Shedding light on the intrinsic transversal momentum distributions of pion and kaon

Abstract

We propose to introduce the intrinsic transversal momentum distribution functions (iTMDs), in conjunction with the light-cone distribution amplitudes (LCDAs), 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 $k_T$ factorization formalism of an exclusive QCD process, which confines perturbative QCD (pQCD) predictions to scenarios involving large momentum transfers. We meticulously investigate the $\pi$ and $K$ electromagnetic form factors using the iTMDs-improved pQCD calculation at next-to-leading order. By analyzing data in the timelike physical regions, we obtain the transversal-size parameters $\beta_\pi^2 = 0.51 \pm 0.04$ GeV$^{-2}$ and $\beta_K^2 = 0.30 \pm 0.05$ GeV$^2$. We then extract the chiral mass of pion to be $m_0^\pi(1 \, {\rm GeV}) = 1.84 \pm 0.07$ GeV and explain the precise measurements of kaon form factor 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 GeV$^2$. This improvement allows for direct comparison with existing measurements and lattice QCD evaluations.