SuperTracer: a calculator of functional supertraces for one-loop EFT matching

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 "Image missing".1

Complete one-loop matching of the type-I seesaw model onto the Standard Model effective field theory

“…approach is more suitable for computer programming. Recently, two such Mathematica packages, i.e., STrEAM [47] and SuperTracer [48], have been made available publicly. Both of them follow the prescription proposed in ref.…”

“…[36]. However, there is an alternative way that is more suitable to be implemented in a computer program [47,48]. Considering that ln det ∆ φ contains pure light loops and then its hard part is scaleless (i.e., vanishing after integration), then by virtue of eqs.…”

“…Moreover, in the last step in eq. (2.28), the fact that K −1 X ∼ M −1 [48] has been taken into account to expand the logarithmic term, i.e., ln 1 − K −1 X . As one can see in eq.…”

“…However, the one-loop matching is in general more complicated and more technical than the tree-level matching. So far there have been only a few examples of complete or partial one-loop matching for the simple extensions of the SM, such as the SM extended with a charged scalar singlet [27], a real scalar singlet [28][29][30][31][32][33], a real scalar triplet [34][35][36], a vector-like quark singlet [37], a light sterile neutrino and heavy fermions and a scalar singlet [38], two scalar leptoquarks [39], and singlet right-handed neutrinos [40] by either diagrammatic calculations or the functional approach [29,[32][33][34][35][36][41][42][43][44][45][46][47][48] (see, e.g., refs. [49][50][51], for earlier works).…”

Parton distributions in the SMEFT from high-energy Drell-Yan tails

“…A powerful framework to identify, parametrise, and correlate in a model-independent manner the possible deviations from the SM predictions that arise in such indirect searches is provided by the effective field theory (EFT) framework, such as the Standard Model EFT (SMEFT) (e.g. [1][2][3][4][5][6][7][8][9][10][11][12][13][14]) or the Higgs EFT (HEFT) (e.g. [15][16][17][18][19][20][21][22]).…”