New Physics Right-Chiral CC Coupling Constant Estimation in Neutrino Oscillation Experiments
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New Physics Right-Chiral CC Coupling Constant Estimation in Neutrino Oscillation Experiments Jacek Syska1 Received: 10 January 2020 / Accepted: 25 September 2020 / © Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract The error probability of the discrimination of the Standard Model (SM) with massive neutrinos and its new physics (NP) model extension in experiments of the muon neutrino oscillation, following the pion decay π + → μ+ + νμ , is calculated. The stability of the estimation of the NP charged current coupling constant εR is analysed and the robustness of this estimation is checked. It is shown that the upper bound on the error probability of erroneous identification of the Standard Model with its NP model extension has reached the significantly small value of approximately 2.3 × 10−6 . Keywords Neutrino oscillation · Density matrix · Relative entropy · Statistical information · Quantum measurements
1 The Muon Neutrino Density Matrix In the Standard Model (SM), the masses of the fermions are generated through Yukawa couplings of the scalar Higgs doublet with the right-handed and left-handed fermion components [1]. However, since the SM does not contain right-handed neutrinos, such a Yukawa interaction cannot be constructed for neutrinos that are therefore massless at the Lagrangian level. At the loop level, the neutrino mass term also could not be generated because it would violate the total lepton symmetry of the SM. Nor can it be induced by non-perturbative corrections because it breaks the baryon minus lepton number (B - L) symmetry of the SM [1]. For this reason, it is necessary to go beyond the SM for the neutrino to have mass [2]. This enables an easy description of its oscillations. Not only that, the existence of a right-handed neutrino also suggests the validity of introducing new neutrino interactions, including right chiral charged current interactions. Their absence would raise the question of the viability of the entire group of models with the left-right symmetry [3–5]. However, the well known modelling of the chiral right-handed currents is connected with left-right symmetric extensions of the SM [6–8]. There are also effective-Lagranganian SM extensions which can
Jacek Syska
[email protected] 1
Institute of Physics, University of Silesia, 75 Pułku Piechoty 1, Pl 41-500 Chorz´ow, Poland
International Journal of Theoretical Physics
be used to inspect the existence of the chiral right-handed interactions [9–11]. This paper follows this path. Let the muon neutrino νμ be produced in the decay π + → μ+ + νμ of pion to muon and the muon Dirac neutrino [12]. The neutrino νμ produced in this process is the relativistic one. The muon flavour neutrino state |νμ is a superposition of the stationary states |νi λ ≡ |p, λ, i [12] of definite masses mi , i = 1, 2, 3, helicities λ = −1 or +1 and four-momentum p [13]. By including new physics (NP) interactions [14], e.g., the chiral right-handed interactions [11], this superposition composes the mixed state [13, 15].
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