Session 3

J. Fujimoto KEK

May 27 , 2005

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

23 talks

Strong motivation of Session 3

From F. Krauss

From A. Lorca

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 !!

Automatic FDC : 1-loop

• Lorca :

• Kryukov: vertex form factors in CompHEP

• J.F. : Precision control in GRACE

• Precision control is mandatory for large scale calculations.• GRACE relies on gauge independent checks for 1-loop calcul

ations.• High precision computation provides an alternative approach.• HMLib (Hitachi in collaboration with GRACE group) is a FOR

TRAN library for Multiprecision operations.• HMLib is fast due to the integer operations and gives the num

ber 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.

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Precision control and GRACE

J.F.

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

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.

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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.