Proposal of a simple method to estimate neutrino oscillation probability and CP violation in matter

Abstract

We study neutrino oscillation within the framework of three generations in matter. We propose a simple method to approximate the coefficients A, B and C which do not depend on the CP phase δ in the oscillation probability P (νe → νµ) = A cos δ + B sin δ + C. An advantage of our method is that an approximate formula of the coefficients A, B and C in arbitrary matter without the usual first order perturbative calculations of the small parameter ∆m 2 21 /∆m 2 31 or sin θ13 can be derived. Furthermore we show that all the approximate formulas for low, intermediate and high energy regions given by other authors in constant matter can be easily derived from our formula. It means that our formula is applicable over a wide energy region. *

Current unknowns in the three-neutrino framework

“…At the lower T2K energies, the ratio |A/∆m 2 | is a factor 3-4 smaller, and the baseline (x = 295 km) is also smaller, so that oscillations are almost vacuum-like. See also [129,130,131,132,133] for recent analytical studies of 3ν probabilities at accelerator baselines and energies. Note that the above form for P µe , despite being useful for later discussions, is not used in our analysis, which is based on full 3ν numerical probabilities in matter (for both appearance and disappearance channels) without any approximation.…”

Leptonic CP Phase in ν[sub μ]→ν[sub μ] Oscillations

“…Eqs. (2.4) and (2.5) hold exactly in the case of θ 23 = 45 • [31], where the coefficients A µα , B µα and C µα (α = e, µ, τ ) are the quantities determined by the parameters except for δ. If we assume the unitarity in the framework of three generations, the sum of these probabilities has to be one for any value of δ.…”

“…See ref. [31] for example. It should be noted that the magnitude of A µµ is as same as that of A µe and is not so small.…”

Why is the neutrino oscillation formula expanded in Δm 21 2 /Δm 31 2 still accurate near the solar resonance in matter?

“…This is important considering that simulation of LBL experiments and performing χ 2 -fits require a fast and simple method to compute a large number of oscillation probabilities. Therefore even though the numerical calculation is always viable, there are still many studies on analytic approximation formulae for neutrino oscillation in matter [13,[30][31][32][33][34][35][36][37][38][39][40][41].…”