Within the framework of a general non-linear effective field theory describing the electroweak symmetry breaking, we perform a detailed analysis of the next-to-leading contributions to the electroweak oblique parameters S and T from hypothetical heavy resonance states strongly coupled to Standard Model fields. This work extends our previous results by including parity-odd operators in the effective Lagrangian, contributions from fermionic cuts, and up-to-date experimental constraints. We demonstrate that in strongly-coupled ultraviolet completions satisfying both Weinberg Sum Rules -as is the case in asymptotically free gauge theories- the vector and axial-vector resonance masses are constrained to lie above 10TeV. Conversely, scenarios allowing for lighter resonances with masses between 2and 10TeV necessarily imply a violation of the second Weinberg Sum Rule.

Using a general (non-linear) effective field theory description of the Standard Model electroweak symmetry breaking, we analyse the impact on the electroweak oblique parameters of hypothetical heavy resonance states strongly coupled to the SM particles. We present a next-to-leading order calculation of S and T that updates and generalizes our previous results, including P-odd operators in the Lagrangian, fermionic cuts and the current experimental bounds. We demonstrate that in any strongly-coupled underlying theory where the two Weinberg Sum Rules are satisfied, as happens in asymptotically free gauge theories, the masses of the heavy vector and axial-vector states must be heavier than 10 TeV. Lighter resonances with masses around 2-3 TeV are only possible in theoretical scenarios where the 2nd Weinberg Sum Rule is not fulfilled.

Experiments have confirmed the presence of a mass gap between the Standard Model and potential New Physics. Consequently, the exploration of effective field theories to detect signals indicative of Physics Beyond the Standard Model is of great interest. In this study, we examine a non-linear realization of the electroweak symmetry breaking, wherein the Higgs is a singlet with independent couplings, and Standard Model fields are additionally coupled to heavy bosonic resonances. We present a next-to-leading-order determination of the oblique S and T parameters. Comparing our predictions with experimental values allows us to impose constraints on resonance masses, requiring them to exceed the TeV scale (M_R > 2TeV). This finding aligns with our earlier analysis, employing a less generalized approach and the experimental bounds of that time, where we computed these observables.

It has been confirmed experimentally the existence of a mass gap between Standard Model (SM) and eventual Beyond Standard Model (BSM) fields. Therefore, the use of effective approaches to search for fingerprints of New Physics is very appealing. A non-linear realizations of the Electroweak Symmetry Breaking is considered here, where the Higgs is a singlet with free couplings and the SM fields are also coupled to bosonic heavy resonances. A one-loop-level calculation of the oblique S and T parameters is presented here. This analysis allows us to constrain resonance masses to be above the TeV scale, Image 1TeV, in good agreement with our previous determinations, where these observables were computed with a more simplified Lagrangian.

Without a doubt the ratios Rτ/p = Γ(τ → Pντ[γ])/Γ(P → μνμ[γ]) (P = π, K) give a convenient scenario to test the lepton universality, the CKM unitarity and to search for non-standard interactions in τ decays. Moreover, the previous theoretical estimation of these observables is more than twenty-five years old and some assumptions of that estimation are unrealistic. Therefore, an update of Rτ/P was timely. The one-loop radiative corrections have been computed by considering an expansion of Chiral Perturbation Theory including the lightest spin-one resonances and respecting the short-distance behavior dictated by QCD. We have reported δRτ/π = (0.18±0.57)% and δRτ/K = (0.97±0.58)%, where the uncertainties have been induced fundamentally by the estimation of the counterterms. We have tested the lepton universality, the CKM unitarity and have searched for new physics in τ decays. As a by-product, we have also determined the theoretical radiative corrections to the τ → Pντ[γ] decay rates, δτπ = —(0.24 ± 0.56)% and δτK = —(0.15 ± 0.57)%.

We have determined Rτ/P ≡ Γ(τ → P ντ [γ])/Γ(P → µνµ[γ]) (P = π, K). Whereas P decays are calculated by using Chiral Perturbation Theory (ChPT), τ decays have been studied with an effective approach where ChPT is enlarged by including the lightest resonances and following the high-energy behavior dictated by QCD. These ratios have allowed us to test the lepton universality and the CKM unitarity and also to search for bounds on non-standard interactions. Our results, δRτ/π = (0.18±0.57)% and δRτ/K = (0.97±0.58)%, are consistent with the previous theoretical determinations, but with much more robust assumptions, yielding a reliable uncertainty.

Abstract We calculate the ratios R τ/P ≡ Γ (τ → Pν τ [γ]) /Γ (P → μν μ [γ]) (P = π, K) at one loop following a large-N C expansion where Chiral Perturbation Theory is enlarged by including the lightest resonances and respecting the short-distance behavior dictated by QCD. We find δR τ/π = (0.18 ± 0.57)% and δR τ/K = (0.97 ± 0.58)%, where the uncertainties are induced fundamentally by the counterterms. We test the lepton universality, obtaining |g τ /g μ | π = 0.9964 ± 0.0038 and |g τ /g μ | K = 0.9857 ± 0.0078, and analyze the CKM unitarity, getting results at 2.1σ and 1.5σ from unitarity via |V us /V ud | and |V us |, respectively. We also update the search for non-standard interactions in τ decays. As a by-product, we report the theoretical radiative corrections to the τ → Pν τ [γ] decay rates: δ τπ = −(0.24 ± 0.56)% and δ τK = −(0.15 ± 0.57)%.

