# The frozen nucleon approximation in two-particle two-hole response functions

## TL;DR

This paper introduces a simplified, fast computational method for 2p-2h electroweak response functions in neutrino and electron scattering, using the frozen nucleon approximation to enable efficient Monte Carlo simulations.

## Contribution

The paper proposes a novel frozen nucleon approximation that reduces the complexity of calculating 2p-2h responses, making it suitable for Monte Carlo event generators.

## Key findings

- Accurately computes 2p-2h responses with a one-dimensional integral.
- The approximation is valid for high and moderate momentum transfers.
- Significantly reduces computational time for response calculations.

## Abstract

We present a fast and efficient method to compute the inclusive two-particle two-hole (2p-2h) electroweak responses in the neutrino and electron quasielastic inclusive cross sections. The method is based on two approximations. The first neglects the motion of the two initial nucleons below the Fermi momentum, which are considered to be at rest. This approximation, which is reasonable for high values of the momentum transfer, turns out also to be quite good for moderate values of the momentum transfer $q\gtrsim k_F$. The second approximation involves using in the "frozen" meson-exchange currents (MEC) an effective $\Delta$-propagator averaged over the Fermi sea. Within the resulting "frozen nucleon approximation", the inclusive 2p-2h responses are accurately calculated with only a one-dimensional integral over the emission angle of one of the final nucleons, thus drastically simplifying the calculation and reducing the computational time. The latter makes this method especially well-suited for implementation in Monte Carlo neutrino event generators.