Bridging a gap between continuum-QCD and ab initio predictions of hadron observables

Daniele Binosi,Lei Chang,Joannis Papavassiliou,Craig D Roberts

doi:10.1016/j.physletb.2015.01.031

Daniele Binosi, Lei Chang + Show 2 more

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https://doi.org/10.1016/j.physletb.2015.01.031

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Abstract

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 initio computation 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 using 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.

Highlights

The last two decades have seen significant progress and phenomenological success in the formulation and use of symmetry preserving methods in continuum-QCD for the computation of observable properties of hadrons [1,2,3,4,5,6,7,8]
It is greater than that required for dynamical chiral symmetry breaking (DCSB) to occur in simple treatments of strong-coupling QED [52, 53] and gap equation models for QCD [54, 55], and consistent with the value often imagined necessary to describe strong-interaction phenomena: αs(0) π
It is possible to compare the prediction yielded by analyses of QCD’s gauge sector with the running-interaction determined using the bottom-up approach; i.e., parametrising the gauge-sector kernel and fitting the parameter in order to explain a wide range of hadron observables

Summary

Introduction

The last two decades have seen significant progress and phenomenological success in the formulation and use of symmetry preserving methods in continuum-QCD for the computation of observable properties of hadrons [1,2,3,4,5,6,7,8]. All scales are completely determined by the original lattice result and the running of αs(ζ2) matches that of perturbative QCD on the perturbative domain (ζ2 ≥ ζ22); viz., the four-loop expression for the running coupling evaluated in the momentum-subtraction scheme with a value of ΛQCD between 0.25 and 0.32 GeV [49, 50].

Results

Conclusion