Simple and compact expressions for neutrino oscillation probabilities in matter

Abstract

We reformulate perturbation theory for neutrino oscillations in matter with an expansion parameter related to the ratio of the solar to the atmospheric ∆m 2 scales. Unlike previous works, we use a renormalized basis in which certain first-order effects are taken into account in the zeroth-order Hamiltonian. We show that the new framework has an exceptional feature that leads to the neutrino oscillation probability in matter with the same structure as in vacuum to first order in the expansion parameter. It facilitates immediate physical interpretation of the formulas, and makes the expressions for the neutrino oscillation probabilities extremely simple and compact. We find, for example, that the ν e disappearance probability at this order is of a simple two-flavor form with an appropriately identified mixing angle and ∆m 2 . More generally, all the oscillation probabilities can be written in the universal form with the channel-discrimination coefficient of 0, ±1 or simple functions of θ 23 . Despite their simple forms they include all order effects of θ 13 and all order effects of the matter potential, to first order in our expansion parameter.

Compact perturbative expressions for neutrino oscillations in matter

“…In this paper we have further developed and expanded upon the recent perturbative framework for neutrino oscillations in uniform matter, introduced in [11]. The new oscillation probabilities are of the same simple, compact functional form with slightly more complicated coefficients, yet, the range of applicability now includes the whole L/E versus matter potential, a, plane, i.e.…”

“…Since s 13 ∼ O( √ ǫ), it is natural to diagonalize the (1-3) sector next, using U 13 (φ), again see [11]. After this rotation the neutrino basis is 14) and the Hamiltonian is given bŷ 16) which is identical to eq.…”

“…After this rotation the neutrino basis is 14) and the Hamiltonian is given bŷ 16) which is identical to eq. 3.1 of [11]. Also c (φ−θ 13 ) ≡ cos(φ − θ 13 ) and s (φ−θ 13 ) ≡ sin(φ − θ 13 ).…”

“…DUNE: NO, δ = 3π/2 First min First max experiments JUNO, [21], and RENO-50, [22,23], a setup where the oscillation probabilities of [11] miss significant physics, since the L/E varies from 6 to 25 km/MeV.…”

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].…”