The Art of Counting: a reappraisal of the HEFT expansion

TL;DR

This paper reexamines the power counting in Higgs Effective Field Theory (HEFT), proposing two viable rules based on different scale assumptions, and provides methods for consistent operator truncation and observable calculations.

Contribution

It introduces two new power counting schemes for HEFT based on fundamental principles, clarifying operator truncation and observable predictions.

Findings

Identifies two consistent power counting rules for HEFT.

Provides quantitative prescriptions for operator truncation.

Illustrates methods with multiple examples.

Abstract

We revisit the power counting of the Higgs Effective Field Theory (HEFT) from first principles, by requiring that predictions for physical observables follow a series expansion in small, dimensionless quantities. Depending on whether HEFT is formulated in terms of a unique low-energy scale $v$ or in terms of two scales $v<f$, this approach identifies two viable power counting rules that can accommodate any operator normalization choice. We provide quantitative prescriptions for the consistent truncation of HEFT operators, amplitudes and observable contributions and we illustrate our arguments with a number of examples.