Amplitude/Operator Basis in Chiral Perturbation Theory

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 $N_f$. 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 $O(p^{10})$ when the number of multiplicity $N$ in an amplitude becomes large: $N>D$. For flavor factors, we include group-theoretic relations at small $N_f$, $N_f\le N$, 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 $O(p^6)$ and $O(p^8)$ for $N=6$ and arbitrary $N_f$, and establish a direct correspondence between the amplitude basis and the operator basis. Furthermore, the redundancy due to the Gram determinant is studied at $O(p^{10})$ for $N=6,8$ and 10.

44 pages, 14 tables

References in corpus (21)

• Dimension-Six Terms in the Standard Model Lagrangian
• Dimension-8 Operators in the Standard Model Effective Field Theory
• Effective Field Theories from Soft Limits
• Complete Set of Dimension-8 Operators in the Standard Model Effective Field Theory
• On-Shell Recursion Relations for Effective Field Theories
• Hilbert series and operator bases with derivatives in effective field theories
• Tree-level Amplitudes in the Nonlinear Sigma Model
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Complete Set of Dimension-9 Operators in the Standard Model Effective Field Theory
• The electroweak effective field theory from on-shell amplitudes
• Operator Bases in Effective Field Theories with Sterile Neutrinos: $d\le 9$
• Constructing effective field theories via their harmonics
• Adler's Zero and Effective Lagrangians for Nonlinearly Realized Symmetry
• Low Energy Effective Field Theory Operator Basis at $d\le 9$
• 2, 12, 117, 1959, 45171, 1170086, ...: A Hilbert series for the QCD chiral Lagrangian
• Soft Bootstrap and Effective Field Theories
• The order $p^8$ mesonic chiral Lagrangian
• A Minimally Symmetric Higgs Boson
• Universal Imprints of a Pseudo-Nambu-Goldstone Higgs Boson
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• Universal Relations in Composite Higgs Models

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