Quark-gluon amplitudes in the dual expansion

The dual representation, which gives a simple analytical form for purely gluonic amplitudes, is extended to amplitudes which include a quark-antiquark pair. To minimize the calculations, supersymmetry is used to relate the purely gluonic amplitudes to those including a gluino pair from which the quark-antiquark amplitudes are easily deduced. We explicitly give simple analytical forms for the full amplitudes for those multi-parton processes which involve a quark-antiquark pair plus two, three and four gluons.     

Complete reduction of integrals in two-loop five-light-parton scattering amplitudes

We reduce all the most complicated Feynman integrals in two-loop five-light-parton scattering amplitudes to basic master integrals, while other integrals can be reduced even easier. Our results are expressed as systems of linear relations in the block-triangular form, very efficient for numerical calculations. Our results are crucial for complete next-to-next-to-leading order quantum chromodynamics calculations for three-jet, photon, and/or hadron production at hadron colliders. To determine the block-triangular relations, we develop an efficient and general method, which may provide a practical solution to the bottleneck problem of reducing multiloop multiscale integrals.     

Test of the Glauber formula for nucleon-deuteron scattering at intermediate energies

A high-precision test of the Glauber formula for the amplitude of nucleon-deuteron scattering is performed. Nucleon-nucleon amplitudes used in the calculations depend on the spins of interacting particles, phase shifts, and mixing parameters. These amplitudes were derived by using the Njim I, Njim II, Njim 93, and Reid 93 realistic potentials. The differential cross sections for nucleon-deuteron scattering were calculated for the projectile-nucleon energies of 65, 95, 135, 150, 190, and 250 MeV, and the results of these calculations were compared with experimental data.     

Simple analytical representation for Delbrück scattering amplitudes at high energies

We use a new representation for the semiclassical Green’s function of the Dirac equation in the Coulomb field to find an exact (in the parameter Zα) expression for the amplitudes of small-angle Delbru ck scattering of high-energy photons. The values of these amplitudes agree with those obtained in earlier calculations, but the structure of the expressions is much simpler than that of previously known representations, which makes numerical calculations much easier. Zh. éksp. Teor. Fiz. 116, 78–84 (July 1999)     

Siebenmann-type cobordisms with borders and topology changes by quantum tunneling

Siebenmann-type cobordisms are constructed to describe topology changes with the Seifert fibered homology spheres in in- and out-states. We study the problem of determining of topology-changing amplitudes for these quantum tunneling processes. The calculations are performed in the stationary phase approximation for Kodama wave functions. In this approximation the amplitudes are expressed in terms of Chern-Simons invariants of flatSU(2)-connections over the cobordism boundary components. The topology-change amplitudes found are factorized into the Kodama wave functions for the lens spaces. The results are compared with those for Fintushel-Stern-type cobordisms which have been previously investigated.     

Quantum mechanics in space-time: The Feynman path amplitude description of physical optics, de Broglie matter waves and quark and neutrino flavour oscillations

Feynman’s laws of quantum dynamics are concisely stated, discussed in comparison with other formulations of quantum mechanics and applied to selected problems in the physical optics of photons and massive particles as well as flavour oscillations. The classical wave theory of light is derived from these laws for the case in which temporal variation of path amplitudes may be neglected, whereas specific experiments, sensitive to the temporal properties of path amplitudes, are suggested. The reflection coefficient of light from the surface of a transparent medium is found to be markedly different to that predicted by the classical Fresnel formula. Except for neutrino oscillations, good agreement is otherwise found with previous calculations of spatially dependent quantum interference effects.     

The influence of the chemical potential oscillations on the de Haas-van Alphen effect in quasi-two-dimensional compounds

The de Haas-van Alphen effect in quasi-two-dimensional metals is studied at arbitrary parameters. Oscillations of the chemical potential can substantially change the temperature dependence of harmonic amplitudes that is commonly used to determine the effective electron mass. The processing of the experimental data using the standard Lifshitz-Kosevich formula can therefore lead to substantial errors even in the strong harmonic damping limit. This can explain the difference between the effective electron masses determined from the de Haas-van Alphen effect and the cyclotron resonance measurements. The oscillations of the chemical potential and the deviations from the Lifshitz-Kosevich formula depend on the reservoir density of states that exists in organic metals due to open sheets of the Fermi surface. This dependence can be used to determine the density of electron states on open sheets of the Fermi surface. We present analytical results of the calculations of harmonic amplitudes in some limiting cases that show the importance of the chemical potential oscillations. We also describe a simple algorithm for a numerical calculation of the harmonic amplitudes for arbitrary reservoir density of states, arbitrary warping, spin-splitting, temperature, and Dingle temperature.     

