Harry Contopanagos

Sudakov factorization and resummation

We present a unified derivation of the resummation of Sudakov logarithms, directly from the factorization properties of cross sections in which they occur. We rederive in this manner the well-known exponentiation of leading and non-leading logarithmic enhancements near the edge of phase space for cross sections such as deeply inelastic scattering, which are induced by an electroweak hard scattering. The relevant factorization theorems are known to hold for many such cross sections of interest, and we conjecture that they apply even more widely. For QCD hard-scattering processes, such as heavy-quark production, we show that the resummation of non-leading logarithms requires in general mixing in the space of the color tensors of the hard scattering. The exponentiation of Sudakov logarithms implies that many weighted cross sections obey particular evolution equations in momentum transfer, which streamline the computation of their Sudakov exponents. We illustrate this method with the resummation of soft-gluon enhancements of the inclusive Drell-Yan cross section, in both DIS and MS factorization schemes.

Principal value resummation

Abstract We present a new resummation formula for the Drell-Yan cross section. The formal resummation of threshold corrections in Drell-Yan hard-scattering functions produces an exponent with singularities from the infrared pole of the QCD running coupling. Our reformulation treats such “infrared renormalons” by a principal value prescription, analogous to a modified Borel transform. The resulting expression includes all large threshold corrections to the hard-scattering function as an asymptotic series in αs, but is a finite function of Q2. We find that the ambiguities of the resummed perturbation theory imply the presence of higher twist corrections to quark-antiquark hard-scattering functions that begin at ʌ QCD /Q . This suggests an important role for higher twist in the phenomenology of hadron-hadron inclusive cross sections. We also discuss the numerical evaluation of the exponent and its asymptotic perturbation series for representative values of Q2.

Effective Parameters for Metamorphic Materials and Metamaterials Through a Resonant Inverse Scattering Approach

We present an inverse scattering approach for the bulk electromagnetic characterization of composite materials, based on a prior proof that artificial metallo-dielectric photonic crystals can be described by effective highly resonant response functions in a wide frequency range, including several passbands/bandgaps. The method becomes complete and unambiguous at high frequencies by employing the analytic continuation of the optical path length and a consistency criterion to ascertain the physical meaning of the extracted effective parameters. It may also be used as a fast simulator or as a measurement-based predictor of the performance of multilayered structures using the scattering matrix (simulated or measured) of a single monolayer of that material. The approach is applied for the characterization of metamorphic materials, which are recently introduced artificial structures that exhibit distinct macroscopic states of behavior as far as the reflected electromagnetic field is concerned. According to interconnect topologies of their scatterers, they appear, at a single frequency, as electric conductors, absorbers, amplifiers, and passive or active magnetic conductors. Detailed evaluations are given of the complex dispersive wave impedance, refractive index, and permittivity and permeability functions for each metamorphic state of a specific three-state metamorphic material. It is found that, as a rule, the electric and magnetic wall states are related to resonant permittivity and permeability values, respectively. Furthermore, the analysis reveals broad regions with negative values of permittivity or permeability. Both resonant and negative values of epsiveff, mueff occur within bandgaps or at band-edges. Finally, the approach is applied to the negative refractive index metamaterial composed of a cylinder and two split-ring resonators, which reveals the existence of a high-frequency band with negative group velocity

Effective response functions for photonic bandgap materials

An effective description is developed for a metalodielectric photonic bandgap (PBG) material far beyond the quasi-static limit of traditional effective-medium theories. An analytic approach, recently presented by the authors, is further advanced to provide the complete effective permittivity and permeability functions. Reflection and transmission coefficients are presented for both TM and TE oblique plane-wave incidence, based on the determination of the equivalent impedance for each lattice plane in the crystal and the transfer-matrix method for reconstructing the effect of successive lattice planes. An analysis of the semi-infinite and slab observables yields the anisotropic effective refractive index, effective permittivity, and effective permeability, thus completing the macroscopic description of the interaction of electromagnetic waves with the medium. Among the novel aspects of the analysis is the equivalence of our PBG system with a physically dispersive system at ultraviolet frequencies and the derivation and explanation of the development of high dispersive magnetization (permeability) for these media, independently of the microscopic magnetic properties of the metallic implants.

