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Session 3

Session 3. J. Fujimoto KEK May 27 , 2005. Feynman Diagram Calculations automatization tree level --- 3 1-loop level --- 3 multi-loop --- 1 Event Generators --- 2

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Session 3

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

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

  6. Precision control and GRACE J.F. • 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 GRACEgroup) 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 computationsandHMLib guarantees the precision of the results.

  7. Automatic FDC : Multi-loop • Nougueria : QGRAF

  8. Event Generators • Krauss : SHERPA • Lonnblad : ThePEG

  9. 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

  10. Theoretical side Implementation on Maple

  11. 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.

  12. Symbolic Systems • Tentyukov: PARFORM • Vollinga : GiNaC

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

  14. Lattice QCD • Wenger : Chiral fermions on the lattice

  15. Quantum Computations • Severyanov : QuPol

  16. click Program “Quantum Polynomials” Vladimir Gerdt Vasily Severyanov • a C# program tool enabling us to assemblean arbitrary quantum • circuit in a particular gate basis and to construct the corresponding • set of polynomial equations over Z2. • 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.

  17. 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.

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