Abstract
Effective field theories are useful tools to search for physics beyond the Standard Model (SM). However, effective theories can lead to non-unitary behavior with fastly growing amplitudes. This unphysical behavior may lead to large sensitivity to SM deviations, making necessary a unitarization of the amplitudes prior to a comparison with experiment. In the present work, we focus on all the processes entering the two-Higgs production by longitudinal $WW$ scattering: we perform a full one-loop calculation of all relevant processes, we determine the necessary counterterms in the on-shell scheme, and we study how the full inclusion of the gauge degrees of freedom modifies the previously computed masses and widths of the dynamical resonances arising from the unitarization process in the vector-isovector channel. Altogether, we are able to provide the technical tools that are needed to study the low-energy couplings in the Higgs effective theory under the requirements of unitarity and causality.
Highlights
Since the discovery in 2012 of a light scalar by ATLAS [1] and CMS [2], so far compatible with the Standard Model (SM) Higgs, a lot of questions have arisen regarding the origin of such a scalar and the properties of the electroweak symmetry breaking sector (EWSBS) [3,4,5,6,7,8,9].To explore the nature of EWSBS beyond the SM (BSM), the scattering of longitudinally polarized electroweak gauge bosons is one of the most sensitive channels
Electromagnetism should not be involved in any strong dynamics that may be present in the EWSBS. (d) custodially breaking operators are not included, as previously indicated; it would be inconsistent to include these and leave out the main source of weak isospin breaking in the SM. (e) The calculation is made in the Landau gauge, which simplifies somewhat the counterterm structure
A precise implementation of the equivalence theorem [31–38] (ET) tells us that corrections to the leading term are given by a succession of subleading contributions, each one lower with respect to the previous by a power of momenta
Summary
Since the discovery in 2012 of a light scalar by ATLAS [1] and CMS [2], so far compatible with the Standard Model (SM) Higgs, a lot of questions have arisen regarding the origin of such a scalar and the properties of the electroweak symmetry breaking sector (EWSBS) [3,4,5,6,7,8,9]. As mentioned, we relax that approximation and allow transverse modes to propagate in the process, improving a weak point of the previous unitarization studies because along with the assumption g 1⁄4 0 in [10,15,16], the authors consistently set MW 1⁄4 0 for the real part of the loop calculation. We make no assumption about the UV strong dynamics, In our model-independent study, the effects of the high-energy theory in the low energy regime are encoded in the so called chiral parameters When these parameters do not have a correspondence in the SM, their presence spoils the unitarity of the amplitudes leading them, after unitarization, to exhibit resonances, i.e., bound states presumably resulting from the underlying strong dynamics. Electromagnetism should not be involved in any strong dynamics that may be present in the EWSBS. (d) custodially breaking operators are not included, as previously indicated; it would be inconsistent to include these and leave out the main source of weak isospin breaking in the SM. (e) The calculation is made in the Landau gauge, which simplifies somewhat the counterterm structure
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