One-loop corrections to h → b b ¯ $$ b\overline{b} $$ and h → τ τ ¯ $$ \tau \overline{\tau} $$ decays in the Standard Model dimension-6 EFT: four-fermion operators and the large-m t limit

We calculate one loop y t and λ dependent corrections toΓ Z ,R 0 f and the partial Z widths due to dimension six operators in the Standard Model Effective Field Theory (SMEFT), including finite terms. We assume CP symmetry and a U(3) 5 symmetry in the UV matching onto the dimension six operators, dominantly broken by the Standard Model Yukawa matrices. Corrections to these observables are predicted using the input parameters {α ew ,M Z ,Ĝ F ,m t ,m h } extracted with one loop corrections in the same limit. We show that at one loop the number of SMEFT parameters contributing to the precise LEPI pseudoobservables exceeds the number of measurements. As a result the SMEFT parameters contributing to LEP data are formally unbounded when the size of loop corrections are reached until other data is considered in a global analysis. The size of these loop effects is generically a correction of order ∼ % to leading effects in the SMEFT, but we find multiple large numerical coefficients in our calculation at this order. We use a MS scheme, modified for the SMEFT, for renormalization. Some subtleties involving novel evanescent scheme dependence present in this result are explained.

Section: 1α Ew Extractionsmentioning

confidence: 97%

“…For results and discussion (with supporting calculations) characterizing various NLO corrections in the SMEFT see refs. [13][14][15][16][17][18][19][20][21][22][23][24][25][26].…”

Section: Jhep03(2017)060mentioning

confidence: 99%

Section: Jhep03(2017)060mentioning

confidence: 99%

“…7 The Class 7 operators contribute directly to Z →b L b L at one loop with the finite terms 22) and through Higgs tadpoles as…”

Section: Jhep03(2017)060mentioning

confidence: 99%

“…The finite terms for these contributions were reported in ref. [22]. The two point function of the W boson is corrected as in figure 9 c).…”

Section: 3ĝ F Extractionsmentioning

confidence: 99%

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101

130

We develop tools for performing effective field theory (EFT) calculations in a manifestly gauge-covariant fashion. We clarify how functional methods account for oneloop diagrams resulting from the exchange of both heavy and light fields, as some confusion has recently arisen in the literature. To efficiently evaluate functional traces containing these "mixed" one-loop terms, we develop a new covariant derivative expansion (CDE) technique that is capable of evaluating a much wider class of traces than previous methods. The technique is detailed in an appendix, so that it can be read independently from the rest of this work. We review the well-known matching procedure to one-loop order with functional methods. What we add to this story is showing how to isolate one-loop terms coming from diagrams involving only heavy propagators from diagrams with mixed heavy and light propagators. This is done using a non-local effective action, which physically connects to the notion of "integrating out" heavy fields. Lastly, we show how to use a CDE to do running analyses in EFTs, i.e. to obtain the anomalous dimension matrix. We demonstrate the methodologies by several explicit example calculations.