Analysis of general power counting rules in effective field theory

Abstract

We derive the general counting rules for a quantum effective field theory (EFT) in d dimensions. The rules are valid for strongly and weakly coupled theories, and they predict that all kinetic energy terms are canonically normalized. They determine the energy dependence of scattering cross sections in the range of validity of the EFT expansion. We show that the size of the cross sections is controlled by the power counting of EFT, not by chiral counting, even for chiral perturbation theory (χ PT). The relation between and f is generalized to d dimensions. We show that the naive dimensional analysis 4π counting is related toh counting. The EFT counting rules are applied to χ PT, low-energy weak interactions, Standard Model EFT and the non-trivial case of Higgs EFT.

ALPs effective field theory and collider signatures

“…(44)- (47) and in the NLO chiral corrections to be discussed below follows the Naive Dimensional Analysis (NDA) master formula for the HEFT Lagrangian as discussed in Refs. [80][81][82][83]. With this convention the gauge boson kinetic terms appear canonically normalised.…”

Revisiting Minimal Lepton Flavour Violation in the light of leptonic CP violation

“…An alternative would be to considered a non-linear realisation and the corresponding effective Lagrangian dubbed HEFT [181][182][183][184][185][186]. In this context, however, a much larger number of operators should be taken into consideration and a slightly different phenomenology is expected [187][188][189][190][191][192][193][194][195][196]. The focus in this paper is on the linear EWSB realisation and therefore the HEFT Lagrangian will not be considered in what follows.…”

The minimal flavour violating axion

“…In order to reproduce the expected value of the EW VEV, v ≡ 245 GeV fixed through the W gauge boson mass, it is then necessary to invoke a large value of the Higgs quartic coupling λ, describing in this way a strongly interacting scenario with a non-linearly realised EWSB mechanism. This is an intriguing possibility, especially considering the recent interest in non-SM descriptions of the Higgs sector, such as composite Higgs models [87][88][89][90][91][92][93][94][95], dilaton models [96][97][98][99][100][101][102][103], or general effective Lagrangians [104][105][106][107][108][109][110][111][112][113][114][115][116][117][118][119][120][121]. In this letter, however, the traditional EWSB mechanism will be considered, and this requires to invoke a fine tuning: either there is cancellation between µ 2 and λ HΦ v 2 Φ , or λ HΦ is artificially small.…”