Two loop renormalization of scalar theories using a geometric approach

Jenkins, Elizabeth E.; Manohar, Aneesh V.; Naterop, Luca; Pagès, Julie

doi:10.1007/jhep02(2024)131

Two loop renormalization of scalar theories using a geometric approach

Journal Article · Fri Feb 16 00:00:00 EST 2024 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep02(2024)131· OSTI ID:2575987

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Univ. of California, San Diego, CA (United States). Dept. of Physics
Univ. of California, San Diego, CA (United States). Dept. of Physics; Univ. of Zurich (Switzerland); Paul Scherrer Inst. (PSI), Villigen (Switzerland)

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order p⁶.

View Accepted Manuscript (DOE)

Research Organization:: Univ. of California, San Diego, CA (United States)

Sponsoring Organization:: Swiss National Science Foundation; USDOE Office of Science (SC)

Grant/Contract Number:: SC0009919

OSTI ID:: 2575987

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 2 Vol. 2024; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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