We present a systematic study of the leading- and next-to-leading-twist light-cone distribution amplitudes (LCDAs) of ground-state pseudoscalar and vector quarkonium within the light-front quark model (LFQM). By implementing the replacement M → M0, we analyze the longitudinal and transverse structures of the LCDAs, together with their Gegenbauer moments, ξ-moments, and transverse momentum moments. We show that charge-conjugation symmetry enforces the exact vanishing of all odd Gegenbauer moments and odd ξ-moments. For pseudoscalar quarkonium, the twist-2 and twist-3 LCDAs become identical, which leads to the same Gegenbauer moments, ξ-moments, and transverse momentum moments. For vector quarkonium, although the twist-2 and twist-3 LCDAs differ in the case of finite quark masses, they progressively converge as the quark mass increases. In the heavy-quark limit, all quarkonium LCDAs satisfy <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>ϕ</mi> <mn>2</mn> <mi>A</mi> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\phi}_2^A $</EquationSource> </InlineEquation> = <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>ϕ</mi> <mn>3</mn> <mi>P</mi> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\phi}_3^P $</EquationSource> </InlineEquation> ≃ <InlineEquation ID="IEq3"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>ϕ</mi> <mn>2</mn> <mo>∥</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\phi}_2^{\parallel } $</EquationSource> </InlineEquation> ≃ <InlineEquation ID="IEq4"> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>ϕ</mi> <mn>3</mn> <mo>⊥</mo> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\phi}_3^{\perp } $</EquationSource> </InlineEquation>, demonstrating an emergent twist-independence of quarkonium distribution amplitudes. We further find that the LCDAs become increasingly peaked and narrower with increasing quark mass, indicating that the meson system becomes increasingly close to a nonrelativistic bound state, with a more uniform and stable distribution of internal longitudinal momentum. For all quarkonium, the peak value exhibits a simple phenomenological scaling behavior governed by the ratio m/β. The transverse momentum moments increase with the meson mass, indicating a progressively more compact bound-state structure. These results reveal a universal and systematic evolution of quarkonium LCDAs driven by the quark mass.

Quarkonium light-cone distribution amplitudes: twist structure and mass dependence

期刊论文
出版模式：

开放获取
发表日期：

2026年5月13日

查看全文

Shuai Xu,
Xiao-Nan Li,
Jin-Zhong Han,
Bai-Hui Cheng,
Li-Li Chen,
Qin Chang

摘要

We present a systematic study of the leading- and next-to-leading-twist light-cone distribution amplitudes (LCDAs) of ground-state pseudoscalar and vector quarkonium within the light-front quark model (LFQM). By implementing the replacement M → M₀, we analyze the longitudinal and transverse structures of the LCDAs, together with their Gegenbauer moments, ξ-moments, and transverse momentum moments. We show that charge-conjugation symmetry enforces the exact vanishing of all odd Gegenbauer moments and odd ξ-moments. For pseudoscalar quarkonium, the twist-2 and twist-3 LCDAs become identical, which leads to the same Gegenbauer moments, ξ-moments, and transverse momentum moments. For vector quarkonium, although the twist-2 and twist-3 LCDAs differ in the case of finite quark masses, they progressively converge as the quark mass increases. In the heavy-quark limit, all quarkonium LCDAs satisfy $ϕ_{2}^{A}$ $ {\phi}_2^A $ = $ϕ_{3}^{P}$ $ {\phi}_3^P $ ≃ $ϕ_{2}^{∥}$ $ {\phi}_2^{\parallel } $ ≃ $ϕ_{3}^{⊥}$ $ {\phi}_3^{\perp } $ , demonstrating an emergent twist-independence of quarkonium distribution amplitudes. We further find that the LCDAs become increasingly peaked and narrower with increasing quark mass, indicating that the meson system becomes increasingly close to a nonrelativistic bound state, with a more uniform and stable distribution of internal longitudinal momentum. For all quarkonium, the peak value exhibits a simple phenomenological scaling behavior governed by the ratio m/β. The transverse momentum moments increase with the meson mass, indicating a progressively more compact bound-state structure. These results reveal a universal and systematic evolution of quarkonium LCDAs driven by the quark mass.