Abstract
We use unitarity and analyticity of scattering amplitudes to constrain fermionic operators in the standard model effective field theory. For four-fermion operators at mass dimension 8, we scatter flavor superpositions in fixed standard model representations and find the Wilson coefficients to be constrained so that their contraction with any pair of pure density matrices is positive. These constraints imply that flavor-violating couplings are upper bounded by their flavor-conserving cousins. For instance, LEP data already appears to preclude certain operators in upcoming μ→3e measurements.
Highlights
Introduction.—Results from the Large Hadron Collider provide a remarkable affirmation of the standard model (SM)
While these results bring into question naturalness arguments that had suggested new physics should emerge at these energies [1,2], they only strengthen the basic principles of quantum field theory, such as unitarity and analyticity, that underlie the SM
At each mass dimension in the SMEFT, there is a basis of gauge and Lorentz invariant operators [3,4]; new physics can be differentiated only through the specific values of the SMEFT Wilson coefficients, the last vestige of the ultraviolet (UV) completion
Summary
For four-fermion operators at mass dimension 8, we scatter flavor superpositions in fixed standard model representations and find the Wilson coefficients to be constrained so that their contraction with any pair of pure density matrices is positive. These constraints imply that flavor-violating couplings are upper bounded by their flavor-conserving cousins. [5,6,7,8], the s2 coefficient of the forward scattering amplitude can, by virtue of analyticity and the optical theorem, be written as an integral over the cross section and must be positive, thereby constraining the Wilson coefficients This principle of bounding EFTs via IR consistency has been used to constrain a litany of theories, including fermionic scattering [9].
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