The pion: an enigma within the Standard Model

Abstract

Quantum Chromodynamics (QCD) is the strongly interacting part of the Standard Model. It is supposed to describe all of nuclear physics; and yet, almost fifty years after the discovery of gluons and quarks, we are only just beginning to understand how QCD builds the basic bricks for nuclei: neutrons and protons, and the pions that bind them together. QCD is characterised by two emergent phenomena: confinement and dynamical chiral symmetry breaking (DCSB). They have far-reaching consequences, expressed with great force in the character of the pion; and pion properties, in turn, suggest that confinement and DCSB are intimately connected. Indeed, since the pion is both a Nambu-Goldstone boson and a quark-antiquark bound-state, it holds a unique position in Nature and, consequently, developing an understanding of its properties is critical to revealing some very basic features of the Standard Model. We describe experimental progress toward meeting this challenge that has been made using electromagnetic probes, highlighting both dramatic improvements in the precision of charged-pion form factor data that have been achieved in the past decade and new results on the neutral-pion transition form factor, both of which challenge existing notions of pion structure. We also provide a theoretical context for these empirical advances, which begins with an explanation of how DCSB works to guarantee that the pion is unnaturally light; but also, nevertheless, ensures that the pion is the best object to study in order to reveal the mechanisms that generate nearly all the mass of hadrons. In canvassing advances in these areas, our discussion unifies many aspects of pion structure and interactions, connecting the charged-pion elastic form factor, the neutral-pion transition form factor and the pion's leading-twist parton distribution amplitude. It also sketches novel ways in which experimental and theoretical studies of the charged-kaon electromagnetic form factor can provide significant contributions. Importantly, it appears that recent predictions for the large-Q 2 behaviour of the chargedpion form factor can be tested by experiments planned at the upgraded 12 GeV Jefferson Laboratory. Those experiments will extend precise charged-pion form factor data up to momentum transfers that it now appears may be large enough to serve in validating factorisation theorems in QCD. If so, they may expose the transition between the nonperturbative and perturbative domains and thereby reach a goal that has driven hadro-particle physics for around thirty-five years.Keywords: Abelian anomaly, confinement, dynamical chiral symmetry breaking, elastic and transition form factors, π-meson, K-meson, non-perturbative QCD, parton distribution amplitudes and functions The pion: an enigma within the Standard Model 2. Form factors: experimental history, current status, and futureForm factors are of primary importance in hadron physics because they provide Poincaré-invariant information about the nonpointlike nature of QCD's observable bound-states, and the d...

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.…”

Aspects of open-flavour mesons in a comprehensive DSBSE study

“…(16) arises in the course of the derivation of the generalized GMOR relation, Eq. (14) [106,107]. The latter one is satisfied by all quark bilinear pseudoscalar mesons which are subject to the avWTI, irrespective of quark content or quark-mass configuration.…”

Pion distribution amplitude from Euclidean correlation functions

“…This discussion has been reinvigorated by the strong scaling violation in the πγ * γ form factor observed by the BABAR [28] and, to a lesser extent, the BELLE [29] collaboration, which is difficult to explain unless the pion DA exhibits strong enhancements near the end points, see, e.g., Refs. [30][31][32] for a review and further references. For illustrative purposes we consider three models: …”