The Soft-Collinear Bootstrap: N=4 Yang-Mills Amplitudes at Six and Seven Loops

Infrared divergences in scattering amplitudes arise when a loop momentum $\ell$ becomes collinear with a massless external momentum $p$. In gauge theories, it is known that the L-loop logarithm of a planar amplitude has much softer infrared singularities than the L-loop amplitude itself. We argue that planar amplitudes in N=4 super-Yang-Mills theory enjoy softer than expected behavior as $\ell \parallel p$ already at the level of the integrand. Moreover, we conjecture that the four-point integrand can be uniquely determined, to any loop-order, by imposing the correct soft-behavior of the logarithm together with dual conformal invariance and dihedral symmetry. We use these simple criteria to determine explicit formulae for the four-point integrand through seven-loops, finding perfect agreement with previously known results through five-loops. As an input to this calculation we enumerate all four-point dual conformally invariant (DCI) integrands through seven-loops, an analysis which is aided by several graph-theoretic theorems we prove about general DCI integrands at arbitrary loop-order. The six- and seven-loop amplitudes receive non-zero contributions from 229 and 1873 individual DCI diagrams respectively.Comment: 27 pages, 48 figures, detailed results including PDF and Mathematica files available at http://goo.gl/qIKe8 v2: minor corrections v3: figure 7 corrected, Lemma 2 remove

Surgical Staging For Epithelial Ovarian-tumors of Low Malignant Potential

From january 1975 to December 1991, 34 patients with a diagnosis of epithelial ovarian tumors of low malignant potential (LMP) were admitted to the Istituto Nazionale Tumori of Milan. Eighteen of them (group 1) underwent complete staging laparotomy and retroperitoneal para-aortic and pelvic lymphadenectomy, as for ovarian cancer. In the remaining 16 cases (group 2), the surgical treatment ranged from unilateral oophorectomy to incomplete staging procedure. In group 1, nine patients (50%) were found to have retroperitoneal nodal involvement. In group 2, all patients had stage I disease. Patients were followed up for 20-222 months (mean 108, median 86). There were two recurrences in group 2 (after 5 years) and none in group 1 (NS). Currently all patients are alive and disease free. Nine of 18 group 1 patients were upstaged to stage III on the basis of lymph node involvement only. However, at least in this retrospective series, lymph node metastases did not affect prognosis or survival

Causes of hide damage in eastern Ethiopia

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