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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26545_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="20" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>β</mi> <mi>π</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\beta}_{\pi}^2 $</EquationSource> </InlineEquation> = 0.51 ± 0.04 GeV−2 and <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26545_Article_IEq2.gif" Format="GIF" Height="21" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>β</mi> <mi>K</mi> <mn>2</mn> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\beta}_K^2 $</EquationSource> </InlineEquation> = 0.30 ± 0.05 GeV−2, the chiral mass of pion meson <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_26545_Article_IEq3.gif" Format="GIF" Height="18" Rendition="HTML" Resolution="72" Type="Linedraw" Width="24" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi>m</mi> <mn>0</mn> <mi>π</mi> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {m}_0^{\pi } $</EquationSource> </InlineEquation> 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 GeV2 for all considered form factors, significantly improving the theory-data consistency.

Form factors of light pseudoscalar mesons from the perturbative QCD approach

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2025年6月24日

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Jian Chai,
Shan Cheng

摘要

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 $β_{π}^{2}$ $ {\beta}_{\pi}^2 $ = 0.51 ± 0.04 GeV⁻² and $β_{K}^{2}$ $ {\beta}_K^2 $ = 0.30 ± 0.05 GeV⁻², the chiral mass of pion meson $m_{0}^{π}$ $ {m}_0^{\pi } $ 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 GeV² for all considered form factors, significantly improving the theory-data consistency.