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Next-to-Next-to-Leading-Order QCD Prediction for the Pion Form Factor

Yao Ji1,2,*, Bo-Xuan Shi3,†, Jian Wang4,5,‡, Ye-Fan Wang6,7,§, Yu-Ming Wang3,∥, and Hui-Xin Yu3,¶

  • *Contact author: yaoji@cuhk.edu.cn
  • †Contact author: shibx@mail.nankai.edu.cn
  • ‡Contact author: j.wang@sdu.edu.cn
  • §Contact author: wangyefan@nnu.edu.cn
  • ∥Contact author: wangyuming@nankai.edu.cn
  • Contact author: yuhuixin@mail.nankai.edu.cn
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Phys. Rev. Lett. 134, 221901 – Published 5 June, 2025

DOI: https://doi.org/10.1103/yx51-lc3q

Abstract

We accomplish for the first time the two-loop computation of the leading-twist contribution to the pion form factor by employing the effective field theory formalism rigorously. The next-to-next-to-leading-order hard function is determined by evaluating the appropriate five-point QCD amplitude with the modern multiloop technique and by implementing the ultraviolet renormalization and infrared subtractions in the presence of evanescent operators. The yielding two-loop correction to this fundamental quantity turns out to be numerically significant at experimentally accessible momentum transfers. We further demonstrate that the newly computed two-loop QCD correction is highly beneficial for an improved determination of the leading-twist pion distribution amplitude.

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Phys. Rev. Lett. 134, 221901– Published 5 June, 2025
  • Received 31 December 2024
  • Revised 16 April 2025
  • Accepted 15 May 2025
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