Equivalence theorems for effective Lagrangians

Two combinatorial theorems relevant to Zimmermann's formulation of Lagrangian perturbation theory are proved in view of application to problems concerning symmetry breaking.     

The equivalence theorem and effective Lagrangians

We point out that the equivalence theorem, which relates the amplitude for a process with external longitudinally polarized vector bosons to the amplitude in which the longitudinal vector bosons are replaced by the corresponding pseudo-Goldstone bosons, is not valid for effective Lagrangians. However, a more general formulation of this theorem also holds for effective interactions. The generalized theorem can be utilized to determine the high-energy behaviour of scattering processes just by power counting and to simplify the calculation of the corresponding amplitudes. We apply this theorem to the phenomenologically most interesting terms describing effective interactions of the electroweak vector and Higgs bosons in order to examine their effects on vector-boson scattering and on vector-boson-pair production in $f\bar f$ annihilation. The use of the equivalence theorem in the literature is examined.     

NLO inspired effective Lagrangians for Higgs physics

Either late autumn this year or latest early next year ATLAS/CMS should have results with 2–3 times the current data which might give first clues on the couplings of the light narrow resonance discovered at the LHC in July 2012, compatible with the Higgs boson of the Standard Model. A strategy for measuring deviations from the Standard Model can be based on using the “full” Standard Model, including all available QCD and electroweak higher-order corrections, and supplement it with d=6$d=6$ local operators. Their Wilson coefficients are assumed to be small enough that they can be treated at leading order. Examples of the connection of local operators with BSM Lagrangians are presented as well as a discussion of Lagrangians with/without decoupling of heavy degrees of freedom. The whole strategy is critically reviewed in the light of internal consistency and an “Effective NLO Approximation” is proposed.     

Dark matter problem and effective curvature Lagrangians

A ‘radical’ conservative unifying model of scalar dark matter and modified gravity is proposed here. After a conformal mapping, the dependence of the effective Lagrangian on the curvature is not only singular but also bifurcates into several almost Einsteinian spaces, distinguished only by a different gravitational strength and cosmological constant. A swallow tail or butterfly catastrophe in the bifurcation set indicates the possibility for the coexistence of different Einsteinian domains in our Universe. This finding may shed new light on the nature and large scale distribution not only of dark matter but also on ‘dark energy’, regarded as an effective cosmological constant.     

Instanton effects in matrix models and string effective Lagrangians

We perform an explicit calculation of the lowest order effects of single eigenvalue instantons on the continuous sector of the collective field theory derived from a d = 1 bosonic matrix model. These effects consist of certain induced operators whose exact form we exhibit.     

Chiral Lagrangians and the Transition Amplitude for Radiative Muon Capture

 The transition operator for the radiative capture of mesons by protons is constructed starting from a chiral Lagrangian of the system obtained within the approach of hidden local symmetries. The transition operator is gauge invariant and its hadron radiative part satisfies exactly two relevant continuity equations. Received October 16, 1998; accepted for publication February 23, 1999     

Flux confinement for a class of effective Lagrangians

Confinement properties recently proved in the leading logarithm model are shown to be generally truc for a wide class of effective Lagrangians. These include nonexistence of isolated quarks, confining static potential between \(q\bar q\) pair and flux confinement within a characteristic acting as a free boundary. A new variational principle is formulated.     

Chiral symmetry restoration in hadron spectra

The evidence and the theoretical justification of chiral symmetry restoration in high-lying hadrons is presented.     

Equations of motion for effective Lagrangians and Penguins in rareB-decays

We study the application of the classical equations of motion (EOM) within the framework of an effective low-energy Lagrangian treated at the loop level. Gauge-fixing and ghost terms, which enter naturally in the EOM, are found to lead to no physical effects—neither through operator mixing nor in matrix elements. Beyond first order in the effective interactions, contact terms have to be included when reducing the effective Lagrangian and we present an explicit procedure to construct them. Applied to (hadronic) rareB-decays, the EOM drastically simplify the effective Lagrangian and its matching to the underlying theory, and certain cancellations of large (logarithmic) contributions become more transparent. Finally, we discuss details of the matching of the effective Lagrangian, which may be helpful in incorporating short distance QCD corrections in further phenomenological studies.