Generalized Unitarity and One-Loop Amplitudes in N=4 Super-Yang-Mills

One-loop amplitudes of gluons in N=4 gauge theory can be written as linear combinations of known scalar box integrals with coefficients that are rational functions. In this paper we show how to use generalized unitarity to basically read off the coefficients. The generalized unitarity cuts we use are quadruple cuts. These can be directly applied to the computation of four-mass scalar integral coefficients, and we explicitly present results in next-to-next-to-MHV amplitudes. For scalar box functions with at least one massless external leg we show that by doing the computation in signature (--++) the coefficients can also be obtained from quadruple cuts, which are not useful in Minkowski signature. As examples, we reproduce the coefficients of some one-, two-, and three-mass scalar box integrals of the seven-gluon next-to-MHV amplitude, and we compute several classes of three-mass and two-mass-hard coefficients of next-to-MHV amplitudes to all multiplicities.Comment: 36 pages, harvmac. 13 figures. v3: References added, typos fixed. Figure 4 added. New n-gluon example with internal fermions and scalars. v4: Footnotes 2, 4 and 6 added, acknowledgments added, minor correction

A consistent model for \pi N transition distribution amplitudes and backward pion electroproduction

The extension of the concept of generalized parton distributions leads to the introduction of baryon to meson transition distribution amplitudes (TDAs), non-diagonal matrix elements of the nonlocal three quark operator between a nucleon and a meson state. We present a general framework for modelling nucleon to pion ($\pi N$) TDAs. Our main tool is the spectral representation for \pi N TDAs in terms of quadruple distributions. We propose a factorized Ansatz for quadruple distributions with input from the soft-pion theorem for \pi N TDAs. The spectral representation is complemented with a D-term like contribution from the nucleon exchange in the cross channel. We then study backward pion electroproduction in the QCD collinear factorization approach in which the non-perturbative part of the amplitude involves \pi N TDAs. Within our two component model for \pi N TDAs we update previous leading-twist estimates of the unpolarized cross section. Finally, we compute the transverse target single spin asymmetry as a function of skewness. We find it to be sizable in the valence region and sensitive to the phenomenological input of our \pi N TDA model.Comment: 39 pages, 9 figure

Convergence of an s-wave calculation of the He ground state

The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as Delta E^N approx A/N^(7/2) + B/N^(8/2) + >... where N is the number of Laguerre basis functions. The electron-electron delta-function expectation converges as Delta delta^N approx A/N^(5/2) + B/N^(6/2) + ... and the variational limit for the l = 0 basis is estimated as 0.1557637174(2) a_0^3. It was seen that extrapolation of the energy to the variational limit is dependent upon the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a non-optimal exponent if one wishes to extrapolate to the variational limit. An investigation of the Natural Orbital asymptotics revealed the energy converged as Delta E^N approx A/N^6 + B/N^7 + ... while the electron-electron delta-function expectation converged as Delta delta^N approx A/N^4 + B/N^5 + >... . The asymptotics of expectation values other than the energy showed fluctuations that depended on whether $N$ was even or odd.Comment: 12 pages, 10 figures, revtex format, submitted to Int.J.Quantum Chemistr

On the Local-Global Conjecture for integral Apollonian gaskets

We prove that a set of density one satisfies the local-global conjecture for integral Apollonian gaskets. That is, for a fixed integral, primitive Apollonian gasket, almost every (in the sense of density) admissible (passing local obstructions) integer is the curvature of some circle in the gasket.Comment: 64 pages, 3 figures; Appendix by Peter Varj

Loop amplitudes in gauge theories: modern analytic approaches

This article reviews on-shell methods for analytic computation of loop amplitudes, emphasizing techniques based on unitarity cuts. Unitarity techniques are formulated generally but have been especially useful for calculating one-loop amplitudes in massless theories such as Yang-Mills theory, QCD, and QED.Comment: 34 pages. Invited review for a special issue of Journal of Physics A devoted to "Scattering Amplitudes in Gauge Theories." v2: typesetting macro error fixe