Renormalization of the Standard Model Effective Field Theory from Geometry

Abstract

$S$-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 $R_{ijkl}$ 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.

40 pages, 8 tables, 1 figure

References in corpus (3)

• Geometry-Kinematics Duality
• Geometry in Scattering Amplitudes
• On the effective action for scalars in a general manifold to any loop order

Cited by in corpus (15)

• Geometry in Scattering Amplitudes
• Constraints on anomalous dimensions from the positivity of the S-matrix
• Impact of dimension-eight SMEFT operators in the EWPO and Triple Gauge Couplings analysis in Universal SMEFT
• Double insertions of SMEFT operators in gluon fusion Higgs boson production
• Effective Field Theories on the Jet Bundle
• Jet Bundle Geometry of Scalar Field Theories
• Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators
• Effective Field Theories as Lagrange Spaces
• Anomalous Dimension of a General Effective Gauge Theory I: Bosonic Sector
• Renormalization-group running of dimension-8 four-fermion operators in the SMEFT
• Walls, bubbles and doom -- the cosmology of HEFT
• Renormalization-group equations of the LEFT at two loops: dimension-five effects
• Complete One-loop Renormalization-group Equations in the Seesaw Effective Field Theories
• Renormalising the Field-Space Geometry
• Field Space Geometry and Nonlinear Supersymmetry