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

KEK Minamitateya group Yoshiaki Yasui (Tokyo Management College) The 8 th ACFA Daegu, Korea July 11-14. Calculation of the Six-Fermion Production at ILC with Grcft -New algorithm for Grace-. Event generator for e + e - collider. @LEP2 e + e - -->4f.

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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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