@misc{10481/91893,
year = {2024},
month = {1},
url = {https://hdl.handle.net/10481/91893},
abstract = {This paper concerns a method of describing hadrons that starts with the canonical front form Hamiltonian
of QCD. The method is developed in the relatively simple context of QCD with only heavy quarks. We
regulate its canonical Hamiltonian by introducing a vanishingly small gluon mass mg. For positive mg, the
small-x gluon divergences become ultraviolet and hence they are renormalized in the sameway the ultraviolet
transverse divergences are. This is done using the renormalization group procedure for effective particles. Up
to the second order of expansion of the renormalized Hamiltonian in powers of the quark-gluon coupling
constant g, only the quark mass-squared and gluon-exchange divergences require counterterms. In these
circumstances, we calculate an effective potential between quarks in heavy quarkonia in an elementary way,
replacing all the quarkonium-state components with gluons of mass mg by only one component with just one
gluon that is assigned a mass mG, comparable to or exceeding the scale of typical relative momenta of bound
quarks. In the limit of mg → 0 and large mG two results are obtained. (1) While the color-singlet quarkonium
mass eigenvalue stays finite and physically reasonable in that limit, the eigenvalues for single quarks and octet
quarkonia are infinite. (2) Besides the coulomb terms, the effective quark-antiquark potential is quadratic as a
function of the distance and spherically symmetric for typical separations between quarks but becomes
logarithmic and no longer spherically symmetric for large separations. Our conclusion indicates how to
systematically improve upon the approximations made in this paper.},
organization = {Senior Scientist
Program funded by Gansu Province, Grant
No. 22JR10KA001},
organization = {Gansu International Collaboration
and Talents Recruitment Base of Particle Physics (2023-2027)},
organization = {Chinese Academy of Sciences President’s
International Fellowship Initiative (PIFI), Grant
No. 2021PM0066},
organization = {Chinese Ministry of Science and
Technology Foreign Expert Project, Grant
No. QN20200143003},
organization = {National Natural Science
Foundation of China (NSFC) under Grant No. 12047555},
organization = {FEDER2020
funds, project Ref. A-FQM-406-UGR20 and from MCIN/AEI/10.13039/501100011033, Project Ref. PID2020–114767 GB-I00},
organization = {Department of Science and Technology (DST), Government of India, for financial support through Grant No. SR/WOS-A/PM-6/2019},
publisher = {American Physical Society},
title = {Dynamics of heavy quarks in the Fock space},
doi = {10.1103/PhysRevD.109.016017},
author = {Serafin, Kamil and Gómez Rocha, María and More, Jai and Głazek, Stanislaw D.},
}