398 research outputs found
IR finite one-loop box scalar integral with massless internal lines
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
Using the Feynman parameter method, we have calculated in an elegant manner a
set of oneloop 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
oneloop 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
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
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
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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