Searching for $a_0(980)$-meson parton distribution function

TL;DR

This paper models the $a_0(980)$-meson’s leading-twist wavefunction using a light-cone harmonic oscillator approach, deriving its distribution functions and Mellin moments at various scales to understand its parton structure.

Contribution

It introduces a novel calculation of the $a_0(980)$-meson’s wavefunction and distribution functions using the LCHO model, providing scale-dependent parton distributions and Mellin moments.

Findings

Derived the $a_0(980)$-meson distribution amplitudes at three scales.

Calculated Mellin moments of the valence quark distribution.

Presented scale evolution of the distribution functions.

Abstract

In this paper, we calculate the scalar $a_0(980)$-meson leading-twist wavefunction by using light-cone harmonic oscillator model (LCHO). In which the model parameters are determined by fitting the $\xi$-moments $\langle\xi_{a_0}^n\rangle_\zeta$ of its light-cone distribution amplitudes. Then, the $a_0(980)$-meson leading-twist light-cone distribution amplitudes with three different scales $\zeta= (1.0, 2.0, 5.2)~{\rm GeV}$ are given. After constructing the relationship between $a_0(980)$-meson leading-twist parton distribution functions/valence quark distribution function and its LCHO wavefunction, we exhibit the $q^{a_0}(x,\zeta)$ and $x q^{a_0}(x,\zeta)$ with different scales. Furthermore, we also calculate the Mellin moments of the $a_0(980)$-meson's valence quark distribution function $\langle x^n q^{a_0}\rangle_\zeta$ with $n = (1,2,3)$, i.e. $\langle x q^{a_0}\rangle_{\zeta_5} = 0.026$, $\langle x^2 q^{a_0}\rangle_{\zeta_5} = 0.017$ and $\langle x^3 q^{a_0}\rangle_{\zeta_5} = 0.012$. Finally, the scale evolution for the ratio of the Mellin moments $x^n_{a_0}(\zeta,\zeta_k)$ are presented.