Amplitude/operator basis in chiral perturbation theory

Ian Low, Jing Shu, Ming Lei Xiao*, Yu Hui Zheng

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

We establish a systematic construction of the on-shell amplitude/operator basis for Chiral Perturbation Theory (ChPT) in D = 4 spacetime dimensions and with an arbitrary number of flavors Nf. For kinematic factors, we employ spinor-helicity variables to construct the soft blocks, which are local amplitudes satisfying the Adler’s zero condition, as well as to take into account the reduction in the kinematic basis due to the Gram determinant, which arises at O(p10) when the number of multiplicity N in an amplitude becomes large: N > D. For flavor factors, we include group-theoretic relations at small Nf, Nf≤ N, which decreases the flavor basis. The result is obtained by adapting the Young tensor method of constructing the operator basis for generic effective field theories to the case of non-linearly realized symmetries. Working in the massless quark limit, we present purely mesonic operators for both even- and odd-parity at O(p6) and O(p8) for N = 6 and arbitrary Nf, and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at O(p10) for N = 6, 8 and 10.

Original languageEnglish (US)
Article number31
JournalJournal of High Energy Physics
Volume2023
Issue number1
DOIs
StatePublished - Jan 2023

Keywords

  • Chiral Lagrangian
  • Effective Field Theories
  • Effective Field Theories of QCD
  • Scattering Amplitudes

ASJC Scopus subject areas

  • Nuclear and High Energy Physics

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