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DOE OSTI · 2564426

Renormalizing two-fermion operators in the SMEFT via supergeometry

Assi, Benoît [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Univ. of Cincinnati, OH (United States)] (ORCID:0000000309243335)·Helset, Andreas [European Organization for Nuclear Research (CERN), Geneva (Switzerland)] (ORCID:0000000259043748)·Pagès, Julie [Univ. of California, San Diego, CA (United States)] (ORCID:0000000206563053)·Shen, Chia-Hsien [National Taiwan Univ., Taipei (Taiwan); Leung Center for Cosmology and Particle Astrophysics, Taipei (Taiwan); National Center for Theoretical Sciences (NCTS), Taipei (Taiwan)] (ORCID:0000000251389971)
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Abstract

We extend the geometric framework of field-space covariance for loop computations, thereby unifying the treatment of scalars, fermions, and gauge bosons in effective field theories. This allows us to derive a manifestly covariant formula for one-loop UV divergences that includes contributions from mixed boson-fermion graphs. The result is expressed in terms of geometric invariants of the field-space supermanifold. As a demonstration of this formula, we compute the renormalization group equations for two-fermion operators at the dimension-eight level in the Standard Model Effective Field Theory.

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72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDSDifferential and Algebraic GeometryEffective Field TheoriesRenormalization GroupSMEFT

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Assi, Benoît [Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States); Univ. of Cincinnati, OH (United States)] (ORCID:0000000309243335), Helset, Andreas [European Organization for Nuclear Research (CERN), Geneva (Switzerland)] (ORCID:0000000259043748), Pagès, Julie [Univ. of California, San Diego, CA (United States)] (ORCID:0000000206563053), Shen, Chia-Hsien [National Taiwan Univ., Taipei (Taiwan); Leung Center for Cosmology and Particle Astrophysics, Taipei (Taiwan); National Center for Theoretical Sciences (NCTS), Taipei (Taiwan)] (ORCID:0000000251389971). 2025-12-11. Renormalizing two-fermion operators in the SMEFT via supergeometry. https://doi.org/10.1007/jhep12(2025)082

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