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Register a new userConstraining resonances by using the electroweak effective theory
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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.
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We consider a non-linear realization of the electroweak symmetry-breaking pattern $SU(2)_Ltimes SU(2)_R/SU(2)_{L+R}$ 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.
We apply on-shell methods to the bottom-up construction of electroweak amplitudes, allowing for both renormalizable and non-renormalizable interactions. We use the little-group covariant massive-spinor formalism, and flesh out some of its details along the way. Thanks to the compact form of the resulting amplitudes, many of their properties, and in particular the constraints of perturbative unitarity, are easily seen in this formalism. Our approach is purely bottom-up, assuming just the standard-model electroweak spectrum as well as the conservation of electric charge and fermion number. The most general massive three-point amplitudes consistent with these symmetries are derived and studied in detail, as the primary building blocks for the construction of scattering amplitudes. We employ a simple argument, based on tree-level unitarity of four-point amplitudes, to identify the three-point amplitudes that are non-renormalizable at tree level. This bottom-up analysis remarkably reproduces many low-energy relations implied by electroweak symmetry through the standard-model Higgs mechanism and beyond it. We then discuss four-point amplitudes. The gluing of three-point amplitudes into four-point amplitudes in the massive spinor helicity formalism is clarified. As an example, we work out the $psi^c psi Zh$ amplitude, including also the non-factorizable part. The latter is an all-order expression in the effective-field-theory expansion. Further constraints on the couplings are obtained by requiring perturbative unitarity. In the $psi^c psi Zh$ example, one for instance obtains the renormalizable-level relations between vector and fermion masses and gauge and Yukawa couplings. We supplement our bottom-up derivations with a matching of three- and four-point amplitude coefficients onto the standard-model effective field theory (SMEFT) in the broken electroweak phase.
We compute the one-loop anomalous dimensions of the low-energy effective Lagrangian below the electroweak scale, up to terms of dimension six. The theory has 70 dimension-five and 3631 dimension-six Hermitian operators that preserve baryon and lepton number, as well as additional operators that violate baryon number and lepton number. The renormalization group equations for the quark and lepton masses and the QCD and QED gauge couplings are modified by dimension-five and dimension-six operator contributions. We compute the renormalization group equations from one insertion of dimension-five and dimension-six operators, as well as two insertions of dimension-five operators, to all terms of dimension less than or equal to six. The use of the equations of motion to eliminate operators can be ambiguous, and we show how to resolve this ambiguity by a careful use of field redefinitions.
We establish the non-perturbative validity of the gauge anomaly cancellation condition in an effective electroweak theory of massless fermions with finite momentum cut-off and Fermi interaction. The requirement that the current is conserved up to terms smaller than the energy divided by the cut-off scale, which is the natural condition as gauge invariance is only emerging, produces the same constraint on charges as in the Standard Model. The result holds at a non-perturbative level as the functional integrals are expressed by convergent power series expansions and are analytic in a finite domain.
We investigate the viability of extending the Standard Model with $S_1$ and $S_3$ scalar leptoquarks when the flavour structure is parametrized in terms of Froggatt-Nielsen charges. In contrast to a similar analysis with a vector leptoquark, we find essentially two solutions for the charges that fit the experimental constraints, which are dominated by the current tensions in $B$ decays. These two scenarios differ in their estimate of the anomalous magnetic moment of the muon, $(g-2)$, but they both predict sizeable contributions to $tautomugamma$, $bar B_stotau^pmmu^mp$ and $B^+to K^+tau^+mu^-$ decays, whose branching ratios are close to the current experimental limits.
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