کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
1844105 1527829 2007 50 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات فیزیک ریاضی
پیش نمایش صفحه اول مقاله
Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation
چکیده انگلیسی

We present an improved form of the integration technique known as NDIM (negative dimensional integration method), which is a powerful tool in the analytical evaluation of Feynman diagrams. Using this technique we study a ϕ3⊕ϕ4ϕ3⊕ϕ4 theory in D=4−2ϵD=4−2ϵ dimensions, considering generic topologies of L loops and E   independent external momenta, and where the propagator powers are arbitrary. The method transforms the Schwinger parametric integral associated to the diagram into a multiple series expansion, whose main characteristic is that the argument contains several Kronecker deltas which appear naturally in the application of the method, and which we call diagram presolution. The optimization we present here consists in a procedure that minimizes the series multiplicity, through appropriate factorizations in the multinomials that appear in the parametric integral, and which maximizes the number of Kronecker deltas that are generated in the process. The solutions are presented in terms of generalized hypergeometric functions, obtained once the Kronecker deltas have been used in the series. Although the technique is general, we apply it to cases in which there are 2 or 3 different energy scales (masses or kinematic variables associated to the external momenta), obtaining solutions in terms of a finite sum of generalized hypergeometric series 1 and 2 variables respectively, each of them expressible as ratios between the different energy scales that characterize the topology. The main result is a method capable of solving Feynman integrals, expressing the solutions as hypergeometric series of multiplicity (n−1)(n−1), where n is the number of energy scales present in the diagram.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Nuclear Physics B - Volume 769, Issues 1–2, 30 April 2007, Pages 124–173
نویسندگان
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