Abstract
The pseudoscalar projection of the pionʼs Poincaré-covariant Bethe–Salpeter amplitude onto the light-front may be understood to provide the probability distribution of the chiral condensate within the pion. Unlike the parton distribution amplitudes usually considered and as befitting a collective effect, this condensate distribution receives contributions from all Fock space components of the pionʼs light-front wave function. We compute this condensate distribution using the Dyson–Schwinger equation (DSE) framework and show the result to be a model-independent feature of quantum chromodynamics (QCD). Our analysis establishes that this condensate is concentrated in the neighbourhood of the boundaries of the distributionʼs domain of support. It thereby confirms the dominant role played by many-particle Fock states within the pionʼs light-front wave function in generating the chiral condensate and verifies that light-front longitudinal zero modes do not play a material role in that process.
Highlights
The action that defines the theory of massless quantum chromodynamics (QCD) is conformally invariant
The conundrum is resolved by noting that classical WGT identities are derived without accounting for the effect of regularisation and renormalisation in four-dimensional quantum field theory. This procedure leads to scale anomalies in the WGT identities originating with the dilatation current [4,5,6]
Knowing that scale invariance is broken by QCD dynamics is not the same as explaining how a proton, constituted from nearly massless current-quarks, itself acquires a mass mp ∼ 1 GeV which is contained within a confinement domain whose radius is rc ∼ 1/σc, with σc ∼ 0.25 GeV ∼ ΛQCD
Summary
Schmidtc aInstitut fur Kernphysik, Forschungszentrum Julich, D-52425 Julich, Germany bPhysics Division, Argonne National Laboratory, Argonne, Illinois 60439, USA cInstitute for Advanced Simulation, Forschungszentrum Julich and JARA, D-52425 Julich, Germany arXiv:1308.4708v2 [nucl-th] 19 Sep 2013
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