Abstract
We present SuperTracer, a Mathematica package aimed at facilitating the functional matching procedure for generic UV models. This package automates the most tedious parts of one-loop functional matching computations. Namely, the determination and evaluation of all relevant supertraces, including loop integration and Dirac algebra manipulations. The current version of SuperTracer also contains a limited set of output simplifications. However, a further reduction of the output to a minimal basis using Fierz identities, integration by parts, simplification of Dirac structures, and/or light field redefinitions might still be necessary. The code and example notebooks are publicly available at .1
Highlights
Processes like rare decays and neutral meson mixing) are generated starting only at one-loop order within the SM
Tools for RGE in the SMEFT and LEFT and one-loop matching of the SMEFT to the LEFT [11,12,13], tree-level EFT matching of generic UV models [14], as well as partial one-loop EFT matching results [25, 27,28,29] are available
We provide here a first building block in this direction by introducing SuperTracer, a Mathematica package aimed at facilitating the one-loop EFT matching of generic UV models using path integral methods
Summary
Consider a general theory LUV[ηH , ηL], whose field content can be split into heavy ηH and light ηL degrees of freedom, satisfying mH mL. The method of expansion by regions states that the contribution of each region is obtained in dimensional regularization by expanding the loop integrand into a Taylor series in the parameters that are small there and integrating every region over the full d-dimensional space of loop momenta This statement holds up to a mismatch of divergences. Since ∆X ∼ mH−1 in the hard region, we can Taylor expand the second logarithm in (2.7) yielding the master formula for one-loop EFT matching [53]: ddx. This formula provides the EFT Lagrangian in terms of two types of terms: log-type and power-type supertraces. As we mentioned before, ∆X is at most of O(mH−1) in the hard momentum expansion, this provides a natural truncation of the series in terms of the EFT expansion in inverse powers of mH
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