Combining Pumping and Absorption Effects in Neutrino Oscillation Probabilities: A Non-Hermitian Framework

Abstract

We study two-flavour neutrino oscillations in which a coherent off-diagonal interaction from a complex background field coexists with an absorptive channel acting on a single mass eigenstate. Since the two do not commute, the effective Hamiltonian is non-normal and oscillations and damping no longer factorise. We formulate the dynamics both as the no-jump sector of a Lindblad evolution and through biorthogonal diagonalisation, and obtain the evolution operator of our model in closed form. The model interpolates between quasi-global damping, standard invisible decay, and a critical point with polynomial-times-exponential evolution; for initially pure states it describes norm loss rather than decoherence. Comparing neutrinos and antineutrinos in the same background, with the mixing phase $\varphi$ reversed and the background phase $\delta$ fixed, we derive closed-form $CP$, $CPT$ and $T$ asymmetries. The $CPT$ asymmetries arise only from this phase assignment. In contrast, the $T$ asymmetry, which is forbidden in unitary two-flavour oscillations, is independent of the prescription: it arises only through the non-normal structure, is proportional to the absorptive coupling, and vanishes only when $\delta +\varphi =n\pi$. For equal initial populations the net neutrino--antineutrino asymmetry vanishes identically, while a non-zero flavour asymmetry survives and requires a non-normal Hamiltonian.

arXiv comment35 pages, 6 figures