Renormalization of the Standard Model Effective Field Theory from geometry

Helset, Andreas; Jenkins, Elizabeth E.; Manohar, Aneesh V.

doi:10.1007/jhep02(2023)063

Renormalization of the Standard Model Effective Field Theory from geometry

Journal Article · Tue Feb 07 00:00:00 EST 2023 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2023)063· OSTI ID:2223085

^[1]; Jenkins, Elizabeth E. ^[2]; Manohar, Aneesh V. ^[2]

California Institute of Technology (CalTech), Pasadena, CA (United States); California Institute of Technology
University of California San Diego, La Jolla, CA (United States)

S-matrix elements are invariant under field redefinitions of the Lagrangian. They are determined by geometric quantities such as the curvature of the field-space manifold of scalar and gauge fields. We present a formalism where scalar and gauge fields are treated together, with a metric on the combined space of both types of fields. Scalar and gauge scattering amplitudes are given by the Riemann curvature Rijkl of this combined space, with indices i, j, k, l chosen to be scalar or gauge indices depending on the type of external particle. One-loop divergences can also be computed in terms of geometric invariants of the combined space, which greatly simplifies the computation of renormalization group equations. We apply our formalism to the Standard Model Effective Field Theory (SMEFT), and compute the renormalization group equations for even-parity bosonic operators to mass dimension eight.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0009919; SC0011632

OSTI ID:: 2223085

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2023; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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