The Mass Gap in QCD and a Restriction on Gluon Masses

Article ID: e030524229628 Pages: 5

  • * (Excluding Mailing and Handling)

Abstract

In this study, we prove that it is necessary to introduce the non-zero gluon masses into the fundamental Lagrangian of Quantum Chromodynamics in order to describe the mass gap in the reaction of electron-positron annihilation into hadrons. Further, in this work, a new restriction on the gluon masses is imposed, and the renormalized theory with non-zero Lagrangian gluon masses is presented.

[1]
Gross, D.J.; Wilczek, F. Ultraviolet behavior of non-abelian gauge theories. Phys. Rev. Lett., 1973, 30(26), 1343-1346.
[http://dx.doi.org/10.1103/PhysRevLett.30.1343]
[2]
Politzer, H.D. Reliable Perturbative Results for Strong Interactions? Phys. Rev. Lett., 1973, 30(26), 1346-1349.
[http://dx.doi.org/10.1103/PhysRevLett.30.1346]
[3]
’t Hooft, G. Report at the Marseille Conference on Yang-Mills Fields Colloquium on Renormalization of Yang-Mills Fields and Applications to Particle Physics. 19 Jun 1972, Marseilles, France, p. 234, 1972
[4]
Higgs, P.W. Broken symmetries, massless particles and gauge fields. Phys. Lett., 1964, 12(2), 132-133.
[http://dx.doi.org/10.1016/0031-9163(64)91136-9]
[5]
Englert, F.; Brout, R. Broken symmetry and the mass of gauge vector mesons. Phys. Rev. Lett., 1964, 13(9), 321-323.
[http://dx.doi.org/10.1103/PhysRevLett.13.321]
[6]
Cornwall, J.M. Quark confinement and vortices in massive gauge-invariant QCD. Nucl. Phys. B, 1979, 157(3), 392-412.
[http://dx.doi.org/10.1016/0550-3213(79)90111-1]
[7]
Cornwall, J.M. Dynamical mass generation in continuum QCD. Phys. Rev. D Part. Fields, 1982, 26, 1453.
[http://dx.doi.org/10.1103/PhysRevD.26.1453]
[8]
Graziani, F.R. The gluon condensate and the effective gluon mass. Z. Phys., 1987, 33, 397.
[9]
Aguilar, A.C.; Papavassiliou, J. Power law running of the effective gluon mass. Eur. Phys. J. A, 2008, 35(2), 189-205.
[http://dx.doi.org/10.1140/epja/i2008-10535-4]
[10]
Leinweber, D.B.; Skullerud, J.I.; Williams, A.G.; Parrinello, C. Asymptotic scaling and infrared behavior of the gluon propagator. Phys. Rev. D Part. Fields, 1999, 60(9), 094507.
[http://dx.doi.org/10.1103/PhysRevD.60.094507]
[11]
Yang, C.N.; Mills, R.L. Conservation of isotopic spin and isotopic gauge invariance. Phys. Rev., 1954, 96(1), 191-195.
[http://dx.doi.org/10.1103/PhysRev.96.191]
[12]
Larin, S.A. On mass-shell renormalizability of the massive Yang-Mills theory. Phys. Part. Nuclei., 2013, 44, 386-390.
[http://dx.doi.org/10.1134/S1063779613020202]
[13]
Faddeev, L.D.; Slavnov, A.A. Gauge fields. Introduction to quantum theory. Front. Phys., 1980, 50, 1-232.
[14]
Faddeev, L.D.; Slavnov, A.A. Gauge fields. Introduction to quantum theory. Front. Phys., 1991, 83, 1-217.
[15]
Davies, J.; Gröber, R.; Maier, A.; Rauh, T.; Steinhauser, M. Top quark mass dependence of the Higgs boson-gluon form factor at three loops. Phys. Rev. D, 2019, 100, 034017.
[http://dx.doi.org/10.1103/PhysRevD.100.034017]
[16]
Burikham, P.; Harko, T.; Lake, M.J. The QCD mass gap and quark deconfinement scales as mass bounds in strong gravity. Eur. Phys. J. C, 2017, 77, 803.
[http://dx.doi.org/10.1140/epjc/s10052-017-5381-9]
[17]
Frasca, M.; Ghoshal, A.; Groote, S. Confinement in QCD and generic Yang-Mills theories with matter representations. Phys. Lett. B, 2023, 846, 138209.
[http://dx.doi.org/10.1016/j.physletb.2023.138209]
[18]
Duarte, A.G.; Oliveira, O.; Silva, P.J. Lattice gluon and ghost propagators and the strong coupling in ure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects. Phys. Rev. D, 2017, 96(9), 098502.
[http://dx.doi.org/10.1103/PhysRevD.94.014502]
[19]
