Tensor Integrals
نویسندگان
چکیده
منابع مشابه
One-Loop Tensor Integrals in Dimensional Regularisation
We show how to evaluate tensor one-loop integrals in momentum space avoiding the usual plague of Gram determinants. We do this by constructing combinations of nand (n− 1)-point scalar integrals that are finite in the limit of vanishing Gram determinant. These non-trivial combinations of dilogarithms, logarithms and constants are systematically obtained by either differentiating with respect to ...
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In this article, we introduce a new method for the accurate and fast computation of singular integrals over cuboids in three-dimensional space. Using a straightforward geometric parametrisation of the domain of integration, we interpret the integral as a smooth function on a high-dimensional parameter space. A standard interpolation scheme then leads to a high-dimensional tensor to which an app...
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We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e − → 4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino–Veltman reduction breaks down owing to the appearance of Gram determinants in th...
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A set of one-loop vertex and box tensor-integrals with massless internal particles has been obtained directly without any reduction method to scalar-integrals. The results with one or two massive external lines for the vertex integral and zero or one massive external lines for the box integral are shown in this report. Dimensional regularization is employed to treat any soft and collinear (IR) ...
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A numerical approach to compute tensor integrals in one-loop calculations is presented. The algorithm is based on a recursion relation which allows to express high rank tensor integrals as a function of lower rank ones. At each level of iteration only inverse square roots of Gram determinants appear. For the phase-space regions where Gram determinants are so small that numerical problems are ex...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1957
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500014267