Abstract
We discuss a general diagrammatic description of n-point functions in the QCD instanton vacuum that resums planar diagrams, enforces gauge invariance and spontaneously broken chiral symmetry. We use these diagrammatic rules to derive the pion and kaon quasi-parton amplitude and distribution functions at leading order in the instanton packing fraction for large but finite momentum. The instanton and anti-instanton zero modes and non-zero modes are found to contribute to the quasi-distributions, but the latter are shown to drop out in the large momentum limit. The pertinent pion and kaon parton distribution amplitudes and functions are made explicit at the low renormalization scale fixed by the inverse instanton size. Assuming that factorization holds, the pion parton distributions are evolved to higher renormalization scales with one-loop DGLAP and compared to existing data.
Highlights
Light-cone distribution amplitudes are central to the description of hard exclusive processes with large momentum transfer
The pertinent pion and kaon parton distribution amplitudes and functions are made explicit at the low renormalization scale fixed by the inverse instanton size
II we briefly review the general aspects of the random instanton vacuum, and detail the planar approximation for the derivation of the quark propagator
Summary
Light-cone distribution amplitudes are central to the description of hard exclusive processes with large momentum transfer. The recent suggestion put forth by Ji [2] and its matching protocol [15], to extract the light-cone distribution functions from equal-time quasidistributions in Euclidean space, has been carried on the lattice with some reasonable success [16]. The latter resums a large class of instanton contributions in the form of nonperturbative integral equations with full chiral and gauge symmetry While these equations are in general involved and require a numerical analysis, we will analyze them relying on the diluteness of the instantons and anti-instantons in the QCD vacuum, where the packing fraction is small with κ ≈ 10−3. The virtual character of the induced effective quark constituents generated by the planar resummation makes their time-like manifestation in the pion distribution amplitude and function very subtle. A number of details can be found in several appendixes, including the LO result for the pion generalized distribution function (GPDF)
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