Low-energy effective field theory below the electroweak scale: matching at one loop

Abstract

We compute the one-loop matching between the Standard Model Effective Field Theory and the low-energy effective field theory below the electroweak scale, where the heavy gauge bosons, the Higgs particle, and the top quark are integrated out. The complete set of matching equations is derived including effects up to dimension six in the power counting of both theories. We present the results for general flavor structures and include both the CP -even and CP -odd sectors. The matching equations express the masses, gauge couplings, as well as the coefficients of dipole, three-gluon, and four-fermion operators in the low-energy theory in terms of the parameters of the Standard Model Effective Field Theory. Using momentum insertion, we also obtain the matching for the CP -violating theta angles. Our results provide an ingredient for a model-independent analysis of constraints on physics beyond the Standard Model. They can be used for fixed-order calculations at one-loop accuracy and represent a first step towards a systematic next-to-leading-log analysis. E SMEFT operator basis 56 F LEFT operator basis 58 G Conventions for the supplemental material 59 References 61

One-loop running of dimension-six Higgs-neutrino operators and implications of a large neutrino dipole moment

“…The necessity of using this framework across a wide range of energies has also triggered the computation of the one-loop renormalisation group equations (RGEs) for the dimension-six operators [7][8][9][10][11][12][13]. The RGEs in the theory valid at energies below the EW scale where the top quark, the Higgs and the W and Z gauge bosons are integrated out, usually referred to as LEFT, are also known [14]; as well as the matching between the SMEFT and the LEFT at up to one loop [15,16]. Likewise, the desire of connecting the SMEFT to ultraviolet (UV) models has stimulated different works on the matching procedure [17][18][19][20][21][22][23][24][25][26]; including more recently the first basis of dimension-six operators suitable for off-shell integration [27].…”

Clustering of $$ \overline{B}\to {D}^{\left(\ast \right)}{\tau}^{-}{\overline{\nu}}_{\tau } $$ kinematic distributions with ClusterKinG

“…In recent years substantial progress has been made in the EFT description of the SM in form of the SM Effective Theory (SMEFT) [6] and the Weak Effective Theory (WET). The calculation of the complete one-loop SMEFT renormalization group equations (RGEs) [7][8][9][10], the complete tree-level and one-loop matching from SMEFT onto WET [11][12][13] and the complete one-loop QCD and QED RGEs within WET [14,15] allow for a general NP analysis of low-energy observables.…”

New Physics Searches with Top Quarks

“…To calculate the impact of O 3 HQ on B → K ( * ) + − , the interactions of the standard model effective theory need to be matched onto the weak effective theory and evolved down to the GeV scale via the renormalization group. The one-loop matching for dimension-six operators has recently been completed [12,13,14]. This allows us to relate LHC observables and flavor observables in a global analysis of top-quark interactions.…”