Angular distributions in electroweak pion production off nucleons: Odd parity hadron terms, strong relative phases, and model dependence

Abstract

The study of pion production in nuclei is important for signal and background determinations in current and future neutrino oscillation experiments. The first step, however, is to understand the pion production reactions at the free nucleon level. We present an exhaustive study of the chargedcurrent and neutral-current neutrino and antineutrino pion production off nucleons, paying special attention to the angular distributions of the outgoing pion. We show, using general arguments, that parity violation and time-reversal odd correlations in the weak differential cross sections are generated from the interference between different contributions to the hadronic current that are not relatively real. Next, we present a detailed comparison of three, state of the art, microscopic models for electroweak pion production off nucleons, and we also confront their predictions with polarized electron data, as a test of the vector content of these models. We also illustrate the importance of carrying out a comprehensive test at the level of outgoing pion angular distributions, going beyond comparisons done for partially integrated cross sections, where model differences cancel to a certain extent. Finally, we observe that all charged and neutral current distributions show sizable anisotropies, and identify channels for which parity-violating effects are clearly visible. Based on the above results, we conclude that the use of isotropic distributions for the pions in the center of mass of the final pion-nucleon system, as assumed by some of the Monte Carlo event generators, needs to be improved by incorporating the findings of microscopic calculations.

Neutrino pion-production on a nucleon

“…where L (2) ππ is the lowest order pion lagrangian. The leading order pion-nucleon χPT lagrangian, L (1) πN , contains the nucleon velocity chosen to be v µ = (1, 0) and the nucleon spin S µ = (0, 1 2 σ ),…”

“…The NLO correction terms are contained in L (2) πN . The explicit expressions for the next order lagrangians, L (2) πN are given in, e.g., Ref. [8].…”

“…where D µ = ∂ µ + · · ·. The kinetic terms of L (2) πN in Eq. (2.4) generate propagator corrections at second order, i.e., 1/(2m N ), as shown by Bernard et al [8,11].…”

“…In the evaluations of these neutrinonuclear reaction processes, neutrino-nucleon interaction models are the basic theoretical inputs, e.g., see a recent discussion in Ref. [2]. Due to the conservation of the vector current (CVC), the vector component of the weak-interaction models has been tested by electron and photo-nucleon and nuclear reactions and we assume that this vector interaction is well known.…”

Further tests of lepton flavor universality from the charged lepton energy distribution in b→c semileptonic decays: The case of Λb→Λ

“…We have not included an antisymmetric term proportional to (p µ q ν − p ν q µ ), since it would lead to time-reversal odd correlations[23,24].…”