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

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 $⟨{\xi }_{a_0}^n{⟩}_{\zeta }$ of its light-cone distribution amplitudes. Then, the $a_0(980)$-meson leading-twist light-cone distribution amplitudes with three different scales $\zeta =(1.0,2.0,5.2)\mathrm{GeV}$ 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 $⟨x^n{q}^{a_0}{⟩}_{\zeta }$ with $n=(1,2,3)$, i.e. $⟨x{q}^{a_0}{⟩}_{{\zeta }_5}=0.026$, $⟨x^2{q}^{a_0}{⟩}_{{\zeta }_5}=0.017$ and $⟨x^3{q}^{a_0}{⟩}_{{\zeta }_5}=0.012$. Finally, the scale evolution for the ratio of the Mellin moments $x_{a_0}^n(\zeta ,{\zeta }_k)$ are presented.

Comments: 7 pages, 3 figures, comments welcome