1. Session 3 J. Fujimoto KEK May 27, 2005

2. Feynman Diagram Calculations automatization tree level --- 3 1-loop level --- 3 multi-loop --- 1 Event Generators --- 2 Analytical Approaches to FDC --- 7 Symbolic system --- 2 Numerical Integration --- 3 Lattice QCD --- 1 Quantum Computation --- 1 23 talks

3. Strong motivation of Session 3 From F. Krauss From A. Lorca

4. Automatic FDC : tree-level Bunichev : FORM in CompHEP Worek : Iterative algorithm based on the Dyson-Shwinger equation in QCD Kaneko : Factorization method of tree amplitude For the multiple-body final states, we need new tools !!

8. Automatic FDC : 1-loop Lorca : Kryukov : vertex form factors in CompHEP J.F. : Precision control in GRACE

11. Precision control is mandatory for large scale calculations. GRACE relies on gauge independent checks for 1-loop calculations. High precision computation provides an alternative approach. HMLib (Hitachi in collaboration with GRACE group) is a FORTRAN library for Multiprecision operations. HMLib is fast due to the integer operations and gives the number of “lost-bits” in the computations. HMLib has been applied to1-loop corrections; We have shown that higher precision computations and HMLib guarantees the precision of the results. Precision control and GRACE J.F.

12. Automatic FDC : Multi-loop Nougueria : QGRAF

14. Event Generators Krauss : SHERPA Lonnblad : ThePEG

17. Analytical Approaches to FDC Gerdt : Theoretical aspect of Janet-like bases Robert: Implementation of Janet-lik bases on Maple Gluza: Two-loop Bhabha Moch: Symbolic summation Brandhuber: Twistor approach Davydychev: Geometrical method Gracy: Three loop renormalization of QCD

18. Theoretical side Implementation on Maple

21. Twistor Approach to One Loop Amplitudes Brandhuber, Andres An interesting connection between twistor-string theory and Yang-Mills theories has been proposed. (Twistor Space = Fourier transform of spinor space) This observation has led to major advances in the calculation of scattering amplitudes in gauge theories. The new “twistor inspired” techniques with particular focus on application to one-loop amplitudes were reviewed. Gluons and massless fermions are OK in this scheme. 1-loop 6-point amplitudes are under progress.

24. Symbolic Systems Tentyukov: PARFORM Vollinga : GiNaC

27. Numerical Integration Krezel : Quasi random number for integration Hahn : Cuba Yuasa : Parallelization of DICE

31. Lattice QCD Wenger : Chiral fermions on the lattice

33. Quantum Computations Severyanov : QuPol

34. 1.a C# program tool enabling us to assemble an arbitrary quantum circuit in a particular gate basis and to construct the corresponding set of polynomial equations over Z2. 2.The number of solutions of the set define the matrix elements of the circuit and therefore the output value of the circuit for any input value. click

35. Conclusion Session 3 covers wide-area theoretical calculations in HEP. Even new subject in this workshop: “Quantum Computing”. For radiative corrections or loop calculations we have “RADCOR”, “Loops & Legs”, “LoopFest” … so on. but our Session3 is keeping the quite unique position in the view point of heavy usage of the computers/AI.