Mass Gap in Quantum Chromodynamics

We present a heuristic argument in support of the assertion that QCD will exhibit a mass gap, if the Callan-Symanzik function β(g) obeys the inequality β(g) < 0, for all g > 0. We begin by summarizing the standard lore attributed to QCD: (A) QCD must have a mass gap, i.e., every excitation above the vacuum state must have energy > △, where △ is a positive constant. The key idea that infrared slavery requires the generation of a mass gap (dynamical gluon mass) in QCD was enunciated in a pioneering paper by Cornwall in 1982 [1]. (B) QCD must exhibit “quark confinement”, i.e., the observed (physical) particle spectrum (pion, proton,...) are color SUC(3) invariant, despite the fact that QCD is described by an underlying Lagrangian of quarks and non-abelian gluons, which transform non-trivially under color SUc(3) symmetry. (C) QCD must exhibit chiral symmetry breakdown, i.e., the flavor axial-vector charges Q 5 (α = 1, 2 . . . 8) must break the flavor SU F (3) ⊗ SU R F (3) spontaneously, i.e. Q 5 |0〉 6 = 0, so that the vacuum is only invariant under a subgroup of ∗Dedicated to honor George Sudarshan on his 75 birthday