Response of Hellinger-distance based coherence to weak decoherence in two-flavor neutrino oscillations

We evaluate the Hellinger-distance coherence of the two-flavor neutrino state subject to Lindblad damping of the mass-eigenstate interference term, and obtain a closed expression in terms of the flavor-basis density-matrix elements. In the two-flavor vacuum treatment with negligible wave-packet separation, the undamped state is pure, and the smallest eigenvalue of the damped state grows linearly with ε=1-κ, where κ=e-ΓL. An expansion about the pure state then yields a nonanalytic sqrtε correction to the Hellinger coherence, with coefficient K=2 sqrt 2,u 2θ/sqrt 1-2u, whereas the flavor-transition probability, the l 1 coherence, the concurrence, the entanglement of formation and the local quantum Fisher information all respond linearly in ε. Using representative Daya Bay, KamLAND and MINOS working points together with a current 90% C.L. bound on energy-independent damping, we find fractional changes in the Hellinger coherence of 0.18%, 9.40% and 21.51%, against 0.0009%, 0.43% and 1.81% for the concurrence. The comparison concerns the response of the quantifiers to the damping parameter and carries no implication about experimental resolution. The same mechanism operates, with a different coefficient, for a correlated dephasing channel acting on the flavor coherence, where the non-Markovian regime produces damped revivals.