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Renormalization of the Standard Model Effective Field Theory from Geometry
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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.
Forward citations
Cited by 9 Pith papers
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geoSCET: Soft Theorems from Power Counting
geoSCET derives geometric soft theorems for scalar field theories directly from effective-field-theory power counting and proves they are exact to all orders in perturbation theory when no potential is present.
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Positivity in the Renormalization of Effective Field Theory
A general theorem fixes the sign of one-loop renormalization of even-dimension EFT couplings induced by equal-even-dimension operator pairs, with applications to SMEFT dimension-eight running and new non-renormalizati...
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Geometry of soft scalars at one loop
The geometric soft theorem for scalar effective field theories is unchanged at one loop in derivative-coupled theories, and receives a universal leading correction when potential interactions are present.
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Renormalization of general Effective Field Theories: Formalism and renormalization of bosonic operators
The authors compute, for the first time, the one-loop renormalization group equations of the bosonic operators of a completely general EFT up to mass dimension 6.
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The complete two-loop renormalization-group equations for the dimension-five LEFT sector, derived in a chirally symmetric scheme, with two methods that avoid gauge-variant nuisance operators.
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Running soft theorems in effective field theory
At one loop, the finite subleading parts of the soft photon and double-soft pion theorems carry Wilson coefficients whose RG running is dictated by the same EFT beta functions, while log terms remain universal.
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The Potential of HEFT and the scale of New Physics
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The goofy-symmetric Standard Model and the Hierarchy Problem
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A covariant one-loop divergence formula for mixed boson-fermion graphs is derived and applied to dimension-eight two-fermion RGEs in the SMEFT.
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