study 4 , LT=300/pb, eta=+/-[1,2] , W+/- (Jan)

 Calculation of error of A_L for LT=300/pb,   for W± , eta=±[1,2],  PT>20 GeV/c

 

  • Input from RHICBOS , GRSV-STD model:
  • The sign of pol cross section from RHICBOS has reversed convention, I have changed  it to Medison convention.
    hpol->Scale(-1.);
  • beam Pol=70%
  • e+,e- reco efficiency is 70%, no PT dependence
  • QCD background to W signal (B/S) contamination, after e/h algo no spin dependece
      A B C
      ET_range
      (EEMC 3x3_cluster)      		 assumed w=backg/signal QCD eve
      suppression needed for(B)
      20-25 GeV  5.0 +/- 20%  - (for W+ or W-)
      25-30 GeV  1.0  +/- 20% 1/539 or 1/520
      30-35 GeV  0.8 +/- 20% 1/196 or 1/169
      35-40 GeV  0.7 +/- 20% 1/43  or 1/ 69
      40-45 GeV  0.6 +/- 20% 1/33 or 1/86
      45-50 GeV  0.5 +/- 20% 1/119 or 1/289
      *) based on full Pythia+GSTAR+BFC simulations of QCD events,
      (study 1 of S/B, A_L, LT=800/pb (Jan) section E)
      after 3x3 EEMC cluster is found
  • eta of the lepton [1,2] (polarized beam is heading toward Endcap)

 

Formulas:

  • Theory yields : unpol=sig0(PT) & pol=delL(pt) , S1=(sig0+delL)/2, S2=(sig0-delL)/2
  • Measured yields N1, N2 , for 2 helicity states
    • N1(PT)= eff*[ sig0 +P*delL + sig0 * w) /2
    • N2(PT)= eff*[ sig0 -P*delL + sig0 * w) /2
    • ALraw(PT)= 1/P (N1-N2)/ (N1+N2)
    • V(ALraw(PT))= 1/P2 1/(N1+N2) <-- variance 
    • ALsig(PT)= (1+w(PT))* ALraw(PT) 
    • V(ALsig)=1/P2 (1+w)2*V(ALraw ) + V(w)*(ALraw)2 
    • dil=1+w
    • QA= |(ALsig)/err(ALsig)| - must be above 3 for meaningful result

Fig 1, W+, eta=[1,2] , ideal detector 

Fig 2, W+, eta=[1,2] , 70% W effi+QCD backg 

 Table 1,  W+ , eta=[1,2] , LT=300/pb

1 2 3 4 5 6 7 8 9 10
reco EMC
ET GeV

 

 reco W+ yield
helicity: S1, S2		 reco W+  
unpol yield		 QCD Pythia
accepted yield		 assumed
B/S		 reco signal 
AL+err		 reco 
AL/err		 AL dilution:
1+B/S		 QCD yield 
w/ EMC cluster		 needed QCD 
suppression *)
20-25 242 ,236 479 2397 5.0 0.019 +/-0.160 0.1 6.00    
25-30 192 ,176 368 368 1.0 0.062 +/-0.105 0.6 2.00 198343 1/539
30-35 190 ,133 323 259 0.8 0.249 +/-0.109 2.3 1.80 50719 1/196
35-40 333 ,141 475 332 0.7 0.576 +/-0.098 5.9 1.70 14334 1/43
40-45 151,61 212 127 0.6 0.606 +/-0.132 4.6 1.60 4234 1/33
45-50 13,6 19 9 0.5 0.457 +/-0.393 1.2 1.50 1182 1/119

    *) after 3x3 EEMC cluster is found, to obtain B/S from column 5

 

Fig 3, W-, eta=[1,2] , ideal detector 

Fig 4, W-, eta=[1,2] , 70% W effi+QCD backg 

Table 2,  W- , eta=[1,2] , LT=300/pb

1 2 3 4 5 6 7 8 9 10
reco EMC 
ET GeV

 

 reco W+ yield 
helicity: S1, S2		 reco W-  
unpol yield		 QCD Pythia
accepted yield		 assumed 
B/S		 reco signal 
AL+err		 reco 
AL/err		 AL dilution: 
1+B/S		 QCD yield 
w/ EMC cluster		 needed QCD 
suppression *)
20-25 116,208 325 1626 5.0 -0.403 +/-0.205 2.0 6.00    
25-30 133,248 381 381 1.0 -0.431 +/-0.112 3.8 2.00 198343 520
30-35 126,247 374 299 0.8 -0.461 +/-0.107 4.3 1.80 50719 169
35-40 97,200 298 208 0.7 -0.495 +/-0.115 4.3 1.70 14334 69
40-45 26,55 82 49 0.6 -0.506 +/-0.203 2.5 1.60 4234 86
45-50 2,5 8 4 0.5 -0.521 +/-0.617 0.8 1.50 1182 293

    *) after 3x3 EEMC cluster is found, to obtain B/S from column 5

 

 

Fig 5, W+, eta=[-2,-1] , ideal detector 

Fig 6, W+, eta=[-2,-1] , 70% W effi+QCD backg 

Table 3,  W+ , eta=[-2,-1] , LT=300/pb

1 2 3 4 5 6 7 8 9 10
reco EMC 
ET GeV

 

 reco W+ yield 
helicity: S1, S2		 reco W-  
unpol yield		 QCD Pythia
accepted yield		 assumed 
B/S		 reco signal 
AL+err		 reco 
AL/err		 AL dilution: 
1+B/S		 QCD yield 
w/ EMC cluster		 needed QCD 
suppression *)
20-25 316,168 484 2424 5.0 0.436 +/-0.175 2.5 6.00    
25-30 235,137 373 373 1.0 0.375 +/-0.111 3.4 2.00 198343 531
30-35 189,132 322 258 0.8 0.252 +/-0.109 2.3 1.80 50719 196
35-40 255,223 479 335 0.7 0.094 +/-0.085 1.1 1.70 14334 43
40-45 109,102 212 127 0.6 0.048 +/-0.124 0.4 1.60 4234 33
45-50 10,9 19 9 0.5 0.027 +/-0.393 0.1 1.50 1182 119

    *) after 3x3 EEMC cluster is found, to obtain B/S from column 5

 

 

 

Fig 7, W-, eta=[-2,-1] , ideal detector 

Fig 8, W-, eta=[-2,-1] , 70% W effi+QCD backg 

Table 3,  W+ , eta=[-2,-1] , LT=300/pb

1 2 3 4 5 6 7 8 9 10
reco EMC 
ET GeV

 

 reco W+ yield 
helicity: S1, S2		 reco W-  
unpol yield		 QCD Pythia
accepted yield		 assumed 
B/S		 reco signal 
AL+err		 reco 
AL/err		 AL dilution: 
1+B/S		 QCD yield 
w/ EMC cluster		 needed QCD 
suppression *)
20-25 157,151 308 1544 5.0 0.024 +/-0.199 0.1 6.00 795943 515
25-30 187,180 367 367 1.0 0.029 +/-0.105 0.3 2.00 198343 540
30-35 187,179 367 293 0.8 0.033 +/-0.100 0.3 1.80 50719 173
35-40 151,144 295 206 0.7 0.033 +/-0.108 0.3 1.70 14334 69
40-45 41,40 81 49 0.6 0.026 +/-0.200 0.1 1.60 4234 86
45-50 3,3 7 3 0.5 0.012 +/-0.624 0.0 1.50 1182 301

    *) after 3x3 EEMC cluster is found, to obtain B/S from column 5