Ding, Minghui
; Gao, Fei
; Chang, Lei
; ... - Physics Letters. Section B

Here, the leading-twist parton distribution amplitudes (PDAs) of ground-state _{1}S_{0} and _{3}S_{1} cc¯- and bb¯quarkonia are calculated using a symmetry-preserving continuum treatment of the meson bound-state problem which unifies the properties of these heavy-quark systems with those of light-quark bound-states, including QCD's Goldstone modes. Analysing the evolution of _{1}S_{0} and _{3}S_{1} PDAs with current-quark mass, m^_{q}, increasing away from the chiral limit, it is found that in all cases there is a value of m^_{q} for which the PDA matches the asymptotic form appropriate to QCD's conformal limit and hence is insensitive to changes in renormalisation scale, ζ. This massmore » lies just above that associated with the s-quark. At current-quark masses associated with heavy-quarkonia, on the other hand, the PDAs are piecewise convex–concave–convex.« less

Binosi, Daniele
; Chang, Lei
; Papavassiliou, Joannis
; ... - Physics Letters. Section B

Within contemporary hadron physics there are two common methods for determining the momentum- dependence of the interaction between quarks: the top-down approach, which works toward an ab initiocomputation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD’s gauge sector coincides with that required in order to describe ground-state hadron observables usingmore » a nonperturbative truncation of QCD’s Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.« less

Mezrag, C.
; Chang, L.
; Moutarde, H.
; ... - Physics Letters. Section B

In order to learn effectively from measurements of generalised parton distributions (GPDs), it is desirable to compute them using a framework that can potentially connect empirical information with basic features of the Standard Model. We sketch an approach to such computations, based upon a rainbow-ladder (RL) truncation of QCD’s Dyson–Schwinger equations and exemplified via the pion’s valence dressed-quark GPD, H^{v}_{π}(x, ξ, t). Our analysis focuses primarily on ξ=0, although we also capitalise on the symmetry-preserving nature of the RL truncation by connecting H^{v}_{π}(x, ξ=±1, t)with the pion’s valence-quark parton distribution amplitude. We explain that the impulse-approximation used hitherto to definemore » the pion’s valence dressed-quark GPD is generally invalid owing to omission of contributions from the gluons which bind dressed-quarks into the pion. A simple correction enables us to identify a practicable improvement to the approximation for H^{v}_{π}(x, 0, t), expressed as the Radon transform of a single amplitude. Therewith we obtain results for H^{v}_{π}(x, 0, t) and the associated impact-parameter dependent distribution, q^{v}_{π}(x, |b⊥|), which provide a qualitatively sound picture of the pion’s dressed-quark structure at a hadronic scale. We evolve the distributions to a scale ζ = 2 GeV, so as to facilitate comparisons in future with results from experiment or other nonperturbative methods.« less

Chang, Lei
; Mezrag, Cédric
; Moutarde, Hervé
; ... - Physics Letters. Section B

The impulse-approximation expression used hitherto to define the pion's valence-quark distribution function is flawed because it omits contributions from the gluons which bind quarks into the pion. A corrected leading-order expression produces the model-independent result that quarks dressed via the rainbow–ladder truncation, or any practical analogue, carry all the pion's light-front momentum at a characteristic hadronic scale. Corrections to the leading contribution may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea-quarks. Working with available empirical information, we use an algebraic model to express the principal impact of both classes of corrections. This enables amore » realistic comparison with experiment that allows us to highlight the basic features of the pion's measurable valence-quark distribution, q^{π}(x); namely, at a characteristic hadronic scale, q^{π}(x)~(1-x)^{2} for x≳0.85; and the valence-quarks carry approximately two-thirds of the pion's light-front momentum.« less

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