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arXiv · 2108.10625

Ground state pseudoscalar mesons on the light front: from the light to heavy sector

Chao Shi·Ming Li·Xurong Chen·Wenbao Jia
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Abstract

We extract the leading Fock-state light front wave functions (LF-LFWFs) of both the light and heavy pseudoscalar mesons, e.g., the pion (at masses of 130 MeV, 310 MeV and 690 MeV), $η_c$ and $η_b$, from their covariant Bethe-Salpeter wave functions within the rainbow-ladder (RL) truncation. It is shown that the LF-LFWFs get narrower in $x$ (the longitudinal momentum fraction of meson carried by the quark) with the increasing current quark mass, and the leading twist parton distribution amplitudes (PDAs) inherit this feature. Meanwhile, we find in the pion the LF-LFWFs only contribute around 30\% to the total Fock-state normalization, indicating the presence of significant higher Fock-states within. In contrast, in the $η_c$ and $η_b$ the LF-LFWFs contribute more than $90$\%, suggesting the $Q\bar{Q}$ valence Fock-state truncation as a good approximation for heavy mesons. We thus study the 3-dimensional parton distributions of the $η_c$ and $η_b$ with the unpolarized generalized parton distribution function (GPD) and the transverse momentum dependent parton distribution function (TMD). Through the gravitational form factors in connection with the GPD, the mass radii of the $η_c$ and $η_b$ in the light-cone frame are determined to be $r_{E,{\rm LC}}^{η_c} =0.150$ fm and $r_{E,{\rm LC}}^{η_b} =0.089$ fm respectively.

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Chao Shi, Ming Li, Xurong Chen, Wenbao Jia. 2021-08-24. Ground state pseudoscalar mesons on the light front: from the light to heavy sector. https://doi.org/10.1103/physrevd.104.094016

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