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Register a new userInterference phenomenon and geometric phase for Dirac neutrino in pion+ decay
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We analyze the geometric phase in the neutrino oscillation phenomenon, which follows the pion decay pi+ --> mu+ + u_{mu}. Its value pi is consistent with the present-day global analysis of the Standard Model neutrino oscillation parameters, accounting for the nonzero value of theta_13. The impact of the charge-parity (CP) violating phase delta, the neutrinos nature, and the new physics is discussed.
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Geometric (Aharonov--Anandan) phases in neutrino oscillations have been claimed [Phys. Lett. B 780 (2018) 216] to be sensitive to the Majorana phases in neutrino mixing. More recently, however, it has been pointed out [Phys. Lett. B 818 (2021) 136376] that the proposed phases are not gauge invariant. Using both kinematic and geometric approaches, we show that all gauge-invariant Aharonov--Anandan phases (including the off-diagonal geometric phases associated with flavor transitions) are independent of the Majorana phases. This finding, which generalizes the well-known fact that conventional oscillation experiments cannot discern the Dirac or Majorana nature of the neutrino, implies that a hypothetical interference experiment cannot distinguish between the two either.
Motivated by recent development in quantum fidelity and fidelity susceptibility, we study relations among Lie algebra, fidelity susceptibility and quantum phase transition for a two-state system and the Lipkin-Meshkov-Glick model. We get the fidelity susceptibility for SU(2) and SU(1,1) algebraic structure models. From this relation, the validity of the fidelity susceptibility to signal for the quantum phase transition is also verified in these two systems. At the same time, we obtain the geometric phase in these two systems in the process of calculating the fidelity susceptibility. In addition, the new method of calculating fidelity susceptibility has been applied to explore the two-dimensional XXZ model and the Bose-Einstein condensate(BEC).
We study the total and the geometric phase associated with neutrino mixing and we show that the phases produced by the neutrino oscillations have different values depending on the representation of the mixing matrix and on the neutrino nature. Therefore the phases represent a possible probe to distinguish between Dirac and Majorana neutrinos.
Kinematical aspects of pion decay $pi to mu u$ is studied, with neutrino mixing taken into account. An attempt is made to derive the transition probability for such a sequence of processes: a $pi^+$ produced at $(vec{x}_{pi},t_{pi})$ with momentum $vec{p}_{pi}$ decays into a $mu^+$ and a $ u_{mu}$ somewhere in space-time and then the $mu^+$ is detected at $(vec{x}_{mu},t_{mu})$ with momentum $vec{p}_{mu}$ and a $ u_{alpha}$ (a neutrino with flavor $alpha = e$, $mu$, $...$) is detected at $(vec{x}_{ u},t_{ u})$ with momentum $vec{p}_{ u}$. It is shown that (1) if all the particles involved are treated as plane-waves, the energy-momentum conservation would eliminate the neutrino oscillating terms, leaving each mass-eigenstate to contribute separately to the transition probability; (2) if one treats all the particles involved as wave-packets, the neutrino oscillating terms would appear and would be multiplied by two suppression factors, which result from distinction in velocity and in energy between the two interfering neutrino mass-eigenstates. An approximate treatment which takes account of the two complementary features, each of the particles involved propagates along its classical trajectory on the one hand and energies and momenta of the particles involved are conserved during the decay on the other hand, is proposed and similarity and difference between our approach and that of Dolgov et al. are discussed.
We argue that neutrino oscillations at JUNO offer a unique opportunity to study Sorkins triple-path interference, which is predicted to be zero in canonical quantum mechanics by virtue of the Born rule. In particular, we compute the expected bounds on triple-path interference at JUNO and demonstrate that they are comparable to those already available from electromagnetic probes. Furthermore, the neutrino probe of the Born rule is much more direct due to an intrinsic independence from any boundary conditions, whereas such dependence on boundary conditions is always present in the case of electromagnetic probes. Thus, neutrino oscillations present an ideal probe of this aspect of the foundations of quantum mechanics.
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