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.     

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.     

Flux confinement in mesoscopic superconductors

We report on flux confinement effects in superconducting submicron line, loop and dot structures. The main idea of our study was to vary the boundary conditions for confinement of the superconducting condensate by taking samples of different topology and, through that, modifying the lowest Landau level E_LLL(H). Since the critical temperature versus applied magnetic field T_c(H) is, in fact,E_LLL (H) measured in temperature units, it is varied as well when the sample topology is changed. We demonstrate that in all the submicron structures studied the shape of theT_c (H) phase boundary is determined by the confinement topology in a unique way.     

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.     

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.     

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.     

Chiral restoration transition in scaled effective Lagrangians

We make a systematic study of the chiral restoration transition in function of the two free parameters of two scaled effective NJL Lagrangians. We show that it is not possible to reproduce with the same set of parameters the temperature behaviours of the quark condensate and of the quark entropy and a critical density at least equal to the normal density of nuclear systems.     

Analytic continued fraction theory for a class of confinement potentials

We study a general class of confinement potentials in Schrödinger theory using the analytic theory of continued fractions. We construct an infinite continued fraction representation for the Green's function and study its convergence, its analytic properties in the major coupling constant and its relation to the perturbation series. We prove the existence of normalizable confined state eigensolutions with equally spaced energy levels if certain constraints on the coupling constants of the theory are satisfied: we also show that under a separate set of constraints neither bound nor confined states exist.     

Flux confinement in the leading logarithm model

We study the statics of quasi-abelian quark and antiquark source charges in the approximation in which leading logarithm radiative corrections are retained in the gauge gluon effective action functional. We show that the partial differential equation for the flux function is of degenerating elliptic type, leading to flux confinement within a free boundary which is a characteristic. The static potential increases linearly for large source separations, with a logarithmic subdominant term.     

Color effective particles and confinement

A brief review of works that are carried out in 2007–2009 and supported by the Russian Foundation for Basic Research, project no. 07-02-01197a, is presented. The idea is evolved that color confinement is realized by a singular interaction at large distances between color effective particles (constituent quarks, diquarks, and massive effective gluons).     

Renormalization of non polynomial Lagrangians in Jaffe's class

It is shown how a renormalized perturbation series can be defined for a theory with strictly local, non-polynomial, interacting Lagrangian so as to preserve locality at every order.