Systematic errors due to linear congruential random-number generators with the Swendsen-Wang algorithm: A warning

We show that linear congruential pseudo-random-number generators can cause systematic errors in Monte Carlo simulations using the Swendsen-Wang algorithm, if the lattice size is a multiple of a very large power of 2 and one random number is used per bond. These systematic errors arise from correlations within a single bond-update half-sweep. The errors can be eliminated (or at least radically reduced) by updating the bonds in a random order or in an aperiodic manner. It also helps to use a generator of large modulus (e.g. 60 or more bits).Comment: Revtex4, 4 page

On the Rational Terms of the one-loop amplitudes

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be derived by using appropriate Feynman rules within a tree-like computation. For the terms that originate from the reduction of the 4-dimensional part of the numerator, we present two different strategies and explicit algorithms to compute them.Comment: 14 pages, 3 figures, uses axodraw.st

Optimizing the Reduction of One-Loop Amplitudes

We present an optimization of the reduction algorithm of one-loop amplitudes in terms of master integrals. It is based on the exploitation of the polynomial structure of the integrand when evaluated at values of the loop-momentum fulfilling multiple cut-conditions, as emerged in the OPP-method. The reconstruction of the polynomials, needed for the complete reduction, is rended very versatile by using a projection-technique based on the Discrete Fourier Transform. The novel implementation is applied in the context of the NLO QCD corrections to u d-bar --> W+ W- W+

CutTools: a program implementing the OPP reduction method to compute one-loop amplitudes

We present a program that implements the OPP reduction method to extract the coefficients of the one-loop scalar integrals from a user defined (sub)-amplitude or Feynman Diagram, as well as the rational terms coming from the 4-dimensional part of the numerator. The rational pieces coming from the epsilon-dimensional part of the numerator are treated as an external input, and can be computed with the help of dedicated tree-level like Feynman rules. Possible numerical instabilities are dealt with the help of arbitrary precision routines, that activate only when needed.Comment: Version published in JHE

Dynamic critical behavior of the Chayes-Machta-Swendsen-Wang algorithm

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial dimensions, by Monte Carlo simulation. We show that the Li-Sokal bound z \ge \alpha/\nu is close to but probably not sharp in d=2, and is far from sharp in d=3, for all q. The conjecture z \ge \beta/\nu is false (for some values of q) in both d=2 and d=3.Comment: Revtex4, 4 pages including 4 figure

Polarizing the Dipoles

We extend the massless dipole formalism of Catani and Seymour, as well as its massive version as developed by Catani, Dittmaier, Seymour and Trocsanyi, to arbitrary helicity eigenstates of the external partons. We modify the real radiation subtraction terms only, the primary aim being an improved efficiency of the numerical Monte Carlo integration of this contribution as part of a complete next-to-leading order calculation. In consequence, our extension is only applicable to unpolarized scattering. Upon summation over the helicities of the emitter pairs, our formulae trivially reduce to their original form. We implement our extension within the framework of Helac-Phegas, and give some examples of results pertinent to recent studies of backgrounds for the LHC. The code is publicly available. Since the integrated dipole contributions do not require any modifications, we do not discuss them, but they are implemented in the software.Comment: 20 pages, 4 figures, Integrated dipoles implemented for massless and massive case

Integrand reduction of one-loop scattering amplitudes through Laurent series expansion

We present a semi-analytic method for the integrand reduction of one-loop amplitudes, based on the systematic application of the Laurent expansions to the integrand-decomposition. In the asymptotic limit, the coefficients of the master integrals are the solutions of a diagonal system of equations, properly corrected by counterterms whose parametric form is konwn a priori. The Laurent expansion of the integrand is implemented through polynomial division. The extension of the integrand-reduction to the case of numerators with rank larger than the number of propagators is discussed as well.Comment: v2: Published version: references and two appendices added. v3: Eq.(6.11) corrected, Appendix B updated accordingl

Intriguing C–H⋯Cu interactions in bis-(phenanthroline)Cu(I) redox mediators for dye-sensitized solar cells

We have synthesized and characterized a series of bis-(phenanthroline) Cu(I) complexes of interest as redox mediators for dye-sensitized solar cells. This study led to the discovery of intriguing anagostic interactions between the hydrogen atom and the copper center as evidenced by X-ray diffraction studies on a single crystal. Remarkably, an anagostic interaction was found between a H atom of a methyl group and a copper sit