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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.

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.