Distribution Functions of Radially Excited Pion using the Light-Front Quark Model

TL;DR

This paper models the internal structure of the pion's ground and excited states using a light-front quark model, analyzing distribution functions, form factors, and decay constants, with results aligning well with experimental data.

Contribution

It introduces a variational approach with harmonic-oscillator eigenstates to study radially excited pion states within the light-front framework, highlighting state mixing effects.

Findings

Ground state distribution amplitude agrees with experimental data.

Parton distribution functions are sensitive to state mixing, especially for higher excitations.

Decay constants decrease with increasing radial excitation.

Abstract

We investigate the internal structure of the ground ($1S$) and the first two radially excited ($2S,3S$) states of the pion within the light-front quark model. The valence Fock sector is described using pure harmonic-oscillator eigenstates and mixed states formed as orthogonal linear combinations of these eigenfunctions. The optimal wavefunction parameters are determined through a variational procedure based on a QCD-motivated effective Hamiltonian. Using the resulting light-front wavefunctions, we study the pion distribution amplitude, parton distribution function, and electromagnetic form factor. After QCD evolution, the ground state distribution amplitude and parton distribution function are found to be in good agreement with available experimental data. At the model scale, the parton distribution functions of the $1S$ and $2S$ states show clear sensitivity to state mixing, while the distribution amplitudes and electromagnetic form factors are weakly sensitive. In contrast, for the $3S$ state, all three observables exhibit a pronounced sensitivity to mixing. The decay constants of the mixed states are also found to decrease sequentially with increasing radial excitation.