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Calculation of the Six-Fermion Production at ILC with Grcft -New algorithm for Grace-

This research by Yoshiaki Yasui from Tokyo Management College focuses on leveraging the GRCFT algorithm to automate Feynman amplitude calculations at ILC, comparing it with traditional methods to improve efficiency. The study demonstrates factorization of Feynman graphs to reduce computational complexity and streamline the process, leading to faster calculations for six-fermion production scenarios at ILC. Performance tests and numerical results are presented to showcase the algorithm's effectiveness in producing reliable outcomes with significant time savings compared to existing approaches. This innovative approach holds promise for enhancing high-energy physics computations for future collider experiments. 8

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Calculation of the Six-Fermion Production at ILC with Grcft -New algorithm for Grace-

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  1. KEK Minamitateya group Yoshiaki Yasui (Tokyo Management College) The 8th ACFA Daegu, Korea July 11-14 Calculation of the Six-Fermion Production at ILC with Grcft-New algorithm for Grace-

  2. Event generator for e+e- collider @LEP2 e+e- -->4f ALPHA, COMPHEP, NEXTCALIBUR , WPHACT, WWGENPV, WTO,...,GRC4F(Grace inside), KORALW(Grace inside) @ILC e+e- -->6f, 8f,.... LUSIFER, WHIZARD, SIXFAP, PHEDAS, EETT6F, AMEGIC++,...,GRACE

  3. What is GRACE • GRACE is the computer code which performs the automatic calculation of the Feynman amplitudes • SM and MSSM (in tree and loop level) • Successfully tested at LEP 2 • What we can do with GRACE? • Generate Feynman diagrams automatically • Create FORTRAN source codes for amplitudes • Cross sections <=BASES (MC integral) • In principle, we can calculate final 6f and 8f but .......

  4. Traditional algorithm • Calculate amplitudes graph by graph • Huge number of Feynman graphs • e+e- --> t t & ZH --> b b u d m n • 435 in Unitary • e+e- -->t t & ZH --> b b u d e n • 870 in Unitary • e+e- --> ZHH --> b b b b n n • 1860 in Unitary • Need new method • GRACE => GRCFT

  5. Factorization of Feynman amplitudes Faster algorithms => ALPHA, HERAC, O'Mega GRCFT (Grace with new algorithm) Idea traditional algorithm size of the code => (G#)2 G#:number of graphs => sub-graphs are calculated repeatedly New algorithm => factorize Feynman graphs size of the code => (GF#)2 GF#:number of factorized graphs

  6. Algorithm for Grcft • construct sub-sets of the sub-graphs automatically !! • tree amplitudes are reconstructed from sub-sets • No need to generate Feynman diagrams • How to factorize?? • How to avoid double counting? • Need some guiding principle

  7. How to factorize • consider decomposition of a graph at propagatorc • fix a root external leg • choose maxk ink ≤ N/2 • the propagator c is uniquely determined • Factorize a graph at vertexVc • Factorize sub-graphs also

  8. Performance test • Compare with traditional GRACE code • Numerical calculation at “fixed” phase space point.

  9. Numerical results for 6f productions • System • CPU: Pentium 4 -3.2GHz • intel fortran compiler ver.8.1 • compare with old GRACE • Input parameters Gmscheme • Dittmaier &Roth Nucl.Phys.B642(2002) • compare with other system LUSIFER Gm =1.16639E-5GeV-2a(0)=1/137.0359895 MW=80.419GeV GW=2.12GeV MZ=91.1882GeV GZ=2.4952GeV mt=174.3GeV Gt=1.6GeV mh=170GeV Gh=0.3835GeV(HDECAY)

  10. e+e- --> b b-bar u d-bar mu nu_mu-bar # of sample points for MC: 100000 keep mass of the external particles <- Cumulative Result -> < CPU time > Estimate(+- Error )order Acc % ( H: M: Sec ) ---------------------------------------------------------------- 1.789043(+-0.004481)E-02[pb] 0.250 1:18:29.47 < CPU time > with traditional algorithm ==> 6:32:16.16 comparison with LUSIFER ==> massless external particles with kinetic cuts LUSIFER GRCFT with cut 1.7095E-02[pb] 1.706E-02[pb] => consistent!

  11. e+e- --> b b-bar u d-bar e nu_e-bar # of sample points for MC: 100000 keep mass of the external particles <- Cumulative Result -> < CPU time > Estimate(+- Error )order Acc % ( H: M: Sec ) -------------------------------------------------------------- 1.782981(+-0.004477)E-02[pb] 0.251 1:32:13.89 < CPU time > with traditional algorithm ==> 8:35:41.02 comparison with LUSIFER ==> massless external particles with kinetic cuts LUSIFER GRCFT with cut 1.7187E-02 [pb] 1.720E-02[pb] => consistent!

  12. e+e- --> b b-bar nu_mu mu+ e nu_e-bar # of sample points for MC: 100000 keep mass of the external particles <- Cumulative Result -> < CPU time > Estimate(+- Error )order Acc % ( H: M: Sec ) --------------------------------------------------------------- 5.972016(+-0.016589)E-03[pb] 0.278 2: 2:40.37 comparison with LUSIFER ==> massless external particles with kinetic cuts LUSIFER GRCFT with cut 5.8188E-03 [pb] 5.8388E-03 [pb] => consistent!

  13. e+e- --> b b-bar nu_mu mu+ mu- nu_mu-bar # of sample points for MC: 100000 keep mass of the external particles <- Cumulative Result -> < CPU time > Estimate(+- Error )order Acc % ( H: M: Sec ) ---------------------------------------------------------------- 5.957871(+-0.015124)E-03[pb] 0.254 1: 57: 32.04 comparison with LUSIFER ==> massless external particles with kinetic cuts LUSIFER GRCFT with cut 5.8091E-03 [pb] 5.82153E-03[pb] => consistent!

  14. e+e- --> b b-bar b b-bar nu_e nu_e-bar • # of sample points for MC: 8000000 • Power4 1.6GHz (8CPU) • keep mass of the external particles • with kinetic cuts <- Cumulative Result -> < CPU time > Estimate(+- Error )order Acc % ( H: M: Sec ) --------------------------------------------------------------- 4.447077(+- .003697)E-05[pb] .083 4:54:21.14 comparison with LUSIFER ==> massless external particles with kinetic cuts LUSIFER 4.352E-05 [pb]

  15. SUMARRY • @ILC • Generator for e+e- -->6f, 8f,.... is important but... • Huge number of the Feynman diagrams appear • Grcft (Upgrade version of Grace) • New algorithm • Factorized calculation of Feynman amplitudes • No need to generate Feynman graphs • Good acceleration for electro-weak theory • O(5-100) times faster than old algorithm • We can include QCD diagrams also

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