Fast Exact Algorithm for Neutrino Oscillation in Constant Matter Density

A recently published method for solving the neutrino evolution equation with constant matter density is further refined and used to lay out an exact algorithm for computing oscillation probabilities, which is moderately faster than previous methods when looping through neutrinos of different energies. In particular, the three examples of $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival, $\overset{\scriptscriptstyle{(-)}}{\nu}_\mu$ survival and $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ appearance probabilities are written in terms of mixing angles, mass differences and matter electron density. A program based on this new method is found to be roughly twice as fast as, and in agreement with, the leading GLoBES package. Furthermore, the behaviour of all relevant effective parameters is sketched out in terms of a range of neutrino energies, or matter electron densities. For instance, the $\overset{\scriptscriptstyle{(-)}}{\nu}_e$ survival probability in constant matter density is found to have no dependence on the mixing angle $\theta_{23}$ or the CP-violating phase $\delta_{13}$.