Form factors of light pseudoscalar mesons from the perturbative QCD approach

A bstract We study the electromagnetic and meson-photon transition form factors (TFF) of light pseudoscalar mesons from the perturbative QCD (pQCD) approach. To comprehensively account for both the longitudinal and transverse nonperturbative dynamics of hadronic constituents, we incorpoarate intrinsic transverse momentum distributions (iTMDs) alongside the conventional light-cone distribution amplitudes (LCDAs). The main motivations of this work are the disjointedness of electromagnetic form factors between the theoretical predictions and the experimental measurements, and the BaBar-Belle tension of pion-photon transition form factor in the large momentum transfers. Our calculation is carried out at the next-to-leading-order for the contributions from leading and subleading twist LCDAs, and leading order for the twist four contributions. Notably, this work presents the first systematic evaluation of higher-twist contributions to meson-photon TFFs. The key findings are: (a) iTMDs play a crucial role in describing form factor data, particularly in the small-to-intermediate momentum transfer region where they induce significant modifications to pQCD predictions. (b) The extracted transverse size parameters for valence quark states are found to be $$ {\beta}_{\pi}^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>β</mml:mi> <mml:mi>π</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> = 0.51 ± 0 . 04 GeV −2 and $$ {\beta}_K^2 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>β</mml:mi> <mml:mi>K</mml:mi> <mml:mn>2</mml:mn> </mml:msubsup> </mml:math> = 0.30 ± 0.05 GeV −2 , the chiral mass of pion meson $$ {m}_0^{\pi } $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>m</mml:mi> <mml:mn>0</mml:mn> <mml:mi>π</mml:mi> </mml:msubsup> </mml:math> at 1 GeV is determined to be 1.84 ± 0.07 GeV. (c) The meson-photon TFFs are predominantly governed by leading-twist LCDAs. The iTMDs-enhanced pQCD results show better agreement with Belle’s pion TFF data across intermediate and large momentum transfers and favor a small η – η ′ mixing angle. (d) Remarkably, the inclusion of iTMDs extends the applicability of pQCD calculations down to a few GeV 2 for all considered form factors, significantly improving the theory-data consistency.