Impact of different neutrino decoherence formalisms at the future long-baseline Experiments

In this paper, we have studied the impact of two different formalisms of quantum decoherence in determining the sensitivities of the two future long-baseline experiments DUNE and P2SO. In Formalism-A, we will assume that the decoherence matrix is defined in a matter mass eigenstate basis which is the basis that diagonalizes the Hamiltonian for neutrinos in matter, with a constant matter density. In Formalism-B, we will define the decoherence matrix in the vacuum mass eigenstate basis and then rotate it to matter mass basis via an unitary transformation. By using different values of the decoherence parameter $\Gamma$, we will show how these two formalisms differ at the probability level and then we will demonstrate how the sensitivities can differ at the $\chi^2$ level. Our results show that if the values of $\Gamma$ is small, then these two formalisms yield same probability in vacuum. However, if the values of $\Gamma$ is large or if there is strong matter effect, then these two formalisms yield very different results.