Abstract
This work presents a first full one-loop computation of vector boson scattering (VBS) within the non-linear effective field theory given by the bosonic sector of the usually called electroweak chiral Lagrangian (EChL). The computation is performed in the most general case of covariant $R_\xi$ gauges and is compared through all this work with the Standard Model case, whose computation in these covariant gauges is also novel and is presented also here. The calculation of the one-loop VBS amplitude is performed using the diagrammatic method by means of the one-particle-irreducible (1PI) Green functions that are involved in these scattering processes. The central part of this work is then devoted to the renormalization of all the n-legs one-loop 1PI Green functions involved. This renormalization is performed in the most general off-shell case with arbitrary external legs momenta. We then describe in full detail the renormalization program, which within this context of the EChL, implies to derive all the counterterms for both the electroweak parameters, like boson masses and gauge couplings, and those for the EChL coefficients. These later are crucial for the renormalization of the new divergences typically appearing when computing loops with the lowest chiral dimension Lagrangian. We present here the full list of involved divergences and counterterms in the $R_\xi$ gauges and derive the complete set of renormalization group equations for the EChL coefficients. In the last part of this work, we present the EChL numerical results for the one-loop cross section in the WZ channel and compare them with the SM results.
Highlights
The use of Effective Field Theories (EFTs) to describe the phenomenology of new physics beyond the Standard Model (SM) of elementary particle interactions is nowadays a quite generalized tool when comparing theoretical predictions with experimental data
This is a novel and full (EW) one-loop computation of the vector boson scattering (VBS) amplitude within the covariant Rξ gauges that accounts for all kind of bosonic loop diagrams including: EW gauge bosons, Goldstone bosons, the Higgs boson and the ghost fields
For this computation we have used a diagrammatic method where the renormalization of the full one-loop amplitude is performed by first computing the involved renormalized 1PI Green functions which is a more demanding computation since it requires the renormalization to be implemented at the off-shell Green functions level, i.e., for arbitrary external legs momenta
Summary
The use of Effective Field Theories (EFTs) to describe the phenomenology of new physics beyond the Standard Model (SM) of elementary particle interactions is nowadays a quite generalized tool when comparing theoretical predictions with experimental data. The most appealing feature of an Effective Field Theory (EFT) approach is that it can be used as a generic test of the new physics without specifying the underlying ultraviolet fundamental theory that originates such low energy theory. For a proper EFT, it is sufficient to require it to preserve the same symmetries of the SM, in particular, the SUð3ÞC × SUð2ÞL × Uð1ÞY gauge invariance, and to be able to deal with quantum corrections, providing a framework for renomalization. The physical active fields in these EFTs are as in the SM, and include fermions (quarks and leptons), gauge bosons
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