Towards studying the structural differences between the pion and its radial excitation

TL;DR

This study uses lattice QCD to compare the valence quark structures of the pion and its radial excitation, providing initial evidence of structural differences and demonstrating the potential for future detailed investigations.

Contribution

It is the first lattice QCD investigation to explore the structural differences between the pion and its radial excitation, specifically the $ ho(1300)$, using a finite volume approach.

Findings

Radial excitation shows nearly double the valence quark momentum fraction.

Evidence suggests the first excited state is a single particle state consistent with $ ho(1300)$.

The work demonstrates the feasibility of future lattice studies with larger operator bases.

Abstract

We present an exploratory lattice QCD investigation of the differences between the valence quark structure of pion and its radial excitation $\pi(1300)$ in a fixed finite volume using the leading-twist factorization approach. We present evidences that the first pion excitation in our lattice computation is a single particle state that is likely to be the finite volume realization of $\pi(1300)$. An analysis with reasonable priors result in better estimates of the excited state PDF and the moments, wherein we find evidence that the radial excitation of pion correlates with an almost two-fold increase in the momentum fraction of valence quarks. This proof-of-principle work establishes the viability of future lattice computations incorporating larger operator basis that can resolve the structural changes accompanying hadronic excitation.