Calculation of the Six-Fermion Six-Fermion Production at ILC with GrcftProduction at ILC with Grcft
-New algorithm for Grace-
KEK Minamitateya group
Yoshiaki Yasui (Tokyo Management College)
The 8th ACFA Daegu, Korea July 11-14
Event generator for eEvent generator for e++ee-- collider collider
@LEP2 e+e- -->4f
@ILC e+e- -->6f, 8f,....
LUSIFER, WHIZARD, SIXFAP, PHEDAS,EETT6F, AMEGIC++,..., GRACE
ALPHA, COMPHEP, NEXTCALIBUR , WPHACT, WWGENPV,WTO,..., GRC4F(Grace inside), KORALW(Grace inside)
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 .......
What is GRACEWhat is GRACE
Traditional algorithmTraditional algorithm
Calculate amplitudes graph by graph
Huge number of Feynman graphse+e- --> t t & ZH --> b b u d
435 in Unitary e+e- -->t t & ZH --> b b u d e
870 in Unitarye+e- --> ZHH --> b b b b
1860 in Unitary
Need new method
GRACE => GRCFT
Factorization of Feynman amplitudesFactorization of Feynman amplitudes
Idea traditional algorithm
New algorithm => factorize Feynman graphs
Faster algorithms => ALPHA, HERAC, O'Mega GRCFT (Grace with new algorithm)
=> sub-graphs are calculated repeatedly
size of the code => (G#)2
G#:number of graphs
size of the code => (GF#)2
GF#:number of factorized graphs
Algorithm for GrcftAlgorithm 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
How to factorize
consider decomposition of a graph at propagator c
fix a root external leg
choose max k in k ≤ N/2
the propagator c is uniquely determined
Factorize a graph at vertex Vc
Factorize sub-graphs also
Performance test
Compare with traditional GRACE codeNumerical calculation at “fixed” phase space point.
Process # graphs CPU-time(OLD/NEW)e+ e- --> e+ e- e+ e- 654 3.60
e+ e- --> e+ e- e+ e- e+ e- 145128 83.70
e+ e- --> e+ e- 12094 15.14
e+ e- --> e+ e- 117689 142.86
Numerical results for 6f productionsNumerical results for 6f productionsSystem
➢ CPU: Pentium 4 -3.2GHz ➢ intel fortran compiler ver.8.1
➢ compare with old GRACE
Input parameters Gscheme
– Dittmaier &Roth Nucl.Phys.B642(2002)➢ compare with other system LUSIFER
G =1.16639E-5GeV-2 (0)=1/137.0359895
MW=80.419GeV W=2.12GeV
MZ=91.1882GeV Z=2.4952GeV
mt=174.3GeV t=1.6GeV
mh=170GeV h=0.3835GeV (HDECAY)
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!
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!
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!
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!
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 particleswith 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]
SUMARRYSUMARRY@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
