Iteration of Planar Amplitudes in Maximally Supersymmetric Yang-Mills Theory at Three Loops and Beyond

We compute the leading-color (planar) three-loop four-point amplitude of N=4 supersymmetric Yang-Mills theory in 4 - 2 epsilon dimensions, as a Laurent expansion about epsilon = 0 including the finite terms. The amplitude was constructed previously via the unitarity method, in terms of two Feynman loop integrals, one of which has been evaluated already. Here we use the Mellin-Barnes integration technique to evaluate the Laurent expansion of the second integral. Strikingly, the amplitude is expressible, through the finite terms, in terms of the corresponding one- and two-loop amplitudes, which provides strong evidence for a previous conjecture that higher-loop planar N = 4 amplitudes have an iterative structure. The infrared singularities of the amplitude agree with the predictions of Sterman and Tejeda-Yeomans based on resummation. Based on the four-point result and the exponentiation of infrared singularities, we give an exponentiated ansatz for the maximally helicity-violating n-point amplitudes to all loop orders. The 1/epsilon^2 pole in the four-point amplitude determines the soft, or cusp, anomalous dimension at three loops in N = 4 supersymmetric Yang-Mills theory. The result confirms a prediction by Kotikov, Lipatov, Onishchenko and Velizhanin, which utilizes the leading-twist anomalous dimensions in QCD computed by Moch, Vermaseren and Vogt. Following similar logic, we are able to predict a term in the three-loop quark and gluon form factors in QCD.Comment: 54 pages, 7 figures. v2: Added references, a few additional words about large spin limit of anomalous dimensions. v3: Expanded Sect. IV.A on multiloop ansatz; remark that form-factor prediction is now confirmed by other work; minor typos correcte

Experiment K-6-17. Structural changes and cell turnover in the rats small intestine induced by spaceflight

The purpose of this project was to test the hypothesis that the generalized, whole body decrease in synthetic activity associated with microgravity conditions of space flight as evidenced by negative nitrogen balance and muscle atrophy (Nicogossian and Parker, 1982; Oganov, 1981), as well as inhibited lymphocyte proliferation (Bechler and Cogoli, 1986), would be evident in cells characterized by a rapid rate of turnover. As a model, researchers chose to study the turnover of mucosal cells lining the jejunum of the small intestine, since these cells are among the most rapidly proliferating in the body. Under normal conditions, epithelial cells that line the small intestine are continually produced in the crypts of Lieberkuhn. These cells migrate out of the crypts onto intestinal villi, are progressively pushed up the villus as new crypt cells are formed, and ultimately reach the tip of villi where they are then descquamated. In rats, the entire process, from initial proliferation in crypts to desquamation, takes approximately 2 days (Cairnie et al., 1965; Lipkin, 1973). In this study, researchers determined the mitotic index for mucosal cells lining the proximal, middle, and distal regions of the jejunum in rats from three treatment groups (synchronous control, vivarium control and flight), and measured the depth of the crypts of Lieberkuhn and the length of villi present in each of the three jejunal regions sampled

Calculation of Infrared-Divergent Feynman Diagrams with Zero Mass Threshold

Two-loop vertex Feynman diagrams with infrared and collinear divergences are investigated by two independent methods. On the one hand, a method of calculating Feynman diagrams from their small momentum expansion extended to diagrams with zero mass thresholds is applied. On the other hand, a numerical method based on a two-fold integral representation is used. The application of the latter method is possible by using lightcone coordinates in the parallel space. The numerical data obtained with the two methods are in impressive agreement.Comment: 20 pages, Latex with epsf-figures, References updated, to appear in Z.Phys.