Pion and kaon parton distributions in the QCD instanton vacuum
Arthur Kock, Yizhuang Liu, Ismaïl Zahed
Abstract
We discuss a general diagrammatic description of $n$-point functions in the QCD instanton vacuum that resums planar diagrams, and enforces gauge invariance and spontaneously broken chiral symmetry. We use these diagrammatic rules to derive the pion and kaon quasiparton 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 nonzero modes are found to contribute to the quasidistributions, 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 evolution and compared to existing data.