Evaluating Feynman integrals by the hypergeometry

The hypergeometric function method naturally provides the analytic expressions of scalar integrals from concerned Feynman diagrams in some connected regions of independent kinematic variables, also presents the systems of homogeneous linear partial differential equations satisfied by the corresponding scalar integrals. Taking examples of the one-loop $B_{_0}$ and massless $C_{_0}$ functions, as well as the scalar integrals of two-loop vacuum and sunset diagrams, we verify our expressions coinciding with the well-known results of literatures. Based on the multiple hypergeometric functions of independent kinematic variables, the systems of homogeneous linear partial differential equations satisfied by the mentioned scalar integrals are established. Using the calculus of variations, one recognizes the system of linear partial differential equations as stationary conditions of a functional under some given restrictions, which is the cornerstone to perform the continuation of the scalar integrals to whole kinematic domains numerically with the finite element methods. In principle this method can be used to evaluate the scalar integrals of any Feynman diagrams.Comment: 39 pages, including 2 ps figure

QCD corrections to polarization of J/\psi and \Upsilon at Fermilab Tevatron and CERN LHC

In this work, we present more detail of the calculation on the NLO QCD corrections to polarization of direct J/psi production via color singlet at Tevatron and LHC, as well as the results for Upsilon for the first time. Our results show that the J/psi polarization status drastically changes from transverse polarization dominant at LO into longitudinal polarization dominant in the whole range of the transverse momentum $p_t$ of J/psi when the NLO corrections are counted. For Upsilon production, the p_t distribution of the polarization status behaves almost the same as that for J/psi except that the NLO result is transverse polarization at small p_t range. Although the theoretical evaluation predicts a larger longitudinal polarization than the measured value at Tevatron, it may provide a solution towards the previous large discrepancy for J/psi and Upsilon polarization between theoretical predication and experimental measurement, and suggests that the next important step is to calculate the NLO corrections to hadronproduction of color octet state J/psi^(8) and Upsilon^(8). Our calculations are performed in two ways, namely we do and do not analytically sum over the polarizations, and then check them with each other.Comment: 12 pages, 12 figures, two columns, use revtex4; to appear in PR

Spatio-temporal linking of multiple SAR satellite data from medium and high resolution Radarsat-2 images

A recent development in Interferometric Synthetic Aperture Radar (InSAR) technology is integrating multiple SAR satellite data to dynamically extract ground features. This paper addresses two relevant challenges: identification of common ground targets from different SAR datasets in space, and concatenation of time series when dealing with temporal dynamics. To address the first challenge, we describe the geolocation uncertainty of InSAR measurements as a three-dimensional error ellipsoid. The points, among InSAR measurements, which have error ellipsoids with a positive cross volume are identified as tie-point pairs representing common ground objects from multiple SAR datasets. The cross volumes are calculated using Monte Carlo methods and serve as weights to achieve the equivalent deformation time series. To address the second challenge, the deformation time series model for each tie-point pair is estimated using probabilistic methods, where potential deformation models are efficiently tested and evaluated. As an application, we integrated two Radarsat-2 datasets in Standard and Extra-Fine modes to map the subsidence of the west of the Netherlands between 2010 and 2017. We identified 18128 tie-point pairs, 5 intersection types of error ellipsoids, 5 deformation models, and constructed their long-term deformation time series. The detected maximum mean subsidence velocity in Line-Of-Sight direction is up to 15 mmyr-1. We conclude that our method removes limitations that exist in single-viewing-geometry SAR when integrating multiple SAR data. In particular, the proposed time-series modeling method is useful to achieve a long-term deformation time series of multiple datasets

Flat Currents of the Green-Schwarz Superstrings in AdS_5 x S^1 and AdS_3 x S^3 backgrounds

We construct a one-parameter family of flat currents in AdS_5 x S^1 and AdS_3 x S^3 Green-Schwarz superstrings, which would naturally lead to a hierarchy of classical conserved nonlocal charges. In the former case we rewrite the AdS_5 x S^1 string using a new Z_4-graded base of the superalgebra su(2,2|2). In both cases the existence of the Z_4 grading in the superalgebras plays a key role in the construction. As a result, we find that the flat currents, when formally written in terms of the G_0-gauge invariant lowercase 1-forms, take the same form as the one in AdS_5 x S^5 case.Comment: 18 pages, LaTeX file. References added and typos correcte