Shedding light on the intrinsic transversal momentum distributions of pions and kaons

Abstract

We propose to introduce the intrinsic transversal momentum distribution functions (iTMDs), in conjunction with the light-cone distribution amplitudes, to elucidate the probability amplitude of encountering a meson state wherein the partons swiftly traverse along the longitudinal axis while gently oscillating in the transversal plane. The primary motivation stems from the oversight of soft transverse dynamics within the kT factorization formalism of an exclusive QCD process, which confines perturbative QCD (pQCD) predictions to scenarios involving large-momentum transfers. We meticulously investigate the π and K electromagnetic form factors using the iTMD-improved pQCD calculation at next-to-leading order. By analyzing data in the timelike physical regions, we obtain the transversal size parameters βπ2=0.51±0.04 GeV−2 and βK2=0.30±0.05 GeV2. We then extract the chiral mass of pions to be m0π(1 GeV)=1.84±0.07 GeV and explain the precise measurements of kaon form factors in the perturbative timelike region. As a remarkable byproduct, we found that the incorporation of iTMDs improves the pQCD predictions for electromagnetic form factors, extending the applicable range to a few GeV2. This improvement allows for direct comparison with existing measurements and lattice QCD evaluations. Published by the American Physical Society 2025