Boucaud, Ph.; De Soto, F.; Rodríguez-Quintero, J.; Zafeiropoulos, S. Lattice gluon and ghost propagators and the strong coupling in pure SU(3) Yang-Mills theory: Finite lattice spacing and volume effects. Phys. Rev. D, 2017, 96(9), 098501.
[http://dx.doi.org/10.1103/PhysRevD.96.098501]
[20]
Duarte, A.G.; Oliveira, O.; Silva, P.J. Lattice gluon and ghost propagators, and the strong coupling in pure su(3) yang-mills theory: finite lattice spacing and volume effects. Phys. Rev. D, 2016, 94(1), 014502.
[http://dx.doi.org/10.1103/PhysRevD.94.014502]
[21]
Narison, S. QCD as a Theory of Hadrons: From Partons to Confinement. Camb. Monogr. Part. Phys. Nucl. Phys. Cosmol., 2002, 17(1)
[http://dx.doi.org/10.48550/arXiv.hep-ph/0205006]
[22]
Gomez Dumm, D.; Grunfeld, A.G.; Scoccola, N.N. On covariant nonlocal chiral quark models with separable interactions. Phys. Rev. D, 2006, 74, 054026.
[http://dx.doi.org/10.1103/PhysRevD.74.054026]
[23]
El-Nabulsi, R.A.; Anukool, W. Spontaneous symmetry breaking and massive photons from a Fresnel-type potential. Pramana -. J. Phys., 2023, 96(186), 4.
[http://dx.doi.org/10.1007/s12043-022-02440-w]
[24]
El-Nabulsi, R.A.; Anukool, W. Spontaneous symmetry breaking and massive photons from a Fresnel-type potential. Pramana, 2022, 96(4), 186.
[http://dx.doi.org/10.1007/s12043-022-02440-w]
[25]
Wetterich, C. Higgs picture of the QCD-vacuum. AIP Conf Proc, 2004, 739(1), 123-59.
[http://dx.doi.org/10.1063/1.1843594]
[26]
Braun, J.; Fister, L.; Pawlowski, J.M.; Rennecke, F. From quarks and gluons to hadrons: Chiral symmetry breaking in dynamical QCD. Phys. Rev. D, 2016, 94(3), 034016.
[http://dx.doi.org/10.1103/PhysRevD.94.034016]
[27]
Larin, S.A. The mass-gap in quantum chromodynamics and a restriction on gluon masses; Part Fiel Phys, 2020, p. 2020050457.
[http://dx.doi.org/10.20944/preprints202005.0457.v3]
[28]
Collins, J.C. Renormalization: An Introduction to Renormalization, the Renormalization Group and the Operator-Product Expansion; Cambridge University Press, 1984.
[http://dx.doi.org/10.1017/CBO9780511622656]
[29]
Gribov, V.N. Quantization of non-Abelian gauge theories. Nucl. Phys. B, 1978, 139(1-2), 1-19.
[http://dx.doi.org/10.1016/0550-3213(78)90175-X]
[30]
Källen, G. On the definition of the renormalization constants in quantum electrodynamics. Helv. Phys. Acta, 1952, 25, 417.
[31]
Lehmann, H. On the Properties of propagation functions and renormalization contants of quantized fields. Nuovo Cim., 1954, 11, 342.
[http://dx.doi.org/10.1007/BF02783624]
[32]
Larin, S.A. Quantum Chromodynamics with massive gluons. AIP Conf Proc, 2016, 1701(1), 070003.
[http://dx.doi.org/10.1063/1.4938688]
[33]
Kniehl, B.A.; Kühn, J.H. QCD corrections to the Z decay rate. Nucl. Phys. B, 1990, 329(3), 547-573.
[http://dx.doi.org/10.1016/0550-3213(90)90070-T]
[34]
Larin, S.A.; van Ritbergen, T.; Vermaseren, J.A.M. The Large quark mass expansion of Gamma (Z0 ---> hadrons) and Gamma (tau- ---> tau-neutrino + hadrons) in the order alpha-s**3. Nucl. Phys. B, 1995, 438(1-2), 278-304.
[http://dx.doi.org/10.1016/0550-3213%2894%2900574-X]
[35]
Bogoliubov, N.N.; Parasiuk, O.S. On the Multiplication of the causal function in the quantum theory of fields. Acta Math., 1957, 97, 227.
[36]
Hepp, K. Proof of the Bogoliubov-Parasiuk theorem on renormalization. Commun. Math. Phys., 1966, 2(1), 301-326.
[http://dx.doi.org/10.1007/BF01773358]
[37]
Symanzik, K. Renormalizable models with simple symmetry breaking. Commun. Math. Phys., 1970, 16(1), 48-80.
[http://dx.doi.org/10.1007/BF01645494]
[38]
Slavnov, A.A. Ward identities in gauge theories. Theor. Math. Phys., 1972, 10(2), 99-104.
[http://dx.doi.org/10.1007/BF01090719]
[39]
Taylor, J.C. Ward identities and charge renormalization of the Yang-Mills field. Nucl. Phys. B, 1971, 33(2), 436-444.
[http://dx.doi.org/10.1016/0550-3213(71)90297-5]