Building blocks of the flavourful SMEFT RG

Machado, C. S., Renner, S. and Sutherland, D. (2023) Building blocks of the flavourful SMEFT RG. Journal of High Energy Physics, 2023(3), 226. (doi: 10.1007/JHEP03(2023)226)

Abstract

A powerful aspect of effective field theories is connecting scales through renormalisation group (RG) flow. The anomalous dimension matrix of the Standard Model Effective Field Theory (SMEFT) encodes clues to where to find relics of heavy new physics in data, but its unwieldy 2499 × 2499 size (at operator dimension 6) makes it difficult to draw general conclusions. In this paper, we study the flavour structure of the SMEFT one loop anomalous dimension matrix of dimension 6 current-current operators, a 1460 × 1460 submatrix. We take an on-shell approach, laying bare simple patterns by factorising the entries of the matrix into their gauge, kinematic and flavour parts. We explore the properties of different diagram topologies, and make explicit the connection between the IR-finiteness of certain diagrams and their gauge and flavour structure. Through a completely general flavour decomposition of the Wilson coefficient matrices, we uncover new flavour selection rules, from which small subsystems emerge which mix almost exclusively amongst themselves. We show that, for example, if we neglect all Yukawa couplings except for that of the top quark, the selection rules produce block diagonalisation within the current-current operators in which the largest block is a 61 × 61 matrix. We provide all the ingredients of the calculations in comprehensive appendices, including SM and SMEFT helicity amplitudes, and explicit results for phase space integrals and gauge contractions. This deconstruction of the matrix, and its resulting block-diagonalisation, provides a first step to understanding the IR-relevant directions in the SMEFT parameter space, hence closing in on natural places for heavy new physics to make itself known.

• Item Type: Articles
• Additional Information: This work was partially supported by a grant from the Simons Foundation. SR is supported by UKRI Stephen Hawking Fellowship EP/W005433/1. CSM is supported by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy EXC 2121 “Quantum Universe” — 390833306.
• Keywords: Scattering amplitudes, SMEFT, flavour symmetries, rare decays.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Sutherland, Dr David and Renner, Dr Sophie
• Authors: Machado, C. S., Renner, S., and Sutherland, D.
• College/School: College of Science and Engineering > School of Physics and Astronomy
• Journal Name: Journal of High Energy Physics
• Publisher: Springer
• ISSN: 1126-6708
• ISSN (Online): 1029-8479
• Published Online: 28 March 2023
• Copyright Holders: Copyright © 2023 The Authors
• First Published: First published in Journal of High Energy Physics 2023(3): 226
• Publisher Policy: Reproduced under a Creative Commons License

Project Code	Award No	Project Name	Principal Investigator	Funder's Name	Funder Ref	Lead Dept
317611		Closing the flavour loophole for physics beyond the Standard Model	Sophie Renner	Engineering and Physical Sciences Research Council (EPSRC)	EP/W005433/1	P&S - Physics & Astronomy