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Pich, A., Rosell, I., & Sanz-Cillero, J. J. (2011). The vector form factor at the next-to-leading order in 1/N-C: chiral couplings L-9(mu) and C-88(mu)-C-90(mu). J. High Energy Phys., 02(2), 109–23pp.
Abstract: Using the Resonance Chiral Theory Lagrangian, we perform a calculation of the vector form factor of the pion at the next-to-leading order (NLO) in the 1/N-C expansion. Imposing the correct QCD short-distance constraints, one fixes the amplitude in terms of the pion decay constant F and resonance masses. Its low momentum expansion determines then the corresponding O(p(4)) and O(p(6)) low-energy chiral couplings at NLO, keeping control of their renormalization scale dependence. At mu(0) = 0.77 GeV, we obtain L-9(mu(0)) = (7.9 +/- 0.4).10(-3) and C-88(mu(0)) – C-90(mu(0)) = (-4.6 +/- 0.4).10(-5).
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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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Krause, C., Pich, A., Rosell, I., Santos, J., & Sanz-Cillero, J. J. (2019). Colorful imprints of heavy states in the electroweak effective theory. J. High Energy Phys., 05(5), 092–51pp.
Abstract: We analyze heavy states from generic ultraviolet completions of the Standard Model in a model-independent way and investigate their implications on the low-energy couplings of the electroweak effective theory. We build a general effective Lagrangian, implementing the electroweak symmetry breaking SU(2)(L) circle times SU(2)(R) SU(2)(L+R) with a non-linear Nambu-Goldstone realization, which couples the known particles to the heavy states. We generalize the formalism developed in previous works [1, 2] to include colored resonances, both of bosonic and fermionic type. We study bosonic heavy states with J(P) = 0(+/-) and J(P) = 1(+/-), in singlet or triplet SU(2)(L+R) representations and in singlet or octet representations of SU(3)(C) , and fermionic resonances with that are electroweak doublets and QCD triplets or singlets. Integrating out the heavy scales, we determine the complete pattern of low-energy couplings at the lowest non-trivial order. Some specific types of (strongly- and weakly-coupled) ultraviolet completions are discussed to illustrate the generality of our approach and to make contact with current experimental searches.
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