Abstract
Modern facilities are poised to tackle fundamental questions within the Standard Model, aiming to reveal the nature of confinement, its relationship to dynamical chiral symmetry breaking (DCSB) - the origin of visible mass - and the connection between these two, key emergent phenomena. There is strong evidence to suggest that they are intimately connected with the appearance of momentum-dependent masses for gluons and quarks in QCD, which are large in the infrared: $m_g \sim 500\,$MeV and $M_q\sim 350\,$MeV. DCSB, expressed in the dynamical generation of a dressed-quark mass, has an enormous variety of verifiable consequences, including an enigmatic result that the properties of the (almost) massless pion are the cleanest expression of the mechanism which is responsible for almost all the visible mass in the Universe. This contribution explains that these emergent phenomena are expressed with particular force in the partonic structure of hadrons, e.g. in valence-quark parton distribution amplitudes and functions, and, consequently, in numerous hadronic observables, so that we are now in a position to exhibit the consequences of confinement and DCSB in a wide range of hadron observables, opening the way to empirical verification of their expression in the Standard Model.
Highlights
Classical chromodynamics (CCD) is a non-Abelian local gauge field theory
Spontaneous symmetry breaking, as realised via the Higgs mechanism, does not solve this problem because normal matter is constituted from light-quarks, u and d, and the masses of the neutron and proton, the kernels of all visible matter, are roughly 100-times larger than anything the Higgs can produce in connection with u- and d-quarks
Where the last equality follows from Eq (1): the energy-momentum tensor is traceless in a scale invariant theory
Summary
Classical chromodynamics (CCD) is a non-Abelian local gauge field theory. As with all such theories formulated in four spacetime dimensions, no length-scale exists in the absence of Lagrangian masses for the fermions. Energy and momentum conservation in a quantum field theory is a consequence of spacetime translational invariance, one of the family of Poincaré transformations. Where β(α) is the β-function of quantum chromodynamics (QCD), ζ is the renormalisation scale, Gaμν is the gluon field-strength tensor, and this expression assumes the chiral limit for all current-quarks. Renormalisation-group-invariance does not entail form invariance of the right-hand-side (rhs) [6] This is important because discussions typically assume (perhaps implicitly) that all operators and identities are expressed in a partonic basis, viz. That perspective is not valid at renormalisation scales ζ mp, where mp is the proton mass; and this is where a metamorphosis from parton-basis to quasiparticle-basis may occur: under reductions in resolving scale, ζ, light partons evolve into heavy dressed-partons, corresponding to complex superpositions of partonic operators; and using these dressed-parton operators, the wave functions can be expressed in a relatively simple form [7]
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