Matching scalar leptoquarks to the SMEFT at one loop
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Springer
Received: April 29, 2020 Accepted: June 29, 2020 Published: July 30, 2020
Valerio Gherardi,a,b David Marzoccab and Elena Venturinic a
SISSA, Via Bonomea 265, Trieste 34136, Italy INFN, Sezione di Trieste, SISSA, Via Bonomea 265, Trieste 34136, Italy c Technische Universit¨ at M¨ unchen, Physik-Department, James-Franck-Straße 1, Garching 85748, Germany b
E-mail: [email protected], [email protected], [email protected] Abstract: In this paper we present the complete one-loop matching conditions, up to dimension-six operators of the Standard Model effective field theory, resulting by integrat¯ 1) 1 and S3 ∼ (3, ¯ 3) 1 . This allows a pheing out the two scalar leptoquarks S1 ∼ (3, 3 3 nomenological study of low-energy constraints on this model at one-loop accuracy, which will be the focus of a subsequent work. Furthermore, it provides a rich comparison for functional and computational methods for one-loop matching, that are being developed. As a corollary result, we derive a complete set of dimension-six operators independent under integration by parts, but not under equations of motions, called Green’s basis, as well as the complete reduction formulae from this set to the Warsaw basis. Keywords: Beyond Standard Model, Heavy Quark Physics ArXiv ePrint: 2003.12525
c The Authors. Open Access, Article funded by SCOAP3 .
https://doi.org/10.1007/JHEP07(2020)225
JHEP07(2020)225
Matching scalar leptoquarks to the SMEFT at one loop
Contents 1 Introduction
1
2 The S1 + S3 model 2.1 Tree-level SMEFT matching conditions
2 4 4 6 8 9 10 11 14
4 Conclusions
19
A A Green’s basis for the SMEFT
20
B Reduction of Green’s basis to Warsaw basis B.1 Renormalizable operators B.2 Purely bosonic operators B.3 Two-fermion operators B.4 Four-fermion operators
24 24 25 25 30
C One-loop matching conditions in the Green’s basis C.1 Renormalizable operators C.2 Purely bosonic operators C.3 Two-fermion operators C.4 Four-fermion operators
36 36 36 38 42
1
Introduction
The Standard Model (SM) of Particle Physics still represents the best description of highenergy phenomena at our disposal. Nevertheless, several experimental and theoretical shortcomings require the presence of some New Physics (NP). The lack of a NP discovery at the LHC and the SM’s impressive phenomenological success could suggest the existence of a large separation between the Electroweak (EW) and NP scales. If this is the case, the SM should really be understood as the leading (renormalizable) approximation of a low energy Effective Field Theory (EFT), known as SMEFT [1–3]. Considering the SM as an EFT is not only conceptually, but also practically advantageous, for it allows to study a whole class of SM extensions in a model independent way. In fact, in the SMEFT framework, the effects of heavy NP are fully encoded in the Wilson Coefficients (WCs) of non-renormalizable operators, in terms of which low-energy observables can be computed without any reference to the specific ultraviolet (UV) model. The WCs for a given concrete UV SM exten
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