Partonic distribution functions and amplitudes using tensor network methods

TL;DR

This paper employs tensor network methods to directly compute parton distribution functions and distribution amplitudes from first principles, providing a novel approach to non-perturbative QCD calculations.

Contribution

It introduces a tensor network framework for calculating PDFs and DAs, demonstrating its effectiveness with the Nambu-Jona-Lasinio model in 1+1 dimensions.

Findings

Tensor network methods successfully extract PDFs and DAs at various couplings.

Results agree with exact diagonalization and quantum circuit simulations.

Method bridges non-perturbative calculations with tensor network techniques.

Abstract

Calculations of the parton distribution function (PDF) and distribution amplitude (DA) are highly relevant to core experimental programs as they provide non-perturbative inputs to inclusive and exclusive processes, respectively. Direct computation of the PDFs and DAs remains challenging because they are non-perturbative quantities defined as light-cone correlators of quark and gluon fields, and are therefore inherently time-dependent. In this work, we use a uniform quantum strategy based on tensor network simulation techniques to directly extract these hadronic quantities from first principles using the matrix product state of the hadrons in the same setup. We present exemplary numerical calculations with the Nambu-Jona-Lasinio model in 1+1 dimensions and compare with available exact diagonalization and quantum circuit simulation results. Using tensor networks, we evaluate the PDF and DA at various strong couplings in the large-qubit limit, which is consistent with expectations at perturbative and non-relativistic limits.