ترغب بنشر مسار تعليمي؟ اضغط هنا

Attacking One-loop Multi-leg Feynman Integrals with the Loop-Tree Duality

96   0   0.0 ( 0 )
 نشر من قبل Grigorios Chachamis
 تاريخ النشر 2016
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

We discuss briefly the first numerical implementation of the Loop-Tree Duality (LTD) method. We apply the LTD method in order to calculate ultraviolet and infrared finite multi-leg one-loop Feynman integrals. We attack scalar and tensor integrals with up to six legs (hexagons). The LTD method shows an excellent performance independently of the number of external legs.

قيم البحث

اقرأ أيضاً

134 - Jochem Fleischer 2010
We present a new algorithm for the reduction of one-loop emph{tensor} Feynman integrals with $nleq 4$ external legs to emph{scalar} Feynman integrals $I_n^D$ with $n=3,4$ legs in $D$ dimensions, where $D=d+2l$ with integer $l geq 0$ and generic dimen sion $d=4-2epsilon$, thus avoiding the appearance of inverse Gram determinants $()_4$. As long as $()_4 eq 0$, the integrals $I_{3,4}^D$ with $D>d$ may be further expressed by the usual dimensionally regularized scalar functions $I_{2,3,4}^d$. The integrals $I_{4}^D$ are known at $()_4 equiv 0$, so that we may extend the numerics to small, non-vanishing $()_4$ by applying a dimensional recurrence relation. A numerical example is worked out. Together with a recursive reduction of 6- and 5-point functions, derived earlier, the calculational scheme allows a stabilized reduction of $n$-point functions with $nleq 6$ at arbitrary phase space points. The algorithm is worked out explicitely for tensors of rank $Rleq n$.
68 - G. Chachamis , G. Rodrigo 2017
We review the recent developments of the Loop-Tree Duality method, focussing our discussion on the first numerical implementation and its use in the direct numerical computation of multi-leg Feynman integrals. Non-trivial examples are presented.
139 - F.Yuasa , T.Ishikawa , Y.Kurihara 2011
In this paper, we describe a numerical approach to evaluate Feynman loop integrals. In this approach the key technique is a combination of a numerical integration method and a numerical extrapolation method. Since the computation is carried out in a fully numerical way, our approach is applicable to one-, two- and multi-loop diagrams. Without any analytic treatment it can compute diagrams with not only real masses but also complex masses for the internal particles. As concrete examples we present numerical results of a scalar one-loop box integral with complex masses and two-loop planar and non-planar box integrals with masses. We discuss the quality of our numerical computation by comparisons with other methods and also propose a self consistency check.
We present a first numerical implementation of the Loop-Tree Duality (LTD) method for the direct numerical computation of multi-leg one-loop Feynman integrals. We discuss in detail the singular structure of the dual integrands and define a suitable c ontour deformation in the loop three-momentum space to carry out the numerical integration. Then, we apply the LTD method to the computation of ultraviolet and infrared finite integrals, and present explicit results for scalar integrals with up to five external legs (pentagons) and tensor integrals with up to six legs (hexagons). The LTD method features an excellent performance independently of the number of external legs.
We present analytic expressions in terms of polylogarithmic functions for all three families of planar two-loop five-point Master Integrals with one off-shell leg. The calculation is based on the Simplified Differential Equations approach. The result s are relevant to the study of many $2to 3$ scattering processes of interest at the LHC, especially for the leading-color $W+2$ jets production.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا