Extending the Universal One-Loop Effective Action: heavy-light coefficients

Abstract

The Universal One-Loop Effective Action (UOLEA) is a general expression for the effective action obtained by evaluating in a model-independent way the one-loop expansion of a functional path integral. It can be used to match UV theories to their low-energy EFTs more efficiently by avoiding redundant steps in the application of functional methods, simplifying the process of obtaining Wilson coefficients of operators up to dimension six. In addition to loops involving only heavy fields, matching may require the inclusion of loops containing both heavy and light particles. Here we use the recentlydeveloped covariant diagram technique to extend the UOLEA to include heavy-light terms which retain the same universal structure as the previously-derived heavy-only terms. As an example of its application, we integrate out a heavy singlet scalar with a linear coupling to a light doublet Higgs. The extension presented here is a first step towards completing the UOLEA to incorporate all possible structures encountered in a covariant derivative expansion of the one-loop path integral.

Singlet night in Feynman-ville: one-loop matching of a real scalar

“…In fact, our expressions (3.12) and (3.13) for γ H,H and γ H,H agree with the results obtained in the articles [3][4][5]. The source of the difference between the first four terms in (3.11) and the rational terms of C (1) H as quoted in [26,29] is unraveled in Appendix A. In addition, the existing calculations do not explicitly include effects stemming from the renormalisation of SSM parameters -cf.…”

“…Thus, the correct description of long-distance physics has to be formulated in terms of the SM couplings and the Wilson coefficient C H evaluated at the low-energy scale. Let us finally mention that (3.9) differs from the expression for C (1) H given in both [26] and [29]. The disagreement has two sources.…”

“…In this work, we repeat the calculation of [29] from scratch, relying entirely on the use of Feynman diagrams. With the help of our independent computation we are able to identify terms that have been missed in the existing calculations [26,29] -small discrepancies in the latter publications have already been noted in the presentation [30], but updated results have not been published so far. We stress that these discrepancies are due to oversights, and not due to structural limitations of the UOLEA approach.…”

“…The matching of (3.1) onto (3.2) can be performed using either Feynman diagrams or functional methods. In fact, the work [26] employed the UOLEA approach to calculate the heavy (i.e. only φ loops) and the heavy-light (i.e.…”

Current and future constraints on Higgs couplings in the nonlinear Effective Theory

“…Indeed, the EFT formalism provides a robust theoretical framework where both physical calculations and the connection with UV scenarios can be performed in a well-defined manner. On the one hand, EFTs can be connected easily to a given UV-model when the heavy degrees of freedom are integrated out [10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]. On the other hand, the precision of the predictions computed with the effective Lagrangian can be systematically improved by including higher orders of both, the EFT expansion as well as perturbation theory.…”