Journal of Particle Physics

Download PDF (209.6 KB) PP. 1 - 4 Pub. Date: October 30, 2019

DOI: 10.22606/jpp.2019.31001

• Herbert M. Fried^*
  Department of Physics, Brown University, Providence, Rhode Island, United States
• Peter H. Tsang^*
  Department of Physics, Brown University, Providence, Rhode Island, United States

We suggest a physical definition of the confinement mass scale in QCD in the framework of non-perturbative, gauge invariant QCD, where all possible gluons exchanged between any pair of quark lines are included; and we insist that a stable, quark bound state should not and must not have transverse quark fluctuations larger than the Compton wavelength of the bound state particle itself. This is possible in our QCD formulation because there are two parameters which describe confinement, a mass scale μ, and a “deformation parameter” ξ, which shrinks the transverse-quarkcoordinate separation distribution φ(b) away from Gaussian. With the mass scale μ defined as equal to the mass of each quark bound state, we show that ξ decreases with increasing bound state mass, mBS, using order-of-magnitude estimates which agree with obvious intuition. Our ξ-values, including a calculation for the recently detected 4-quark system, display the predicted behavior: ξ decreases with increasing mBS. Our results for φ(b), when the quark bound state is a nucleon or heavier, then show agreement with the form of Gaussian momentum-space fall-offs in recent Light-Front holographic analyses.

QCD, confinement, hadron spectrum, light front QCD

[1] H. M. Fried, Y. Gabellini, T. Grandou, and Y. M. Sheu, “Gauge-invariant summation of all qcd virtual gluon exchanges,” European Physical Journal C, vol. 65, pp. 395–411, 2010. [Online]. Available: https://link.springer.com/article/10.1140/epjc/s10052-009-1224-7

[2] H. M. Fried and Y. Gabellini, “On the summation of feynman graphs,” Annals of Physics, vol. 327, pp. 1645–1667, 2012. [Online]. Available: https://doi.org/10.1016/j.aop.2012.03.001

[3] H. M. Fried, Y. Gabellini, T. Grandou, and Y. M. Sheu, “Analytic, non-perturbative, gauge-invariant quantum chromodynamics: Nucleon scattering and binding potentials,” Annals of Physics, vol. 338, pp. 107–122, 2013. [Online]. Available: https://doi.org/10.1016/j.aop.2013.07.006

[4] H. M. Fried, “A new, analytic, non-perturbative, gauge-invariant, realistic formulation of qcd,” Modern Physics Letters A, vol. 28, no. 1, p. 1230045, 2013. [Online]. Available: https://www.worldscientific.com/doi/10.1142/S0217732312300455

[5] H. M. Fried, T. Grandou, and Y. M. Sheu, “Non-perturbative qcd amplitudes in quenched and eikonal approximations,” Annals of Physics, vol. 344C, pp. 78–96, 2014. [Online]. Available: https://doi.org/10.1016/j.aop.2014.02.015

[6] T. Grandou, “On the casimir operator dependences of qcd amplitudes,” Europhysics Letters, vol. 107, no. 1, p. 11001, 2014. [Online]. Available: https://iopscience.iop.org/article/10.1209/0295-5075/107/11001

[7] H. G. Dosch, S. Brodsky, and G. F. de Teramond, “Superconformal baryon-meson symmetry and light-front holopgrahic qcd,” Physical Review D, vol. 91, p. 085016, 2015. [Online]. Available: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.91.085016

[8] S. Brodsky and R. Shrock, “Maximum wavelength of confined quarks and gluons and properties of quantum chromodynamics,” Physics Letters B, vol. 666, no. 1, pp. 95–99, 2008. [Online]. Available: https://doi.org/10.1016/j.physletb.2008.06.054

[9] R. A. et al* (LHCb Collaboration), “Observation of the resonant character of the z(4430) aLS state,” Physical Review Letters, vol. 112, p. 222002, 2008. [Online]. Available: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.112.222002

[10] J. B. et al. (Particle Data Group), “Review of particle physics,” Physical Review D, vol. 86, 2001. [Online]. Available: https://doi.org/10.1103/PhysRevD.86.010001