A method for resummation of perturbative series based on the stochastic solution of Schwinger-Dyson equations

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the “worm” algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.     

Asymptotic structure of perturbative series for tau lepton observables

We analyze lepton decay observables, namely the moments of the hadronic spectral density in the finite energy interval , within finite order perturbation theory including corrections. The start of the asymptotic growth of the perturbation theory series is found at this order in a scheme-invariant manner. We establish the ultimate accuracy of finite order perturbation theory predictions and discuss the construction of optimal observables. Received: 6 September 1999 / Published online: 21 December 1999     

A fast,accurate phase unwrapping method for wavelet-transform profilometry

A novel phase unwrapping method used in wavelet-transform profilometry is presented to improve the accuracy and speed of the unwrapping process. The wrapped phase of the fringe image is extracted by using wavelet transform. How to establish quality map using scale factor at wavelet ridge is discussed firstly. The proposed method can reflect the reliability of the pixels in fringe image effectively. As the consuming time of traditional flood-fill phase unwrapping algorithm is too long, an improved quality-guided method is used in phase unwrapping process. We divide the wrapped phase map into two levels following the established quality map, and process these two levels using different algorithms. Compared with the traditional flood-fill algorithm, we can get the accurate result while the consuming time of the phase unwrapping process is much less by using the proposed method. Simulation and experiment results verify that the 3D information of the measured object can be obtained rapidly and accurately by using the proposed method. Also the dynamic object can be measured too.     

Soft-gluon resummation for single-particle inclusive hadroproduction at high transverse momentum

We consider the cross section for one-particle inclusive production at high transverse momentum in hadronic collisions. We present the all-order resummation formula that controls the logarithmically-enhanced perturbative QCD contributions to the partonic cross section in the threshold region, at fixed rapidity of the observed parton (hadron). The explicit resummation up to next-to-leading logarithmic accuracy is supplemented with the computation of the general structure of the near-threshold contributions to the next-to-leading order cross section. This next-to-leading order computation allows us to extract the one-loop hard-virtual amplitude that enters into the resummation formula. This is a necessary ingredient to explicitly extend the soft-gluon resummation beyond the next-to-leading logarithmic accuracy. These results equally apply to both spin-unpolarized and spin-polarized scattering processes.     

A fast and accurate calibration method for the structured light system based on trapezoidal phase-shifting pattern

Calibration plays an important part in the structured light system. It used to be regarded as time-consuming, expensive and hard to implement. In this paper, we introduce a novel and fast method to calibrate the structured light system by using the camera to control the projector to “capture” images. Firstly, we projected just six trapezoidal grayscale pattern to establish the corresponding pixel between the camera and the projector, then we converted the camera image to its corresponding projector image. Thus the structured light system can be easy controlled by the camera calibration. Experiments showed that the present calibration method is fast, easy and accurate.     

A fast and accurate method for the determination of precious alloys caratage by Laser Induced Plasma Spectroscopy

The purpose of this paper is to present a new and efficient technique for precious alloys caratage based on the Laser Induced Plasma Spectroscopy (LIPS) method. The LIPS analysis can be carried out in few minutes and in an essentially non-destructive way on samples of arbitrary shape. Experimental results showing the feasibility of the method for fast and precise analysis of gold jewellery without the need of calibration are presented. Using a new technique of LIPS spectra analysis, recently developed and patented by the Applied Laser Spectroscopy Laboratory at IFAM, we were able to obtain quantitative information about all the alloy components, including trace elements at concentration down to the order of 1 ppm. Matrix effects do not affect the accuracy of the technique. Received 10 July 2000 and Received in final form 13 November 2000     

Combined effect of QCD resummation and QED radiative correction to W boson observables at the Tevatron

A precise determination of the W boson mass at the Fermilab Tevatron requires a theoretical calculation in which the effects of the initial-state multiple soft-gluon emission and the final-state photonic correction are simultaneously included. Here, we present such a calculation and discuss its prediction on the transverse mass distribution of the W boson and the transverse momentum distribution of its decay charged lepton, which are the most relevant observables for measuring the W boson mass at hadron colliders.     

A perturbative nonequilibrium renormalization group method for dissipative quantum mechanics

We study a generic problem of dissipative quantum mechanics, a small local quantum system with discrete states coupled in an arbitrary way (i.e. not necessarily linear) to several infinitely large particle or heat reservoirs. For both bosonic or fermionic reservoirs we develop a quantum field-theoretical diagrammatic formulation in Liouville space by expanding systematically in the reservoir-system coupling and integrating out the reservoir degrees of freedom. As a result we obtain a kinetic equation for the reduced density matrix of the quantum system. Based on this formalism, we present a formally exact perturbative renormalization group (RG) method from which the kernel of this kinetic equation can be calculated. It is demonstrated how the nonequilibrium stationary state (induced by several reservoirs kept at different chemical potentials or temperatures), arbitrary observables such as the transport current, and the time evolution into the stationary state can be calculated. Most importantly, we show how RG equations for the relaxation and dephasing rates can be derived and how they cut off generically the RG flow of the vertices. The method is based on a previously derived real-time RG technique [1-4] but formulated here in Laplace space and generalized to arbitrary reservoir-system couplings. Furthermore, for fermionic reservoirs with flat density of states, we make use of a recently introduced cutoff scheme on the imaginary frequency axis [5] which has several technical advantages. Besides the formal set-up of the RG equations for generic problems of dissipative quantum mechanics, we demonstrate the method by applying it to the nonequilibrium isotropic Kondo model. We present a systematic way to solve the RG equations analytically in the weak-coupling limit and provide an outlook of the applicability to the strong-coupling case.