Angular distribution in two-particle emission induced by neutrinos and electrons

TL;DR

This paper analyzes the angular distribution of two-particle emission reactions induced by neutrinos and electrons, providing analytical formulas and confirming previous results through transformations between the center of mass and laboratory systems.

Contribution

It introduces an analytical method to compute the phase-space distribution in the CM system for two-particle emissions, confirming previous Lab frame calculations and exploring applications to hadronic tensor computations.

Findings

Derived analytical formulas for angular distributions in CM and Lab frames.

Confirmed previous Lab frame results through CM frame analysis.

Identified potential for computing hadronic tensors via boosts to CM system.

Abstract

The angular distribution of the phase space arising in two-particle emission reactions induced by electrons and neutrinos is computed in the laboratory (Lab) system by boosting the isotropic distribution in the center of mass (CM) system used in Monte Carlo generators. The Lab distribution has a singularity for some angular values, coming from the Jacobian of the angular transformation between CM and Lab systems. We recover the formula we obtained in a previous calculation for the Lab angular distribution. This is in accordance with the Monte Carlo method used to generate two-particle events for neutrino scattering\cite{Sob12}. Inversely, by performing the transformation to the CM system, it can be shown that the phase-space function, which is proportional to the two particle-two hole (2p-2h) hadronic tensor for a constant current operator, can be computed analytically in the frozen nucleon approximation, if Pauli blocking is absent. The results in the CM frame confirm our previous work done using an alternative approach in the Lab frame. The possibilities of using this method to compute the hadronic tensor by a boost to the CM system are analyzed.