Maximum Entropy Method for Valence Quark Distributions in Exotic Hadrons: A Study of the Z_c(3900) Case
arxiv(2024)
Abstract
In this study we demonstrate the application of the Maximum Entropy Method
(MEM) to determine the valence quark distribution of exotic hadrons. Our
investigation yields three key findings. Firstly, we observe a significant
shift towards smaller Bjorken scale x in the peak position of the valence
quark distribution for hadrons with an increasing number of valence quarks,
consistent with previous results by Kawamura and Kumano. Secondly, assuming
that the Z_c(3900) initially consists of four valence quarks, we employ MEM
to determine its initial valence quark distribution, estimating a radius of
r_c=1.276 fm at an extremely low resolution scale Q^2. Furthermore, we
identify a notable discrepancy between our computed charge form factor G_c(q)
at leading order and the outcomes of hadron molecular state calculations. We
propose that this form factor can be extracted from the QCD counting rule
cross-section, which is grounded in Generalized Distribution Amplitudes (GDA)
linked to the multi-quark states.
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