Evolving images of the proton: hadron physics over the past 40 years

Abstract

Once upon a time, the world was simple: the proton contained three quarks, two ups and a down. How these give the proton its mass and its spin seemed obvious. Over the past forty years the proton has become more complicated, and how even these most obvious of its properties is explained in a universe of quarks, antiquarks and gluons remains a challenge. That this should be so should come as no surprise. Quantum Chromodynamics, the theory of the strong interaction, is seemingly simple, and its consequences are straightforward in the domain of hard scattering where perturbation theory applies. However, the beauty of the hadron world is its diversity. The existence of hadrons, their properties, and their binding into nuclei do not appear in the Lagrangian of QCD. They all emerge as a result of its strong coupling. Strong coupling QCD creates complex phenomena, much richer than known 40 years ago: a richness that ensures colour confinement and accounts for more than 95% of the mass of the visible Universe. How strong coupling QCD really works requires a synergy between experiment and theory. A very personal view of these fascinating developments in cold QCD is presented. arXiv:1604.01441v1 [hep-ph] 5 Apr 2016Fifty years ago there was no microscopic theory of hadron dynamics. Other than protons, hadrons appeared as resonances in scattering processes. These all have definite quantum numbers: spin J, parity P , isospin I, and in the case of mesons, charge conjugation C. The description of their interactions is governed by the general properties of scattering and reaction theory. Guided only by the requirement that interactions should be causal, relativistic and conserve probability, the S-(or scattering) matrix obeys analyticity, crossing symmetry and unitarity [9,10]. Almost everything else was modelling. Nevertheless, it was established that the definition of the state in the spectrum of hadrons is a pole of the S-matrix in the complex energy plane. This will produce a textbook "resonant" peak in the cross-section for scattering in a channel to which the resonance couples, if this state is isolated from other resonances and other strongly coupled thresholds. The search for resonances, states in the spectrum of hadrons, is often thought of as bump-hunting, but really it is pole-vaulting. Reconciling unitarity in a direct channel process with unitarity in the crossed channel gave a whole new meaning to Regge's potential model ideas that angular momentum could be continued from integers to complex values [11]. It was through these S-matrix principles combined with Regge theory that the concept of nuclear democracy and the bootstrap were to be realised. The power of three of the basic properties, crossing, analyticity and Regge theory, to determine reaction amplitudes was explicitly exhibited in the seemingly magic formula of Veneziano [8]. This combined poles in energy with zeros in scattering angles: zeros that give hadrons their spin. This remarkable success in representing scattering by a ratio of Gamma functions led ...

Leading-twist distribution amplitudes of scalar and vector mesons

“…Using QCD's Dyson-Schwinger equations (DSEs) [24][25][26][27], low-twist PDAs of pseudoscalar-and vector-meson ground-states and pseudoscalar-meson radial-excitations have recently been computed [10,22,28,29]; and, where a meaningful comparison is possible, the results agree with those determined via numerical simulations of lattice-regularised QCD [14,30,31]. Hence, given the features highlighted above, we consider it interesting to use this approach to compute the leading-twist PDAs of scalar-meson ground-states and radial excitations, and the radial excitations of vector mesons, all constituted from light quarks.…”

Constraints from a large- Nc analysis on meson-baryon interactions at chiral order Q3

“…The important merit of all building blocks B, U µ , H µν and D µν lies in their identical chiral transformation properties. Thus, the action of the covariant derivatives is implied by the example case (2).…”

On SU(3)F positive-parity octet and decuplet baryons

“…We emphasise that the continuum analyses indicated above form part of the body of Dyson-Schwinger equation (DSE) studies of hadron structure [29,[31][32][33][34][35][36][37][38][39][40][41][42][43][44][45][46][47][48][49]. In this approach, the challenge is a need to employ a truncation so as to define a tractable problem.…”