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Pich, A., Rosell, I., Santos, J., & Sanz-Cillero, J. J. (2017). Fingerprints of heavy scales in electroweak effective Lagrangians. J. High Energy Phys., 04(4), 012–60pp.
Abstract: The couplings of the electroweak effective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general effective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2)(L) circle times SU(2)(R) -> SU(2)(L+R), which couples the known particle fields to heavier states with bosonic quantum numbers J(P) = 0(+/-) and 1(+/-). We consider colour-singlet heavy fields that are in singlet or triplet representations of the electroweak group. Integrating out these heavy scales, we analyze the pattern of low-energy couplings among the light fields which are generated by the massive states. We adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs, without making any assumption about its possible doublet structure. Special attention is given to the different possible descriptions of massive spin-1 fields and the differences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.
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Pich, A., Rosell, I., Santos, J., & Sanz-Cillero, J. J. (2016). Low-energy signals of strongly-coupled electroweak symmetry-breaking scenarios. Phys. Rev. D, 93(5), 055041–6pp.
Abstract: The nonobservation of new particles at the LHC suggests the existence of a mass gap above the electroweak scale. This situation is adequately described through a general electroweak effective theory with the established fields and Standard Model symmetries. Its couplings contain all information about the unknown short-distance dynamics which is accessible at low energies. We consider a generic strongly coupled scenario of electroweak symmetry breaking, with heavy states above the gap, and analyze the imprints that its lightest bosonic excitations leave on the effective Lagrangian couplings. Different quantum numbers of the heavy states imply different patterns of low-energy couplings, with characteristic correlations which could be identified in future data samples. The predictions can be sharpened with mild assumptions about the ultraviolet behaviour of the underlying fundamental theory.
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Pich, A., Rosell, I., & Sanz-Cillero, J. J. (2020). Bottom-up approach within the electroweak effective theory: Constraining heavy resonances. Phys. Rev. D, 102(3), 035012–12pp.
Abstract: The LHC has confirmed the existence of a mass gap between the known particles and possible new states. Effective field theory is then the appropriate tool to search for low-energy signals of physics beyond the Standard Model. We adopt the general formalism of the electroweak effective theory, with a nonlinear realization of the electroweak symmetry breaking, where the Higgs is a singlet with independent couplings. At higher energies we consider a generic resonance Lagrangian which follows the above-mentioned nonlinear realization and couples the light particles to bosonic heavy resonances with J(P) = 0(+/-) and J(P) = 1(+/-). Integrating out the resonances and assuming a proper short-distance behavior, it is possible to determine or to constrain most of the bosonic low-energy constants in terms of resonance masses. Therefore, the current experimental bounds on these bosonic low-energy constants allow us to constrain the resonance masses above the TeV scale, by following a typical bottom-up approach, i.e., the fit of the low-energy constants to precise experimental data enables us to learn about the high-energy scales, the underlying theory behind the Standard Model.
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Pich, A., Rosell, I., & Sanz-Cillero, J. J. (2014). Oblique S and T constraints on electroweak strongly-coupled models with a light Higgs. J. High Energy Phys., 01(1), 157–35pp.
Abstract: Using a general effective Lagrangian implementing the chiral symmetry breaking SU(2)(L) circle times SU(2)(R) -> SU(2)(L+R), we present a one-loop calculation of the oblique S and T parameters within electroweak strongly-coupled models with a light scalar. Imposing a proper ultraviolet behaviour, we determine S and T at next-to-leading order in terms of a few resonance parameters. The constraints from the global fit to electroweak precision data force the massive vector and axial-vector states to be heavy, with masses above the TeV scale, and suggest that the W+W- and and ZZ couplings of the Higgs-like scalar should be close to the Standard Model value. Our findings are generic, since they only rely on soft requirements on the short-distance properties of the underlying strongly-coupled theory, which are widely satisfied in more specific scenarios.
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Pich, A., Rosell, I., & Sanz-Cillero, J. J. (2013). Viability of Strongly Coupled Scenarios with a Light Higgs-like Boson. Phys. Rev. Lett., 110(18), 181801–4pp.
Abstract: We present a one-loop calculation of the oblique S and T parameters within strongly coupled models of electroweak symmetry breaking with a light Higgs-like boson. We use a general effective Lagrangian, implementing the chiral symmetry breaking SU(2)(L) circle times SU(2)(R) -> SU(2)(L+R) with Goldstone bosons, gauge bosons, the Higgs-like scalar, and one multiplet of vector and axial-vector massive resonance states. Using a dispersive representation and imposing a proper ultraviolet behavior, we obtain S and T at the next-to-leading order in terms of a few resonance parameters. The experimentally allowed range forces the vector and axial-vector states to be heavy, with masses above the TeV scale, and suggests that the Higgs-like scalar should have a WW coupling close to the standard model one. Our conclusions are generic and apply to more specific scenarios such as the minimal SO(5)/SO(4) composite Higgs model.
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