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 $K=2\sqrt{2}\,u\sin2θ/\sqrt{1-2u}$, 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.