A Light-Front approach to the $^3$He spectral function

TL;DR

This paper develops a light-front covariant framework for the spin-dependent spectral function of polarized helium-3, crucial for extracting neutron quark distributions from electron scattering experiments.

Contribution

It introduces a Poincaré covariant generalization of the spectral function within a light-front dynamics approach, revealing dependencies among transverse-momentum distributions.

Findings

Only three of six leading twist T-even distributions are independent.

The framework accounts for final state interactions in a relativistic setting.

The approach is applicable to semi-inclusive deep inelastic scattering experiments.

Abstract

The analysis of semi-inclusive deep inelastic electron scattering off polarized $^3$He at finite momentum transfers, aimed at the extraction of the quark transverse-momentum distributions in the neutron, requires the use of a distorted spin-dependent spectral function for $^3$He, which takes care of the final state interaction effects. This quantity is introduced in the non-relativistic case, and its generalization in a Poincar\'e covariant framework, in plane wave impulse approximation for the moment being, is outlined. Studying the light-front spin-dependent spectral function for a J=1/2 system, such as the nucleon, it is found that, within the light-front dynamics with a fixed number of constituents and in the valence approximation, only three of the six leading twist T-even transverse-momentum distributions are independent.