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=del_L(pt) , S1=(sig₀+del_L)/2, S2=(sig₀-del_L)/2
• Measured yields N1, N2 , for 2 helicity states
  • N1(PT)= eff*[ sig₀ +P*del_L + sig₀ * w) /2
  • N2(PT)= eff*[ sig₀ -P*del_L + sig₀ * w) /2
  • A_L^raw(PT)= 1/P (N1-N2)/ (N1+N2)
  • V(A_L^raw(PT))= 1/P² 1/(N1+N2) <-- variance 
  • A_L^sig(PT)= (1+w(PT))* A_L^raw(PT) 
  • V(A_L^sig)=1/P² (1+w)²*V(A_L^raw ) + V(w)*(A_L^raw)² 
  • dil=1+w
  • QA= |(A_L^sig)/err(A_L^sig)| - must be above 3 for meaningful result

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

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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

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

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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

 

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

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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

 

 

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

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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