Thin frequency-selective lattices integrated in novel compact MIC, MMIC, and PCA architectures

We analyze and optimize the design of novel composite materials for ICs and printed circuit antenna (PCA) applications. We are using a variety of finite artificial lattices (FALs) carrying passive metalo-dielectric unit cells. We first examine and optimize these lattices as freestanding structures, regarding them as FSSs and space filters. We obtain several designs for appropriate metalo-dielectric unit cells, as well as stacking geometries for constructing thin laterally infinite artificial lattices. Further, we examine the action of the corresponding FAL within integrated architectures, emphasizing crosstalk suppression, circuit-coupling tailoring, and gain enhancement. We find very significant directive gain enhancements for compact packaged PCA applications. Finally, anomalous scaling of the resulting circuits and tunable designs are also presented.

Perturbative gluon resummation of the top quark production cross-section

Abstract We present a calculation of the total cross section for top quark production based on a new perturbative resummation of gluon radiative corrections to the basic QCD subprocesses. We use Principal Value Resummation to calculate all relevant large threshold corrections. Advantages of this method include its independence from arbitrary infrared cutoffs and specification of the perturbative regime of applicability. For p p collisions at center-of-mass energy s =1.8 TeV and a top mass of 175 GeV, we compute σ(t t ) = 5.52 −0.45 +0.07 pb.

Threshold resummation of the total cross-section for heavy quark production in hadronic collisions

We discuss calculations of the inclusive total cross section for heavy quark production at hadron collider energies within the context of perturbative quantum chromodynamics, including resummation of the effects of initial-state soft gluon radiation to all orders in the strong coupling strength. We resum the universal leading-logarithm contributions, and we restrict our integrations to the region of phase space that is demonstrably perturbative. We include a detailed comparison of the differences between ours and other methods. We provide predictions of the physical cross section as a function of the heavy quark mass in proton-antiproton reactions at center-of-mass energies of 1.8 and 2.0 TeV, and we discuss the estimated uncertainties. {copyright} {ital 1997} {ital The American Physical Society}

Electromagnetic properties of periodic multilayers of ultrathin metallic films from dc to ultraviolet frequencies

Ultrathin metallic films have an interesting electromagnetic behavior as the frequency of the incident field is varied over several orders of magnitude, because of the dramatic dispersion exhibited by the metal permittivity. We study a finite multilayer of periodically placed planar conducting films for frequencies varying from the dc limit to the far ultraviolet. We provide the optimized reflectivity and transmittivity of the system for the various frequency regimes involved. Further, we produce the dispersion diagrams of the corresponding photonic bandgap structures, which clearly show the transition of the system from a metallic (low frequencies) to a dielectric (optical frequencies) behavior. In addition, simple design formulas for maximum reflectivity of finite film number N are presented in terms of film thickness and film spacing in each of the representative frequency ranges.

High-Q radio-frequency structures using one-dimensionally periodic metallic films

High-Q structures are very interesting theoretically, and very important practically, for a variety of engineering applications in communication systems. We address the issue of designing a thin-film metal structure of reflectivity higher than the intrinsic reflectivity of the bulk metal itself. We study a finite array of planar conducting layers of arbitrary thickness periodically placed an arbitrary distance apart, and we arrive at an exact analytical formula for the reflection and transmission coefficients. These structures are equivalent to a one-dimensional metallic photonic bandgap (PBG) system. We apply our formulas to the microwave regime and fully explore the systems three-dimensional parameter space, consisting of the number of layers, their thickness, and their spacing. We find very significant enhancements of the radio frequency-Q, relative to the bulk metal, in narrow regions of the parameter space.

Normalization of the Drell-Yan cross section in QCD

Abstract We analyze the Drell-Yan cross section in perturbative QCD, resummed to include large corrections associated with threshold behavior in the partonic hard scattering. Resummed threshold corrections are known to exponentiate in the space of moments. Here, we derive an explicit expression for the hard scattering function directly in momentum space, as it appears in the factorized form of the cross section. We show that leading logarithms exponentiate, while non-leading contributions appear as calculable multiplicative corrections. We also discuss the range of validity of perturbation theory in the calculation of the hard scattering corrections. We conclude that our new resummed formula in momentum space organizes all large and order unity threshold corrections in the entire region where perturbation theory gives the dominant contribution. To evaluate the resummed form at this level of accuracy as an asymptotic series, it is only necessary to use existing one- and two-loop calculations.