Abstract
We formulate a model of quark–antiquark interaction related to the limit transition to the light-front Hamiltonian in quantum chromodynamics. As ultraviolet regularization, we use a lattice in the space of transverse coordinates, and we additionally introduce a longitudinal light-front coordinate cutoff and also corresponding periodic boundary conditions. We regard the zero mode with respect to this coordinate as an independent dynamical variable. The state space of the model is limited to a quark and an antiquark that interact only via the zero mode of the gluon field on the light front. In this framework, we obtain a discrete mass spectrum of bound states. This spectrum is determined by an equation that with respect to the longitudinal coordinate turns out to be analogous to the’ t Hooft equation in two-dimensional quantum chromodynamics. The equation also contains a quark–antiquark potential that ensures confinement in the transverse space.
Similar content being viewed by others
References
R. A. Zubov, E. V. Prokhvatilov, and M. Yu. Malyshev, “Limit transition to the light-front QCD and a quark–antiquark approximation,” Theor. Math. Phys., 184, 1287–1294 (2015).
P. A. M. Dirac, “Forms of relativistic dynamics,” Rev. Modern Phys., 21, 392–398 (1949).
M. Burkardt and A. Langnau, “Hamiltonian formulation of (2+1)-dimensional QED on the light cone,” Phys. Rev. D, 44, 1187–1197 (1991).
M. Burkardt and A. Langnau, “Rotational invariance in light-cone quantization,” Phys. Rev. D, 44, 3857–3867 (1991).
S. A. Paston and V. A. Franke, “Comparison of quantum field perturbation theory for the light front with the theory in Lorentz coordinates,” Theor. Math. Phys., 112, 1117–1130 (1997); arXiv:hep-th/9901110v1 (1999).
V. A. Franke, Yu. V. Novozhilov, S. A. Paston, and E. V. Prokhvatilov, “Quantization of field theory on the light front,” in: Focus on Quantum Field Theory (O. Kovras, ed.), Nova Science, New York (2005), pp. 23–81; arXiv:hep-th/0404031v2 (2004).
S. A. Paston, E. V. Prokhvatilov, and V. A. Franke, Theor. Math. Phys., 120, 1164–1181 (1999); arXiv:hep-th/ 0002062v3 (2000).
E. V. Prokhvatilov and V. A. Franke, “Limiting transition of light-front coordinates in field theory and the QCD Hamiltonian,” Sov. J. Nucl. Phys., 49, 688–692 (1989).
V. A. Franke, Yu. V. Novozhilov, and E. V. Prokhvatilov, “On the light-cone formulation of classical non-abelian gauge theory,” Lett. Math. Phys., 5, 239–245 (1981).
V. A. Franke, Yu. V. Novozhilov, and E. V. Prokhvatilov, “On the light-cone quantization of non-abelian gauge theory,” Lett. Math. Phys., 5, 437–444 (1981).
E. V. Prokhvatilov, H. W. L. Naus, and H.-J. Pirner, “Effective light-front quantization of scalar field theories and two-dimensional electrodynamics,” Phys. Rev. D, 51, 2933–2942 (1995).
E. M. Ilgenfriz, S. A. Paston, H. J. Pirner, E. V. Prokhvatilov, and V. A. Franke, “Quantum fields on the light front, formulation in coordinates close to the light front, lattice approximation,” Theor. Math. Phys., 148, 948–959 (2006); arXiv:hep-th/0610020v1 (2006).
E. V. Prokhvatilov and V. A. Franke, “Approximate description of QCD condensates in light cone coordinates,” Sov. J. Nucl. Phys., 47, 559 (1988).
M. Yu. Malyshev and E. V. Prokhvatilov, “Construction of the light-front QCD Hamiltonian with zero modes modeling the vacuum,” Theor. Math. Phys., 169, 1600–1610 (2011).
G. ’t Hooft, “A two-dimensional model for mesons,” Nucl. Phys. B, 75, 461–470 (1974).
D. V. Bugg, “Four sorts of meson,” Phys. Rep., 397, 257–358 (2004).
S. S. Afonin, “Experimental indication on chiral symmetry restoration in meson spectrum,” Phys. Lett. B, 639, 258–262 (2006); arXiv:hep-ph/0603166v2 (2006).
S. S. Afonin, “Light meson spectrum and classical symmetries of QCD,” Eur. Phys. J. A, 29, 327–335 (2006); arXiv:hep-ph/0606310v2 (2006).
M. Shifman and A. Vainshtein, “Highly excited mesons, linear Regge trajectories, and the pattern of the chiral symmetry realization,” Phys. Rev. D, 77, 034002 (2008);arXiv:0710.0863v3 [hep-ph] (2007).
S. J. Brodsky, T. Huang, and G. P. Lepage, “Hadronic wave functions and high momentum transfer interactions in quantum chromodynamics,” in: Particles and Fields 2 (Summer institute, Banff, Canada, 16–27 August 1981, A. Z. Capri and A. N. Kamal, eds), Plenum, New York (1983), pp. 143–199.
A. Vega, I. Schmidt, T. Branz, T. Gutsche, and V. E. Lyubovitskij, “Meson wave function from holographic models,” Phys. Rev. D, 80, 055014 (2009);arXiv:0906.1220v1 [hep-ph] (2009).
A. V. Radyushkin, “Nonforward parton densities and soft mechanism for form factors and wide-angle Compton scattering in QCD,” Phys. Rev. D, 58, 114008 (1998);arXiv:hep-ph/9803316v2 (1998).
S. S. Afonin, “Towards understanding broad degeneracy in non-strange mesons,” Modern Phys. Lett. A, 22, 1359–1371 (2007); arXiv:hep-ph/0701089v2 (2007).
S. S. Afonin, “Properties of possible new unflavored mesons below 2.4 GeV,” Phys. Rev. C, 76, 015202 (2007);arXiv:0707.0824v1 [hep-ph] (2007).
S. S. Afonin, “Hydrogen like classification for light nonstrange mesons,” Internat. J. Modern Phys. A, 23, 4205–4217 (2008); arXiv:0709.4444v2 [hep-ph] (2007).
P. Bicudo, “Large degeneracy of excited hadrons and quark models,” Phys. Rev. D, 76, 094005 (2007);arXiv:hep-ph/0703114v2 (2007).
J. Alfaro, P. Labrana, and A. A. Andrianov, “Extended QCD2 from dimensional projection of QCD4,” JHEP, 0407, 067 (2004);arXiv:hep-th/0309110v3 (2003).
S. J. Brodsky and G. F. de Téramond, “Hadronic spectra and light-front wave functions in holographic QCD,” Phys. Rev. Lett., 96, 201601 (2006);arXiv:hep-ph/0602252v2 (2006).
S. S. Chabysheva and J. R. Hiller, “Dynamical model for longitudinal wave functions in light-front holographic QCD,” Ann. Phys., 337, 143–152 (2013); arXiv:1207.7128v2 [hep-ph] (2012).
Author information
Authors and Affiliations
Corresponding author
Additional information
This research was supported by St. Petersburg State University (Research Grant No. 11.38.189.2014).
Prepared from an English manuscript submitted by the authors; for the Russian version, see Teoreticheskaya i Matematicheskaya Fizika, Vol. 190, No. 3, pp. 440–454, March, 2017.
Rights and permissions
About this article
Cite this article
Zubov, R.A., Prokhvatilov, E.V. & Malyshev, M.Y. Model of quark–antiquark interaction in quantum chromodynamics on the light front. Theor Math Phys 190, 378–390 (2017). https://doi.org/10.1134/S0040577917030072
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0040577917030072