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.     

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.     

Photon production in a dense medium

On the basis of diagram formalism for two-particle Green functions, the bremsstrahlung of charged particles interacting in a dense medium is investigated. In the case of production of soft photons, exact expressions for two-particle Green functions corresponding to the process of particle bremsstrahlung in the substance are obtained. The Green functions found are fully determined by the set of closed irreducible diagrams. It is shown that, in the case of radiation in a sufficiently dense medium in a far long-wave region of the spectrum, the coherent multiple particle scattering results in an additional (as compared that reported earlier in [1–13]) suppression of the bremsstrahlung photon yield.     

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.     

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.     

Vibrational relaxation of a molecule in a dense medium

In this paper we consider some features of vibrational relaxation of a guest molecule in a host matrix. The model system involves a harmonic molecule interacting with a harmonic medium. The molecule-medium coupling was handled by the rotating wave approximation considering linear terms in the intramolecular displacements and high terms in the medium displacements. Three specific models for the molecule-medium coupling were considered, which involve single phonon decay, vibron-phonon decay and multiphonon decay. Within the framework of the random phase approximation the Heisenberg equations of motion for the system could be expressed in terms of a unified scheme which is valid for both single phonon and multiphonon processes. Explicit solutions were derived utilizing the Wigner-Weisskopf approximation. This generalized formalism was applied for the study of the time evolution of the distribution, the cooling and the heating processes of the oscillator by a thermal field and for the coupling between vibrational relaxation and infra-red emission.     

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.     

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.     

Gradient echo memory in a tripod-like dense atomic medium

We analyze the storage and retrieval of a weak light pulse, having two orthogonally (circularly) polarized components, onto an atomic ensemble of four-level atoms of the tripod type driven by a far detuned coupling field. The atoms are subject to a longitudinal magnetic field which produces a spatially varying Zeeman splitting of the lower levels along the medium and allows for a spatial encoding of the different angular frequencies of the input pulse during the storage phase. A single reversion of the external magnetic field results in a rephasing of the dipoles and leads to the release of the stored signals. The shape of the recovered pulse is a time-reversal copy of the input pulse. The application of an additional reversion of the magnetic field during the storage phase allows the release of a copy of the input pulse without time reversal. We also show that the system may operate like an all-optical multiplexer when considering two impinging optical fields which have orthogonal components. The proposal has potential applications in quantum information processing.