Tunneling and reflection of an exciton incident upon a quantum heterostructure barrier

We investigate, in one spatial dimension, the quantum mechanical tunneling of an exciton incident upon a heterostructure barrier. We model the relative motion eigenstates of the exciton using a form of the one-dimensional hydrogen atom which avoids difficulties previously associated with 1D hydrogenic states. We obtain probabilities of reflection and transmission using the method of variable transmission and reflection amplitudes. Our calculations may be broadly divided into two sets. In the first set, we consider general qualitative aspects of exciton tunneling, such as the effect of different effective masses for electrons and holes and a relative difference in electron and hole barrier strengths. The second set models the tunneling of an exciton in a GaAs/Al(x)Ga(1-x)As heterostructure. In these calculations we find that, for energies such that the two lowest exciton states are coupled, the probability spectrum for transition from the ground state to the first excited state is identical to that for transition from the first excited state to the ground state. In addition, narrow peaks in the probability spectrum for transition are observed across this energy range for low dopant concentration x. Other interesting phenomena correlated with these peaks in the transition probability are reported.     

Antiproton-Nucleus Interaction and Coulomb Effect at High Energies

The Coulomb effect in high energy antiproton-nucleus elastic and inelastic scattering from ¹²C and ¹⁶O is studied in the framework of Glauber multiple scattering theory for five kinetic energies ranged from 0.23 to 1.83 GeV. A microscopic shell-model nuclear wave functions, Woods-Saxon single-particle wave functions, and experimental pN amplitudes are used in the calculations. The results show that the Coulomb effect is of paramount importance for filling up the dips of differential cross sections. We claim that the present result for inelastic scattering of antiproton-¹²C is sufficiently reliable to be a guide for measurements in the very near future. We also believe that antiproton nucleus elastic and inelastic scattering may produce new information on both the nuclear structure and the antinucleon-nucleon interaction, in particular the p-neutron interaction.     

Nuclear physics from lattice QCD

We review recent progress toward establishing lattice Quantum Chromodynamics as a predictive calculational framework for nuclear physics. A survey of the current techniques that are used to extract low-energy hadronic scattering amplitudes and interactions is followed by a review of recent two-body and few-body calculations by the NPLQCD collaboration and others. An outline of the nuclear physics that is expected to be accomplished with Lattice QCD in the next decade, along with estimates of the required computational resources, is presented.     

Analysis of directCP violation in B^- \to D^0 D_s^-, D^0 D^- decays

We show that the semi-leptonic decay can be used as a source of information for two-pion distribution amplitudes. The connection between these amplitudes and the B-meson decay width is achieved by the light cone sum rule method. We show the relevant distribution amplitudes and give the formula for the decay width. Received: 11 April 2001 / Published online: 19 July 2001     

Improved Light-Cone QCD Sum Rule Analysis of Rare Decays Λb → Λγ and Λb → Λl+l-

We present a systematic light-cone QCD sum rule study of the exclusive rare radiative decay Λ_b → Λ_γ and rare semileptonic decay Λ_b → Λl⁺l^- within the framework of the standard model. Although some light-cone sum rule (LCSR) studies on these rare processes can be found in different literatures, it is necessary to reanalyze them systematically for the reason that either the baryonic distribution amplitudes are improved or different interpolating currents for the Λ_b baryon may lead to quite different results. In addition, the rare process Λ_b → Λ_γ has not yet been analyzed by LCSR with the Ioffe-type current. Taking all these reasons into account, we perform LCSR calculations of both the processes with two types of interpolating currents. Our calculations show that the choice of the interpolating current for the Λ_b baryon can affect the predictions significantly, especially for the rare radiative decay process.     

