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Th.Diakonidis - ACAT2010 Jaipur, India1 Calculating one loop multileg processes A program for the case of In collaboration with B.Tausk ( T.Riemann & J.

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Presentation on theme: "Th.Diakonidis - ACAT2010 Jaipur, India1 Calculating one loop multileg processes A program for the case of In collaboration with B.Tausk ( T.Riemann & J."— Presentation transcript:

1 Th.Diakonidis - ACAT2010 Jaipur, India1 Calculating one loop multileg processes A program for the case of In collaboration with B.Tausk ( T.Riemann & J. Fleischer )

2 Th.Diakonidis - ACAT2010 Jaipur, India 2 Motivation and goals Recent years have seen the emergence of first results for 2 → 4 scattering processes To that scope one of the challenges posed is the need to compute one-loop tensor integrals with up to 6 legs (Tord Riemann’s talk) Public code produced for this reduction (hexagon.m by K. Kajda) Fortran code (used for the process) Program for NLO corrections of the process

3 Th.Diakonidis - ACAT2010 Jaipur, India 3 Fortran Package For Tensor integrals, we have a Fortran implementation package (Th. Diakonidis & B. Tausk) The present implementation includes: Six point functions up to rank five (Hexagon.F) Five point functions (all 5 ranks) (Pentagon.F) Boxes (all 4 ranks) (Box.F) Triangles (all 3 ranks) (Triangle.F) Bubbles (all 2 ranks) (Bubble.F)

4 Th.Diakonidis - ACAT2010 Jaipur, India 4 The code so far uses: QCDLoop (R.K. Ellis and G. Zanderighi) (Finite part and and terms) To calculate the scalar master integrals after the reduction It can be adapted to any Fortran package for 1,2,3,4 point functions A lot of cross checks have been done so far (shown after) and we also cross checked the results with an independent code by Peter Uwer

5 Th.Diakonidis - ACAT2010 Jaipur, India 5 The triangle Here we have to add some extra terms in the cases of boxes, triangles and bubbles with the exception of 1 st rank

6 Th.Diakonidis - ACAT2010 Jaipur, India 6 Starting from a pentagon For the randomly chosen phase space point: A mixed case of massless and massive particles

7 Th.Diakonidis - ACAT2010 Jaipur, India 7 Pentagon

8 Th.Diakonidis - ACAT2010 Jaipur, India 8 Box case

9 Th.Diakonidis - ACAT2010 Jaipur, India 9 Triangle

10 Th.Diakonidis - ACAT2010 Jaipur, India 10 Bubble

11 Th.Diakonidis - ACAT2010 Jaipur, India 11 Some sample results for hexagons For the randomly chosen phase space point given by:

12 Th.Diakonidis - ACAT2010 Jaipur, India 12 Results for scalar, vector and 2 nd rank six point functions:

13 Th.Diakonidis - ACAT2010 Jaipur, India 13 3 rd rank 6 point functions

14 Th.Diakonidis - ACAT2010 Jaipur, India 14 4 th rank 6-point

15 Th.Diakonidis - ACAT2010 Jaipur, India 15 More results (massless case) For the phase space point given by: p1 =(0.5, 0, 0, 0.5) p2 =(0.5, 0, 0, -0.5) p3 =(-0.19178191,-0.12741180,-0.08262477,-0.11713105) p4 =(-0.33662712, 0.06648281, 0.31893785, 0.08471424) p5 =(-0.21604814, 0.20363139,-0.04415762,-0.05710657) p6 =-(p1+p2+p3+p4+p5) M1=0, M2=0, M3=0, M4=0, M5=0, M6=0 Golem95: T.Binoth, J.-Ph.Guillet, G. Heinrich, E.Pilon, T.Reiter [arXiv:hep- ph/0810.0992]

16 Th.Diakonidis - ACAT2010 Jaipur, India 16 Comparisons with golem95 (for 5 th rank) A good agreement (8 digits) (QCDLoop was used for the scalar master integrals)

17 Th.Diakonidis - ACAT2010 Jaipur, India 17 Study of the process Part of the process Les Houches wishlist C.Buttar et al. Les Houches Physics at TeV Colliders 2005, Standard Model and Higgs working group: Summary report, hep-ph/0604120 Z. Bern et al., The NLO multileg working group: Summary report, hep-ph/0803.0494 To the same direction: Bredenstein et al. NLO QCD corrections to production at the LHC: 1. quark-antiquark annihilation JHEP08 108 (2008) hep-ph/ 0807.1248 2. gluon-gluon annihilation hep-ph/ 0905.0110 (1001.4727,1001.4006) G. Bevilaqua et al. Assault on the NLO Wishlist: hep-ph/0907.4723, 1002.4009

18 Th.Diakonidis - ACAT2010 Jaipur, India 18 One Loop Diagrams for the process The diagram construction was done using DIANA. A Feynman Diagram Analyser DIANA M. Tentyukov, J. Fleischer hep-ph/ 9904258 After applying all the Feynman rules the final output of Diana gives: Hexagons Pentagons Boxes Triangles Bubbles 4510 loop diagrams in total

19 Th.Diakonidis - ACAT2010 Jaipur, India 19 DIANA

20 Th.Diakonidis - ACAT2010 Jaipur, India 20 Color Manipulation Total number of C.S = 50 Divided in 4 categories: 1. 24 2. 12 3. 8 4. 6 g1 g2 g3 g4 g2 g1 g3 g4 g1 g3 g2 g4

21 Th.Diakonidis - ACAT2010 Jaipur, India 21 DIANA Diagram construction Output (form) hex_m.frm : bub_m.frm 50 different Structures color.F Color2fortran.frm SUn.prc MAPLE INPUT cRank0.m(1…4) : cRank5.m(1…4) OPTIMIZATION ggttgg.m FORTRAN OPT cFi_rtSum3(1…4) : cS_rtSum23(1…4) hex_mf.frm : bub_mf.frm Passrt_hex.F : Passrt_bub.F Hex(Sum_6(4)) : Bubble(Sum_2(4)) Main fortran program gm(line,n1,…,n9) Spinor structures MADGRAPH momenta.dat

22 Th.Diakonidis - ACAT2010 Jaipur, India 22 Conclusions Results from the analytical recursive reduction presented by T.Riemann Reduction formulas have been implemented in a Mathematica and a Fortran program Fortran program for the calculation of the NLO contribution of the process shown explicitly

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