398 research outputs found

    IR finite one-loop box scalar integral with massless internal lines

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    The IR finite one-loop box scalar integral with massless internal lines has been recalculated. The result is very compact, simple and valid for arbitrary values of the relevant kinematic variables. It is given in terms of only two dilogarithms and a few logarithms, all of very simple arguments.Comment: 7 pages, 2 figure

    Dimensionally regulated one-loop box scalar integrals with massless internal lines

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    Using the Feynman parameter method, we have calculated in an elegant manner a set of one−-loop box scalar integrals with massless internal lines, but containing 0, 1, 2, or 3 external massive lines. To treat IR divergences (both soft and collinear), the dimensional regularization method has been employed. The results for these integrals, which appear in the process of evaluating one−-loop (N≄5)−(N\ge 5)-point integrals and in subdiagrams in QCD loop calculations, have been obtained for arbitrary values of the relevant kinematic variables and presented in a simple and compact form.Comment: 14 pages, 2 figures included, SVJour, journal versio

    K0 form factor at order p^6 of chiral perturbation theory

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    This paper describes the calculation of the electromagnetic form factor of the K0 meson at order p^6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p^4 result achieved by Gasser and Leutwyler. On the one hand, at order p^6 the chiral expansion contains 1- and 2-loop diagrams which are discussed in detail. Especially, a numerical procedure for calculating the irreducible 2-loop graphs of the sunset topology is presented. On the other hand, the chiral Lagrangian L^6 produces a direct coupling of the K0 current with the electromagnetic field tensor. Due to this coupling one of the unknown parameters of L^6 occurs in the contribution to the K0 charge radius.Comment: 22 pages Latex with 8 figures, Typos corrected, one reference adde

    Package-X: A Mathematica package for the analytic calculation of one-loop integrals

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    Package-X, a Mathematica package for the analytic computation of one-loop integrals dimensionally regulated near 4 spacetime dimensions is described. Package-X computes arbitrarily high rank tensor integrals with up to three propagators, and gives compact expressions of UV divergent, IR divergent, and finite parts for any kinematic configuration involving real-valued external invariants and internal masses. Output expressions can be readily evaluated numerically and manipulated symbolically with built-in Mathematica functions. Emphasis is on evaluation speed, on readability of results, and especially on user-friendliness. Also included is a routine to compute traces of products of Dirac matrices, and a collection of projectors to facilitate the computation of fermion form factors at one-loop. The package is intended to be used both as a research tool and as an educational tool.Comment: Package files are available at http://packagex.hepforge.or

    A note on two-loop superloop

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    We explore the duality between supersymmetric Wilson loop on null polygonal contours in maximally supersymmetric Yang-Mills theory and next-to-maximal helicity violating (NMHV) scattering amplitudes. Earlier analyses demonstrated that the use of a dimensional regulator for ultraviolet divergences, induced due to presence of the cusps on the loop, yields anomalies that break both conformal symmetry and supersymmetry. At one-loop order, these are present only in Grassmann components localized in the vicinity of a single cusp and result in a universal function for any number of sites of the polygon that can be subtracted away in a systematic manner leaving a well-defined supersymmetric remainder dual to corresponding components of the superamplitude. The question remains though whether components which were free from the aforementioned supersymmetric anomaly at leading order of perturbation theory remain so once computed at higher orders. Presently we verify this fact by calculating a particular component of the null polygonal super Wilson loop at two loops restricting the contour kinematics to a two-dimensional subspace. This allows one to perform all computations in a concise analytical form and trace the pattern of cancellations between individual Feynman graphs in a transparent fashion. As a consequence of our consideration we obtain a dual conformally invariant result for the remainder function in agreement with one-loop NMHV amplitudes.Comment: 14 pages, 3 figure
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