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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 J. Fujimoto KEK May 27 , 2005
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
Strong motivation of Session 3 From F. Krauss From A. Lorca
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
Automatic FDC : 1-loop • Lorca : • Kryukov: vertex form factors in CompHEP • J.F. : Precision control in GRACE
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.
Automatic FDC : Multi-loop • Nougueria : QGRAF
Event Generators • Krauss : SHERPA • Lonnblad : ThePEG
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
Theoretical side Implementation on Maple
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.
Symbolic Systems • Tentyukov: PARFORM • Vollinga : GiNaC
Numerical Integration • Krezel : Quasi random number for integration • Hahn : Cuba • Yuasa : Parallelization of DICE
Lattice QCD • Wenger : Chiral fermions on the lattice
Quantum Computations • Severyanov : QuPol
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.
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.