mml:mo>=</mml:mo><mml:mn>0.14</mml:mn></mml:mrow></math></inline-formula> vs threshold <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961757.png" baseline="-0.5" display="inline" id="mathml_M5" overflow="scroll"><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>&#x03B1;</mml:mi><mml:mo>=</mml:mo><mml:mn>0.1</mml:mn></mml:mrow></math></inline-formula>. Anisotropic Lorentz invariance violation (LIV) can accommodate this tension by introducing a location-dependent angle <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961758.png" baseline="-0.5" display="inline" id="mathml_M6" overflow="scroll"> <mml:mrow class="MJX-TeXAtom-ORD"><mml:msup><mml:mi>&#x03B8;</mml:mi><mml:mtext>LIV</mml:mtext></mml:msup></mml:mrow></math></inline-formula> relative to the earth&#x2019;s axis. It is found that anisotropic LIV improve the fit to data up to <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961759.png" baseline="-0.5" display="inline" id="mathml_M7" overflow="scroll"> <mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>1.9</mml:mn><mml:mi>&#x03C3;</mml:mi></mml:mrow></math></inline-formula> confidence level significance, with the coefficient <inline-formula><math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="c:\heptemp\HML47961760.png" baseline="-3.5" display="inline" id="mathml_M8" overflow="scroll"><mml:mrow class="MJX-TeXAtom-ORD"><mml:msubsup><mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">A</mml:mi></mml:mrow> <mml:mrow class="MJX-TeXAtom-ORD"><mml:mn>31</mml:mn></mml:mrow><mml:mrow class="MJX-TeXAtom-ORD"><mml:mi>C</mml:mi><mml:mo stretchy="false">(</mml:mo> <mml:mn>0</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><mml:mo>=</mml:mo><mml:mn>2.43</mml:mn><mml:mo>&#x00D7;</mml:mo><mml:msup><mml:mn>10</mml:mn> <mml:mrow class="MJX-TeXAtom-ORD"><mml:mo>&#x2212;</mml:mo><mml:mn>17</mml:mn></mml:mrow></mml:msup><mml:mspace width="thickmathspace" /><mml:mtext>MeV</mml:mtext></mml:mrow></math></inline-formula> yielding the best fit, while Parameter Goodness-of-fit (PG) is significantly improved within the LIV formalism.