The existence of a mass gap between the Standard Model (SM) and possible new states encourages us to use effective field theories. Here we follow the non-linear realization of the electroweak symmetry breaking: the electroweak effective theory (EWET), also known as Higgs effective field theory (HEFT) or electroweak chiral Lagrangian (EWChL). At short distances an effective resonance Lagrangian which couples the SM states to bosonic and fermionic resonances is considered. After integrating out the resonances and assuming a well-behaved high-energy behavior, we estimate or bound purely bosonic low-energy constants in terms of only resonance masses. Current experimental information on these low-energy constants allows us to constrain the high-energy resonance masses.

We consider a non-linear realization of the electroweak symmetry-breaking pattern S U(2)L × S U(2)R/S U(2)L+R to construct a low-energy effective theory, later extended by the inclusion of heavy new-physics resonances. After assuming appropriate high-energy constraints given by Weinberg sum-rules and the asymptotic behaviour of form-factors, we obtain relations between resonance masses and some low-energy effective couplings. These predictions are compared with current experimental data and some resonance mass bounds are inferred.

The ratios $R_{\tau/P}\equiv \Gamma(\tau \to P \nu_\tau [\gamma]) / \Gamma(P \to\mu \nu_\mu[\gamma])$ ($P=\pi, K$) provide sensitive tests of lepton universality $\left|g_\tau/g_\mu\right|=1$ and are a useful tool for new physics searches. The radiative corrections to $R_{\tau/P}$ are computed following a large-$N_C$ expansion to deal with hadronic effects: Chiral Perturbation Theory is enlarged by including the lightest multiplets of spin-one heavy states such that the relevant Green functions are well-behaved at high energies. We find $\delta R_{\tau/\pi}=(0.18\pm 0.57 )\%$ and $\delta R_{\tau/K}=(0.97\pm 0.58 )\%$, which imply $\left|g_\tau/g_\mu\right|_\pi=0.9964\pm 0.0038$ and $\left|g_\tau/g_\mu\right|_K=0.9857\pm 0.0078$, compatible with and at $1.8\sigma$ of lepton universality, respectively. We test unitarity and bind non-standard effective interactions with the $\tau \to P \nu_\tau [\gamma]$ decays.

M. A. Arroyo-Ureña, G. Hernández-Tomé, G. López-Castro, P. Roig, and I. Rosell 1 Departamento de F́ısica, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Apartado Postal 14-740, 07000 Ciudad de México, México and 2 Departamento de Matemáticas, F́ısica y Ciencias Tecnológicas, Universidad Cardenal Herrera-CEU, CEU Universities, 46115 Alfara del Patriarca, València, Spain

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 non-linear 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 non-linear realization and couples the light particles to bosonic heavy resonances with $J^P=0^\pm$ and $J^P=1^\pm$. 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.

In the light of the mass gap between Standard Model (SM) states and possible new particles, effective field theories are a suitable approach. We take on the non-linear realization of the electroweak symmetry breaking: the electroweak effective theory (EWET), also known as Higgs effective field theory (HEFT) or electroweak chiral Lagrangian (EWChL). At higher scales we consider a resonance electroweak Lagrangian, coupling SM fields to resonances. Integrating out these resonances and assuming a well-behaved high-energy behavior, some of the bosonic low-energy constants are determined or constrained in terms of resonance masses. Present experimental bounds on these low-energy constants allow us to push the resonance mass scale to the TeV range, $M_R \geq 2\,$TeV, in good agreement with previous estimations.

The high-energy scattering of massive electroweak bosons, known as vector boson scattering (VBS), is a sensitive probe of new physics. VBS signatures will be thoroughly and systematically investigated at the LHC with the large data samples available and those that will be collected in the near future. Searches for deviations from Standard Model (SM) expectations in VBS facilitate tests of the Electroweak Symmetry Breaking (EWSB) mechanism. Current state-of-the-art tools and theory developments, together with the latest experimental results, and the studies foreseen for the near future are summarized. A review of the existing Beyond the SM (BSM) models that could be tested with such studies as well as data analysis strategies to understand the interplay between models and the effective field theory paradigm for interpreting experimental results are discussed. This document is a summary of the EU COST network "VBScan" workshop on the sensitivity of VBS processes for BSM frameworks that took place December 4-5, 2019 at the LIP facilities in Lisbon, Portugal. In this manuscript we outline the scope of the workshop, summarize the different contributions from theory and experiment, and discuss the relevant findings.

Due to the mass gap between the Standard Model and possible New Physics states, electroweak effective approaches are appropriate. Although a linear realization of the electroweak symmetry breaking with the Higgs forming a doublet together with the Goldstone bosons of the EWSB is a first possibility (SMEFT), we adopt the more general non-linear realization, where the Higgs is a singlet with independent couplings (EWET, HEFT or EWChL). We present the effective Lagrangian at low energies (the EWET, with only the SM fields) and at high energies (the resonance theory, with also a set of resonances). Taking into account the high scale of these resonances, their experimental searches seem to be more accessible by considering their imprints at low-energies, i.e., their imprints in the Low Energy Constants (LECs) of the EWET at energies lower than the resonance masses. We give some examples of these phenomenological connections.

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 ⊗ 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 JP = 0± and JP = 1±, in singlet or triplet SU(2)L+R representations and in singlet or octet representations of SU(3)C , and fermionic resonances with $$ J=\frac{1}{2} $$ 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.

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 $J^P=0^\pm$ and $J^P=1^\pm$ (in electroweak triplets or singlets and in QCD octets or singlets) and fermionic states with $J=\frac{1}{2}$ (in electroweak doublets and in QCD triplets or singlets). By integrating out these heavy resonances, the pattern of next-to-leading order low-energy constants among the light fields can be studied. A phenomenological study trying to estimate the scale of these resonances is also shown.

Taking into account the negative 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 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 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.