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Automating Feynman Diagram Calculations: Advances in multi-loop and Quantum Computation

This session focuses on the automation of Feynman diagram calculations, addressing tree-level, 1-loop, and multi-loop processes in high-energy physics. It features discussions on new tools for multiple-body final states, iterative algorithms based on Dyson-Shwinger equations, and high-precision computation techniques. Key topics include event generators, symbolic systems, and numerical integration methods, alongside advancements in quantum computation. Experts present innovative approaches and implications for accuracy in theoretical calculations, providing insights into the future of automated Feynman diagram assessments.

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Automating Feynman Diagram Calculations: Advances in multi-loop and Quantum Computation

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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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