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The couplings of the electroweak e ective theory contain information on the heavy-mass scales which are no-longer present in the low-energy Lagrangian. We build a general e ective Lagrangian, implementing the electroweak chiral symmetry breaking SU(2)L SU(2)R ! SU(2)L+R, which couples the known particle elds to heavier states with bosonic quantum numbers JP = 0 and 1 . We consider colour-singlet heavy elds 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 elds 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 di erent possible descriptions of massive spin-1 elds and the di erences arising from naive implementations of these formalisms, showing their full equivalence once a proper short-distance behaviour is required.

Accepting that there is a mass gap above the electroweak scale, the Electroweak E ective Theory (EWET) is an appropriate tool to describe this situation. Since the EWET couplings contain information on the unknown high-energy dynamics, we consider a generic strongly-coupled scenario of electroweak symmetry breaking, where the known particle fields are coupled to heavier states. Then, and by integrating out these heavy fields, we study the tracks of the lightest resonances into the couplings. The determination of the low-energy couplings (LECs) in terms of resonance parameters can be made more precise by considering a proper short-distance behaviour on the Lagrangian with heavy states, since the number of resonance couplings is then reduced. Notice that we adopt a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs.

We have calculated the ratios R(P) e/m ≡ G(P → en¯e[g ])/G(P →mn¯m [g ]) (P = p ,K) in Chiral Perturbation Theory up to O(e2p4), finding R(p) e/m = (1.2352±0.0001)×10−4 and R(K) e/m = (2.477± 0.001)×10−5. This observable is helicity suppressed in the Standard Model, so that it is a sensitive probe of all Standard Model extensions that induce pseudoscalar currents and nonuniversal corrections to the lepton couplings. Ongoing experimental searches plan to reach uncertainties that are comparable to these results. At the moment R(K) e/m is in agreement with the final result by the KLOE Collaboration at DAFNE and it is at 1.4s of the preliminary result by the NA62 Experiment at CERN. New measurements of R(p) e/m are under way by the PEN Collaboration at PSI and by the PIENU Collaboration at TRIUMF.

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⊗SU(2)R →SU(2)L+R with Goldstones, gauge bosons, the Higgs-like scalar and one multiplet of vector and axial-vector massive resonance states. The estimation is based on the short-distance constraints and a dispersive approach. 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.

Contrary to what is sometimes stated, the current electroweak precision data easily allow for massive composite resonance states at the natural EW scale, i.e., well over the TeV. The oblique parameters S and T are analyzed by means of an effective Lagrangian that implements the SU(2)L⊗SU(2)R→SU(2)L+R pattern of electroweak symmetry breaking. They are computed at the one-loop level and incorporating the newly discovered Higgs-like boson and possible spin–1 composite resonances. Imposing a proper ultraviolet behaviour is crucial and allows us to de- termine S and T at next-to-leading order in terms of a few resonance parameters. Electroweak precision data force the vector and axial-vector states to have masses above the TeV scale and suggest that the W+W− and ZZ couplings to the Higgs-like scalar should be close to the Stan- dard Model value. Our findings are generic: they only rely on symmetry principles and soft requirements on the short-distance properties of the underlying strongly-coupled theory, which are widely satisfied in more specific scenarios.

We present a one-loop calculation of the oblique S parameter within Higgsless models of electroweak symmetry breaking. We have used a general effective Lagrangian with at most two derivatives, implementing the chiral symmetry breaking SU(2)L ⊗ SU(2)R → SU(2)L+R with Goldstones, gauge bosons and one multiplet of vector and axial-vector resonances. The estimation is based on the short-distance constraints and the dispersive approach proposed by Peskin and Takeuchi.

A proper estimation of the chiral low-energy constants of Chiral Perturbation Theory is a very important task. To this end resonance chiral Lagrangians have been used fruitfully. We have studied the determination of chiral couplings at next-to-leading (NLO) order in the 1=NC expansion, keeping full control of the renormalization scale dependence. We find that, by imposing shortdistance constraints coming from QCD, resonance saturation at NLO in 1=NC is satisfied. In other words, the chiral couplings can be written in terms of the resonance masses and couplings and do not depend explicitly on the coefficients of the chiral operators in the Goldstone boson sector of Resonance Chiral Theory.

Taking into account the negative results of the searches for New Physics at the LHC, electroweak effective theories are appropriate to deal with current energies. Tracks of new, higher scales can be studied through next-to-leading order corrections of the electroweak effective theory. We assume a generic non-linear realization of the electroweak symmetry breaking with a singlet Higgs and a strongly-coupled UV-completion. We further consider a high-energy Lagrangian that incorporates explicitly a general set of new heavy fields. After integrating out these heavy resonances, we study the pattern of low-energy constants among the light fields, which are generated by the massive states.

Taking into account the negative results of direct searches for beyond the Standard Model fields and the consequent mass gap between Standard Model and possible unknown states, the use of electroweak effective theories is justified. Whereas at low energies we consider a non-linear realization of the electroweak symmetry breaking with a singlet Higgs and a strongly-coupled ultraviolet completion, at higher energies the known particles are assumed to be coupled to heavy states: bosonic fields with JP = 0 and JP = 1 (in electroweak triplets or singlets and in QCD octets or singlets) and fermionic states with J = 1 2 (in electroweak doublets and in QCD triplets or singlets). By integrating out these heavy resonances, the pattern of next-to-leading order lowenergy constants among the light fields can be studied. A phenomenological study trying to estimate the scale of these resonances is also shown.