Two-δ- Function Generalized Plasma Pole Model for First Principle Calculations of Quasiparticle Energies in Many-Electron Systems

To evaluate the dynamical effects of the screened interaction in the calculations of quasiparticle energies in many-electron systems a two-δ-function generalized plasma pole model (GPP) is introduced to simulate the dynamical dielectric function. The usual single δ-function GPP model has the drawback of over simplifications and for the crystals without.the center of symmetry is inappropriate to describe the finite frequency behavior for dielectric function matrices. The discrete frequency summation method requires too much computation to achieve converged results since ab initio calculations of dielectric function matrices are to be carried out for many different frequencies. The two-δ GPP model is an op timization of the two approaches. We analyze the two-δ GPP model and propose a method to determine from the first principle calculations the amplitudes and effective frequencies of these δ functions. Analytical solutions are found for the second order equations for the parameter matrices entering the model. This enables realistic applications of the method to the first principle quasiparticle calculations and makes the calculations truly adjustable parameter free.     

Dilepton production in nucleon-nucleon collisions around 1 GeV/nucleon: A theoretical update

We present a fully relativistic and gauge invariant framework for calculating the cross-sections of dilepton production in nucleon-nucleon (NN) collisions which is based on the meson-exchange approximation for the NN scattering amplitudes. Predictions of our model are compared with those of other covariant models that have been used to describe this reaction. We discuss the comparison of our calculations with the old DLS and the recent HADES data.     

Radiative corrections to QCD amplitudes in quasi-multi-Regge kinematics

Radiative corrections to QCD amplitudes in the quasi-multi-Regge kinematics are interesting, in particular, since the Reggeized form of these amplitudes is used in the derivation of the NLO BFKL. This form is a hypothesis which must be at least carefully checked, if not proved. We calculate the radiative corrections in the one-loop approximation using the s-channel unitarity. Compatibility of the Reggeized form of the amplitudes with the s-channel unitarity requires fulfillment of the set of nonlinear equations for the Reggeon vertices. We show that these equations are satisfied.     

Superpropagator and superconformal invariants

We construct a superpropagator in maximally supersymmetric Yang–Mills theory which is invariant off-shell under a chiral half of supersymmetries. Motivated by the duality with scattering amplitudes in this theory, we apply this superpropagator to supersymmetric Wilson loop on polygonal contours. By performing explicit one-loop calculations we confirm the absence of anomalies and verify the duality between the object under study and NMHV amplitudes.     

All-optical measurement of high-harmonic amplitudes and phases in aligned molecules

We report a new all-optical approach to measuring the phase and amplitude of high-harmonic emission from aligned molecules. We combine the transient grating technique with a continuous rotation of the molecular alignment axis and develop an analytical model that enables the simultaneous determination of phases and amplitudes. Measurements in N(2) molecules are shown to be in qualitative agreement with the results of ab initio quantum scattering calculations.     

Extended projection method for massive fermions

Tensor reduction is of considerable importance in calculations of multi-loop amplitudes,and the projection method is one of the most popular approaches for tensor reduction.However,the projection method can be problematic when applied to amplitudes with massive fermions,due to the inconsistency between helicity and chirality.We propose an extended projection method for reducing the loop amplitude which contains a fermion chain with two massive spinors.The extension is achieved by decomposing one of the massive spinors into two massless spinors,the"null spinor"and the"reference spinor".The extended projection method can be effectively applied in all processes,including the production of massive fermions.We present the tensor reduction for a virtual Z boson decaying into a top-quark pair as a demonstration of our approach.     

Heavy-heavy form factors and generalized factorization

We reanalyze and data to extract a set of parameters which give the relevant hadronic matrix elements in terms of factorized amplitudes. Various sources of theoretical uncertainties are studied, in particular those depending on the model adopted for the form factors. We find that the fit to the branching ratios substantially depends on the model describing the Isgur-Wise function and on the value of its slope. This dependence can be reduced by substituting the with suitable ratios of non-leptonic to differential semileptonic BRs. In this way, we obtain a model-independent determination of these parameters. Using these results, the form factors at can be extracted from a fit of the . The comparison between the form factors obtained in this way and the corresponding measurements in semileptonic decays can be used as a test of (generalized) factorization free from the uncertainties due to heavy-heavy form factor modeling. Finally, we present predictions for as-yet-unmeasured and branching ratios and extract and from decays. We find MeV and MeV, in good agreement with recent measurements and lattice calculations. Received: 7 October 1998 / Revised version: 4 December 1998 / Published online: 20 May 1999