Neutrino oscillations and Lorentz invariance violation Standard Model

Neutrino oscillations and Lorentz invariance violation

`Standard Model’ Neutrinos Two families of elementary particles … Neutrinos: • Come in three `flavors’ ( e, ) • Are massless • Interact weakly • Cannot change flavor 2

Brief history of neutrinos Pauli postulated neutrinos to explain how beta decay could conserve energy, momentum, and spin 1930. Detection of the neutrino (1995 Nobel prize） μ-neutrino discovery（1988 Nobel prize ） Pontecorvo proposed neutrino oscillation 1957 Detection of cosmic neutrinos (2002 Nobel prize ） Discovery of neutrino oscillations（2015 Nobel prize ） 3

Neutrino oscillation : ⧫. is a quantum mechanical phenomenon ⧫ ⧫. A neutrino created with a specific lepton flavor (electron, muon, or tau) can later be changed to a different flavor. ⧫ ⧫ ⧫. The probability of measuring a particular flavor for a neutrino varies periodically as it propagates through space. 4

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Neutrino Oscillation in Vaccum 7

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Neutrino oscillations in normal media 9

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Neutrino Oscillation in nuclrar media 12

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Lorentz invariance is one of the main and basic concepts in special relativity (for more than one century). It states that : The laws of physics are invariant under Lorentz transformation. Lorentz invariance imply that spacetime structure is the same at all scales; that is, Lorentz symmetry assumes a scale-free nature of spacetime. there is no fundamental length scale associated with the Lorentz group. A departure from Lorentz invariance can therefore lead to discontinuous spacetime framework and vice versa. 15

But the existence of fundamental length and discreteness of space are predicted by some theories including, quantum gravity, string theory and noncommutative geometry. So there is possibility of Lorentz invariance violation (LIV) in nature. A question : Can we check Lorentz invariance violation by neutrino oscillations? 16

To formulate the neutrino oscillation in a discrete space (lattice) we follow the method proposed in : K. G. Wilson, Phys. Rev. D 10 (1974) 2445. J. B. Kogut, Rev. Mod. Phys. 55 (1983) 775. I. Motie, She-Sheng Xue, IJMPA 19 (2012) 1250104. 17

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In conclusion, high energy neutrinos oscillations may help us to get information about LIV. 25

Thank you and the organizing committee 26