Abstract
We simplify the one-loop functional matching formalism to develop a streamlined prescription. The functional approach is conceptually appealing: all calculations are performed within the UV theory at the matching scale, and no prior determination of an Effective Field Theory (EFT) operator basis is required. Our prescription accommodates any relativistic UV theory that contains generic interactions (including derivative couplings) among scalar, fermion, and vector fields. As an example application, we match the singlet scalar extended Standard Model (SM) onto SMEFT.
Highlights
Our focus here is on the methodology for matching a UV theory onto an Effective Field Theory (EFT) in this top-down approach
One must first work out all the EFT operators, leaving only their coefficients {ci} to be determined, and identify a set of amplitudes to compute that can be used to solve for all these coefficients
Only the heavy fields that are charged under the EFT gauge group need to be included; otherwise, if Pμ = i∂μ, the supertrace would evaluate to a constant
Summary
When φi represents a pair of conjugate fields, as in the case of a complex scalar s or a Dirac fermion f in eq (2.4), a 2 × 2 identity matrix in this field space is implicitly understood in eq (2.8); the kinetic and mass terms are written in a symmetric way between the two fields:. Note that there is no distinction between quantities before and after setting Φ = Φc[φ] for the inverse propagator part, since K does not depend on the heavy background fields At this point, we can substitute eqs. We reiterate that the utility of functional methods (in particular the prescription presented in this work) does not rely on the series in eq (2.14) truncating after the first or second order; derivative interactions with any number of open covariant derivatives are all accommodated
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