New test of neutrino oscillation coherence with Leggett–Garg inequality
Xingzhi Wang, Bo-Qiang Ma
Abstract
Abstract Leggett–Garg inequality (LGI) is a time analogue of Bell’s inequality that concerns measurements performed on a system at different times. Violation to LGI indicates quantum coherence. We present a Leggett–Garg-type inequality compatible with more general neutrino oscillation frameworks, allowing the effects of decoherence to be taken into consideration. The inequality is applied to test coherence for data from Daya Bay, MINOS, and KamLAND experiments, and their results are compared to theoretical predictions to investigate decoherence. Both Daya Bay and MINOS data exhibit clear violations of over $$10\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>10</mml:mn><mml:mi>σ</mml:mi></mml:mrow></mml:math> , and of over 90 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>%</mml:mo></mml:math> of theoretical predictions, while the KamLAND data exhibit violation of $$1.9\sigma $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mn>1.9</mml:mn><mml:mi>σ</mml:mi></mml:mrow></mml:math> , being of 58 $$\%$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>%</mml:mo></mml:math> of the theoretical prediction. The present work is the first to have considered the energy uncertainties in neutrino coherence tests.