Automatic Computation of Cross Sections in HEP

Abstract

For the study of reactions in High Energy Physics (HEP) automatic computation systems have been developed and are widely used nowadays. GRACE is one of such systems and it has achieved much success in analyzing experimental data. Since we deal with the cross section whose value can be given by calculating hundreds of Feynman diagrams, we manage the large scale calculation, so that effective symbolic manipulation, the treat of singularity in the numerical integration are required. The talk will describe the software design of GRACE system and computational techniques in the GRACE. §1. IntroductionHigh energy experimental physics has produced excellent results thanks to the progress of the detectors and the development of the high energy accelerators with high luminosity. Accordingly, the accurate theoretical computation is required to compare experimental results with theoretical predictions. On the other hand, as the beam energy becomes higher, there appear the physics processes with many final state particles. As a matter of course the number of relevant Feynman diagrams becomes huge. This means that Feynman amplitude calculation is practically impossible when one calculates cross sections by hands.Since the perturbative calculation in quantum field theory is well-defined, it can be realized as an automatic computation system. There appeared several systems, for instance, CompHEP 1) and FeynArt/FeynCalc 2) , in HEP and nowadays the automatic computation of Feynman amplitudes becomes common.We have developed an automatic computation system named GRACE. 3) In section 2, we describe the feature of GRACE system as a concrete example of such system. In section 3, several physical achievements by GRACE are briefly explained. In section 4, we discuss the techniques in GRACE from the view point of computing.

The automated computation of tree-level and next-to-leading order differential cross sections, and their matching to parton shower simulations

“…The number of codes which have been developed, either restricted to leading order (LO henceforth) predictions [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53], or including NLO capabilities ] is truly staggering. The level of automation and the physics scope of such codes, not to mention other, perhaps less crucial, characteristics, is extremely diverse, and we shall make no attempt to review this matter here.…”

“…Furthermore, the majority of physics models (see section 2.1) have not yet been extended to include NLO corrections, and in these cases the whole procedure could not even be conceived. 41 As in MadGraph5, scripting commands is of course possible.…”

Event shapes in e+e annihilation and deep inelastic scattering

“…It is also to be noted that the isolation cuts on the photon will bias the distribution of the event shapes, in some cases [89,93] similarly to an event-shape energy-flow correlation [65,76]. Therefore we would argue that before relying on these data, one should at the very least compare the factorisation approximation with exact LO calculations, which can be straightforwardly obtained using packages such as Grace [111], CompHEP [112] or Amegic++ [113].…”

Compactifying formulas with FORM

“….end w(1)=x ** 2 w(2)=x+z w(2)=z * w(2) w(2)=w (1)+w (2) w(2)=6 * w(2) w(3)=-z * x w(1)=-w(1)+w (3) w(1)=3 * z * w(1) F2=y * w(2)+3 * y ** 3+w (1) PoS(RADCOR 2013)015 This is very convenient in the GRACE [3] system where we have the Feynman parameters outside the brackets and need to evaluate the coefficients. For three outputs from the GRACE system we obtain the results in Tab.5.…”

“…I did however keep contact with the automated program scene which was coming up about then. This was mainly with the GRACE [3] group which started also in the 80's. It kept me constantly aware of the needs in this field.…”