Title: Operator counting and soft blocks in chiral perturbation theory

Abstract

Chiral perturbation theory (ChPT) is a low-energy effective field theory of QCD and also a nonlinear sigma model based on the symmetry breaking pattern SU(N_f) x SU(N_f) → SU(N_f). In the limit of massless N_f quarks, we enumerate the independent operators without external sources in ChPT using an on-shell method, by counting and presenting the soft blocks at each order in the derivative expansion, up to $$\mathcal{O}(p^{10})$$. Given the massless on-shell condition and total momentum conservation, soft blocks are homogeneous polynomials of kinematic invariants exhibiting Adler's zero when any external momentum becomes soft and vanishing. In addition, soft blocks are seeds for recursively generating all tree amplitudes of Nambu-Goldstone bosons without recourse to ChPT, and in one-to-one correspondence with the "lowenergy constants" which are theWilson coefficients. Relations among operators, such as those arising from equations of motion, integration by parts, Hermiticity, and symmetry structure, manifest themselves in the soft blocks in simple ways. We find agreements with the existing results up to next-to-next-to-next-to-leading order (NNNLO) and make a prediction at N⁴LO.

Authors:

Dai, Lin ;

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• Search DOE PAGES for ORCID "0000-0002-0802-6884"

Low, Ian; Mehen, Thomas; Mohapatra, Abhishek

• Search DOE PAGES for author "Mohapatra, Abhishek"
• Search DOE PAGES for ORCID "0000-0001-5863-408X"

Publication Date:

Wed Dec 16 00:00:00 EST 2020

Research Org.:

Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Nuclear Physics (NP)

OSTI Identifier:

1773546

Alternate Identifier(s):

OSTI ID: 1818280

Grant/Contract Number:  

AC02-06CH11357; SC0010143; FG02-05ER41368

Resource Type:

Published Article

Journal Name:

Physical Review D

Additional Journal Information:

Journal Name: Physical Review D Journal Volume: 102 Journal Issue: 11; Journal ID: ISSN 2470-0010

Publisher:

American Physical Society

Country of Publication:

United States

Language:

English

Subject:

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; chiral perturbation theory; nonlinear sigma model; scattering amplitudes; spontaneous symmetry breaking