Wave packet treatment of neutrino flavor oscillations in various spacetimes

Plane-wave and wave-packet neutrino flavor oscillations in vacuum in conformal coupling models

“…The counterparts of these integrals in the case of neutrinos not conformally coupled are, respectively, the integrals T , I 1 and I 2 obtained in Ref. [44].…”

“…1 in view of its application to neutrino oscillations within modified gravity theories [44,47] and in view of its application to neutrino oscillations within the gravitational field inside matter [44]. The usual case A(r)B(r) = 1 of the exterior Schwarzschild solution found within general relativity will be dealt with in Sec.…”

“…Now, the above procedure of averaging over time is amply justified in the absence of a conformal coupling of neutrinos. Indeed, the time-integral T just reduces then to the total unmeasured time T [44]. However, when neutrinos interact with a scalar field that displays a non-negligible variation with position along the path of the neutrinos towards the detector, actually performing the integral T becomes ambiguous.…”

“…In Refs. [43,44], the effect of curved spacetime on the flavor oscillations within the wavepacket formalism has been investigated in much detail and shown to give rise to an oscillation phase that contains the ratio I/L jk osc , where I is an integral involving the components of the metric. In addition, however, the oscillation phase contains extra metricdependent terms, as well as a damping term that also depends in a nontrivial way on the metric components.…”

“…We therefore expect that while the plane-wave formalism might lead to simple expressions for the effect of a conformal coupling on neutrino oscillations, the wavepacket formalism could potentially display a more involved expression for the effect. Furthermore, the wavepacket approach in curved spacetime brings with it an additional complication due to the two possible ways of dealing with the propagation of the mass eigenstates wavepackets [44].…”