Modern Feynman Diagrammatic One-Loop Calculations

Reiter, Thomas; Kleinschmidt, Tobias; Guillet, Jean-Philippe; Koch-Janusz, Maciej; Karg, Stefan; Cullen, Gavin; Ossola, Giovanni; Kauer, Nikolas; Wigmore, Ioan; Luisoni, Gionata; Guffanti, Alberto; Mastrolia, Pierpaolo; Rodgers, Mark; Tramontano, Francesco; Heinrich, Gudrun; Pilon, Eric; Greiner, Nicolas

doi:10.22323/1.131.0003

Article
Report number	arXiv:1011.6632
Title	Modern Feynman Diagrammatic One-Loop Calculations
Related title	Modern Feynman Diagrammatic One-Loop Calculations
Author(s)	Reiter, Thomas (NIKHEF, Amsterdam) ; Cullen, Gavin (Edinburgh U.) ; Greiner, Nicolas (Illinois U., Urbana) ; Guffanti, Alberto (Freiburg U.) ; Guillet, Jean-Philippe (Annecy, LAPTH) ; Heinrich, Gudrun (Durham U., IPPP) ; Karg, Stefan (Aachen, Tech. Hochsch.) ; Kauer, Nikolas (Royal Holloway, U. of London) ; Kleinschmidt, Tobias (Durham U., IPPP) ; Koch-Janusz, Maciej (NIKHEF, Amsterdam) ; Luisoni, Gionata (Durham U., IPPP) ; Mastrolia, Pierpaolo (Enrico Fermi Ctr., Rome ; Salerno U. ; CERN) ; Ossola, Giovanni (New York City Coll. Tech.) ; Pilon, Eric (Annecy, LAPTH) ; Rodgers, Mark (Durham U., IPPP) ; Tramontano, Francesco (CERN) ; Wigmore, Ioan (Edinburgh U.)
Publication	2010
Imprint	01 Dec 2010
Number of pages	11
Note	Comments: 10 pages, 2 figures; contribution to the proceedings of the CPP2010 Workshop, 23-25 Sep. 2010, KEK, Tsukuba, Japan 10 pages, 2 figures; contribution to the proceedings of the CPP2010 Workshop, 23-25 Sep. 2010, KEK, Tsukuba, Japan
In:	PoS CPP2010 (2010) pp.003
DOI	10.22323/1.131.0003
Subject category	Particle Physics - Phenomenology
Abstract	In this talk we present techniques for calculating one-loop amplitudes for multi-leg processes using Feynman diagrammatic methods in a semi-algebraic context. Our approach combines the advantages of the different methods allowing for a fast evaluation of the amplitude while monitoring the numerical stability of the calculation. In phase space regions close to singular kinematics we use a method avoiding spurious Gram determinants in the calculation. As an application of our approach we report on the status of the calculation of the amplitude for the process $pp\to b\bar{b}b\bar{b}+X$.
Copyright/License	preprint: (License: arXiv nonexclusive-distrib 1.0)

$Possible ways of using \textsc{Samurai} and Golem95 together with tensorial reconstruction. On the left branch \textsc{Samurai} is called with the numerator reconstructed according to Eq.~\eqref{eq:tensrec}, which can speed up the calculation. If the consistency check in \textsc{Samurai} fails Golem95 is called as a rescue system. On the right branch the call to \textsc{Samurai} is skipped and Golem95 is used as the sole tensor reduction method.$ $Born (dashed) matrix element squared and the interference term between Born and virtual corrections (straight line) of the $gg\rightarrow b\bar{b}b\bar{b}$ amplitude. The curves have been obtained by rotating the final state particles about the $z$-axis. The amplitude peaks around $\theta_0\approx 2{.}32$ and $\theta_1=\theta_0+\pi$ which are points close to double parton scattering kinematics.$