Soft bootstrap and effective field theories

Ian Low, Zhewei Yin*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

29 Scopus citations


The soft bootstrap program aims to construct consistent effective field theories (EFT’s) by recursively imposing the desired soft limit on tree-level scattering amplitudes through on-shell recursion relations. A prime example is the leading two-derivative opera­ tor in the EFT of SU(N) x SU(N)/SU(N) nonlinear sigma model (NLSM), where 𝒪(p2) amplitudes with an arbitrary multiplicity of external particles can be soft-bootstrapped. We extend the program to 𝒪(p4) operators and introduce the “soft blocks,” which are the seeds for soft bootstrap. The number of soft blocks coincides with the number of independent operators at a given order in the derivative expansion and the incalculable Wilson coefficient emerges naturally. We also uncover a new soft-constructible EFT involving the “multi-trace” operator at the leading two-derivative order, which is matched to SO(N + 1) /SO(N) NLSM. In addition, we consider Wess-Zumino-Witten (WZW) terms, the existence of which, or the lack thereof, depends on the number of flavors in the EFT, after a novel application of Bose symmetry. Remarkably, we find agreements with group­ theoretic considerations on the existence of WZW terms in SU(N) NLSM for N ≥ 3 and the absence of WZW terms in SO(N) NLSM for N ≠ 5.

Original languageEnglish (US)
Article number78
JournalJournal of High Energy Physics
Issue number11
StatePublished - Nov 1 2019


  • Chiral Lagrangians
  • Effective Field Theories
  • Scattering Amplitudes
  • Sigma Models

ASJC Scopus subject areas

  • Nuclear and High Energy Physics


Dive into the research topics of 'Soft bootstrap and effective field theories'. Together they form a unique fingerprint.

Cite this