Twistor Space Structure of the Box Coefficients of N=1 One-loop Amplitudes

We examine the coefficients of the box functions in N=1 supersymmetric one-loop amplitudes. We present the box coefficients for all six point N=1 amplitudes and certain all $n$ example coefficients. We find for ``next-to MHV'' amplitudes that these box coefficients have coplanar support in twistor space.Comment: 14 pages, minor typos correcte

On a conjecture regarding the upper graph box dimension of bounded subsets of the real line

Let X \subset R be a bounded set; we introduce a formula that calculates the upper graph box dimension of X (i.e.the supremum of the upper box dimension of the graph over all uniformly continuous functions defined on X). We demonstrate the strength of the formula by calculating the upper graph box dimension for some sets and by giving an "one line" proof, alternative to the one given in [1], of the fact that if X has finitely many isolated points then its upper graph box dimension is equal to the upper box dimension plus one. Furthermore we construct a collection of sets X with infinitely many isolated points, having upper box dimension a taking values from zero to one while their graph box dimension takes any value in [max{2a,1},a + 1], answering this way, negatively to a conjecture posed in [1]

Functional equations for one-loop master integrals for heavy-quark production and Bhabha scattering

The method for obtaining functional equations, recently proposed by one of the authors, is applied to one-loop box integrals needed in calculations of radiative corrections to heavy-quark production and Bhabha scattering. We present relationships between these integrals with different arguments and box integrals with all propagators being massless. It turns out that functional equations are rather useful for finding imaginary parts and performing analytic continuations of Feynman integrals. For the box master integral needed in Bhabha scattering, a new representation in terms of hypergeometric functions admitting one-fold integral representation is derived. The hypergeometric representation of a master integral for heavy-quark production follows from the functional equation.Comment: 14 pages, 3 figure

Analytical Results for Dimensionally Regularized Massless On-shell Double Boxes with Arbitrary Indices and Numerators

We present an algorithm for the analytical evaluation of dimensionally regularized massless on-shell double box Feynman diagrams with arbitrary polynomials in numerators and general integer powers of propagators. Recurrence relations following from integration by parts are solved explicitly and any given double box diagram is expressed as a linear combination of two master double boxes and a family of simpler diagrams. The first master double box corresponds to all powers of the propagators equal to one and no numerators, and the second master double box differs from the first one by the second power of the middle propagator. By use of differential relations, the second master double box is expressed through the first one up to a similar linear combination of simpler double boxes so that the analytical evaluation of the first master double box provides explicit analytical results, in terms of polylogarithms \Li{a}{-t/s}, up to $a=4$, and generalized polylogarithms $S_{a,b}(-t/s)$, with $a=1,2$ and $b=2$, dependent on the Mandelstam variables $s$ and $t$, for an arbitrary diagram under consideration.Comment: LaTeX, 16 pages; misprints in ff. (8), (24), (30) corrected; some explanations adde

W+W-, WZ and ZZ production in the POWHEG BOX V2

We present an implementation of the vector boson pair production processes ZZ, W+W- and WZ within the POWHEG BOX V2. This implementation, derived from the POWHEG BOX version, has several improvements over the old one, among which the inclusion of all decay modes of the vector bosons, the possibility to generate different decay modes in the same run, speed optimization and phase space improvements in the handling of interference and singly resonant contributions.Comment: 4 pages, v2 corrects one referenc

Dynamics of a particle confined in a two-dimensional dilating and deforming domain

Some recent results concerning a particle confined in a one-dimensional box with moving walls are briefly reviewed. By exploiting the same techniques used for the 1D problem, we investigate the behavior of a quantum particle confined in a two-dimensional box (a 2D billiard) whose walls are moving, by recasting the relevant mathematical problem with moving boundaries in the form of a problem with fixed boundaries and time-dependent Hamiltonian. Changes of the shape of the box are shown to be important, as it clearly emerges from the comparison between the "pantographic", case (same shape of the box through all the process) and the case with deformation.Comment: 13 pages, 2 figure

Gamma-Z box contributions to parity violating elastic e-p scattering

Parity-violating (PV) elastic electron-proton scattering measures Q-weak for the proton, $Q_W^p$. To extract $Q_W^p$ from data, all radiative corrections must be well-known. Recently, disagreement on the gamma-Z box contribution to $Q_W^p$ has prompted the need for further analysis of this term. Here, we support one choice of a debated factor, go beyond the previously assumed equality of electromagnetic and gamma-Z structure functions, and find an analytic result for one of the gamma-Z box integrals. Our numerical evaluation of the gamma-Z box is in agreement within errors with previous reports, albeit somewhat larger in central value, and is within the uncertainty requirements of current experiments.Comment: 4 pages, 4 figures, v2: reference added, typo fixe