The One-Loop One-Mass Hexagon Integral in D=6 Dimensions

We evaluate analytically the one-loop one-mass hexagon in six dimensions. The result is given in terms of standard polylogarithms of uniform transcendental weight three.Comment: 9 page

Loop lessons from Wilson loops in N=4 supersymmetric Yang-Mills theory

N=4 supersymmetric Yang-Mills theory exhibits a rather surprising duality of Wilson-loop vacuum expectation values and scattering amplitudes. In this paper, we investigate this correspondence at the diagram level. We find that one-loop triangles, one-loop boxes, and two-loop diagonal boxes can be cast as simple one- and two- parametric integrals over a single propagator in configuration space. We observe that the two-loop Wilson-loop "hard-diagram" corresponds to a four-loop hexagon Feynman diagram. Guided by the diagrammatic correspondence of the configuration-space propagator and loop Feynman diagrams, we derive Feynman parameterizations of complicated planar and non-planar Feynman diagrams which simplify their evaluation. For illustration, we compute numerically a four-loop hexagon scalar Feynman diagram.Comment: 20 pages, many figures. Two references added. Published versio

Conformal or Walking? Monte Carlo renormalization group studies of SU(3) gauge models with fundamental fermions

Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of SU(3) gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the N_f=8 flavor system, thus verifying its QCD-like nature. With N_f=12 flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free field value.Comment: 26 pages, 11 figure

Symbols of One-Loop Integrals From Mixed Tate Motives

We use a result on mixed Tate motives due to Goncharov (arXiv:alg-geom/9601021) to show that the symbol of an arbitrary one-loop 2m-gon integral in 2m dimensions may be read off directly from its Feynman parameterization. The algorithm proceeds via recursion in m seeded by the well-known box integrals in four dimensions. As a simple application of this method we write down the symbol of a three-mass hexagon integral in six dimensions.Comment: 13 pages, v2: minor typos correcte

Simulated synchrotron and Inverse Compton emission from Pulsar Wind Nebulae

We present a complete set of diagnostic tools aimed at reproducing synthetic non-thermal (synchrotron and/or Inverse Compton, IC) emissivity, integrated flux energy, polarization and spectral index simulated maps in comparison to observations. The time dependent relativistic magnetohydrodynamic (RMHD) equations are solved with a shock capturing code together with the evolution of the maximum particles energy. Applications to Pulsar Wind Nebulae (PWNe) are shown.Comment: 3 pages, 7 figures, proceeding of the conference "40 Years of Pulsars ", 12-17 August 2007, Montreal, Canada, submitted to AI

Self-Organizing Maps Algorithm for Parton Distribution Functions Extraction

We describe a new method to extract parton distribution functions from hard scattering processes based on Self-Organizing Maps. The extension to a larger, and more complex class of soft matrix elements, including generalized parton distributions is also discussed.Comment: 6 pages, 3 figures, to be published in the proceedings of ACAT 2011, 14th International Workshop on Advanced Computing and Analysis Techniques in Physics Researc

Monodromy--like Relations for Finite Loop Amplitudes

We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs.Comment: 24 pages, 6 figures, v2 typos corrected, reference adde

The one-loop six-dimensional hexagon integral and its relation to MHV amplitudes in N=4 SYM

We provide an analytic formula for the (rescaled) one-loop scalar hexagon integral $\tilde\Phi_6$ with all external legs massless, in terms of classical polylogarithms. We show that this integral is closely connected to two integrals appearing in one- and two-loop amplitudes in planar $\\mathcal{N}=4$ super-Yang-Mills theory, $\Omega^{(1)}$ and $\Omega^{(2)}$. The derivative of $\Omega^{(2)}$ with respect to one of the conformal invariants yields $\tilde\Phi_6$, while another first-order differential operator applied to $\tilde\Phi_6$ yields $\Omega^{(1)}$. We also introduce some kinematic variables that rationalize the arguments of the polylogarithms, making it easy to verify the latter differential equation. We also give a further example of a six-dimensional integral relevant for amplitudes in $\\mathcal{N}=4$ super-Yang-Mills.Comment: 18 pages, 2 figure

Next-to-next-to-leading logarithmic corrections at small transverse momentum in hadronic collisions

We study the region of small transverse momenta in qqbar- and gg-initiated processes with no colored particle detected in the final state. We present the universal expression of the O(alpha_s^2) logarithmically enhanced contributions up to next-to-next-to-leading logarithmic accuracy. From there we extract the coefficients that allow the resummation of the large logarithmic contributions. We find that the coefficient known in the literature as B^{(2)} is process dependent, since it receives a hard contamination from the one loop correction to the leading order subprocess. We present the general result of B^{(2)} for both quark and gluon channels. In particular, in the case of Higgs production, this result will be relevant to improve the matching between resummed predictions and fixed order calculations.Comment: LaTeX, 8 pages. Few typos corrected, particularly Eq.(25). Two references added, to be published in PR