Gravitational form factors of heavy quarkonia and their nonrelativistic expansion in a self-consistent light-front quark model
Abstract
We investigate the gravitational form factors of the pseudoscalar heavy quarkonia ηc(1S,2S) and ηb(1S,2S) in a light-front quark model with physical radial wave functions represented by orthogonal mixtures of the two lowest harmonic-oscillator basis states ϕ1S and ϕ2S. The Bakamjian--Thomas prescription is applied consistently to constituent matrix elements and Lorentz prefactors at the integrand level. Working in the Δ+=0 frame with Δ=P'−P and t=Δ2, we extract Aq(t) from the quark energy--momentum tensor components Tq++, Tq+i, and Tqij, and Dq(t) from Tq+−, Tq−i, and Tqii using appropriate momentum-transfer projections. The independent extractions agree in the full relativistic calculation and in the analytic nonrelativistic expansions through $ O(v^2)$, where v=β/mQ, β is the Gaussian width, and mQ is the constituent mass. At zero momentum transfer, the expansions give Dqϕ1S(0)=−v2+ O(v4) and Dqϕ2S(0)=−2/3−(13/3)v2+O(v4). The interference, defined as the sum of the two cross overlaps, first contributes as Dqcross(0)=−(4/√6)v2+O(v4). Thus, the pure Gaussian 1S contribution is suppressed, whereas a nonzero 2S admixture at fixed mixing angle leaves an O(v0) D-term in the physical ground state. Full numerical results for the mixed states illustrate the effects of heavy-quark flavor and radial structure on mass distributions and internal stresses.
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BibTeX
@misc{choi2026gravitational,
title = {{Gravitational form factors of heavy quarkonia and their nonrelativistic expansion in a self-consistent light-front quark model}},
author = {Ho-Meoyng Choi and Chueng-Ryong Ji and Hyeon-Dong Son},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.00952},
eprint = {2611.00952},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.00952},
}
RIS
TY - UNPB
TI - Gravitational form factors of heavy quarkonia and their nonrelativistic expansion in a self-consistent light-front quark model
AU - Ho-Meoyng Choi
AU - Chueng-Ryong Ji
AU - Hyeon-Dong Son
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.00952
UR - https://arxiv.org/abs/2611.00952
AB - We investigate the gravitational form factors of the pseudoscalar heavy quarkonia η_c(1S,2S) and η_b(1S,2S) in a light-front quark model with physical radial wave functions represented by orthogonal mixtures of the two lowest harmonic-oscillator basis states ϕ_1S and ϕ_2S. The Bakamjian--Thomas prescription is applied consistently to constituent matrix elements and Lorentz prefactors at the integrand level. Working in the Δ^+=0 frame with Δ=P'−P and t=Δ^2, we extract A_q(t) from the quark energy--momentum tensor components T_q^++, T_q^+i, and T_q^ij, and D_q(t) from T_q^+−, T_q^−i, and T_q^ii using appropriate momentum-transfer projections. The independent extractions agree in the full relativistic calculation and in the analytic nonrelativistic expansions through $ O(v^2)$, where v=β/m_Q, β is the Gaussian width, and m_Q is the constituent mass. At zero momentum transfer, the expansions give D_q^ϕ_1S(0)=−v^2+ O(v^4) and D_q^ϕ_2S(0)=−2/3−(13/3)v^2+O(v^4). The interference, defined as the sum of the two cross overlaps, first contributes as D_q^cross(0)=−(4/√6)v^2+O(v^4). Thus, the pure Gaussian 1S contribution is suppressed, whereas a nonzero 2S admixture at fixed mixing angle leaves an O(v^0) D-term in the physical ground state. Full numerical results for the mixed states illustrate the effects of heavy-quark flavor and radial structure on mass distributions and internal stresses.
ER -