study 2 , err(AL) , eta=[1,2], LT=800/pb (Jan)

A_L on this has a WRONG sign, I did not know RHICBOS is using different sign convention, JAN

Section A) Theoretical calculations:

Assumed LT=800/pb

fpol=new TFile("rb800.w+pola_grsv00_2.root"); <--GRSV-VAL (maximal W polarization)
funp=new TFile("rb800.w+unp_ct5m.root");

histo 215

Total W+ yield for lepton ET[20,45] GeV and eta [1,2] is of 7101 for unpolarized cross section and of -2556 for the helicity dependent part.

Assuming 70% beam polarization measured spin dependent asymmetry:

eps_L= P* del/sum= -0.25 +/-0.012

(assuming err(eps)=1/sqrt(sum) )

Fig 1 , W+ : top row - unpol & pol cross section GRSV-VAL (maximal W polarization),

bottom left: integrated over eta, black=unpol, red=pol

bottom right: asy=P *pol/unpol vs. lepton PT, green=fit

Total W- yield for lepton ET[20,45] GeV and eta [1,2] is of 5574 for unpolarized cross section and of +2588 for the helicity dependent part.

fpol=new TFile("rb800.w-pola_grsv00_2.root");
funp=new TFile("rb800.w-unp_ct5m.root");

histo 215

Assuming 70% beam polarization measured spin dependent asymmetry:

eps_L= P* del/sum= +0.325 +/-0.013

Fig 2. W- GRSV-VAL (maximal W polarization)

Section B) Folding in e+,e- reconstruction and QCD background

Assumptions:

LT=800/pb
beam pol P=0.7
e+,e- reco efficiency is 70%, no PT dependence
QCD background to W contamination, after e/h algo no spin dependece

lepton PT range	w=backg/signal
20-25 GeV	5.0 +/- 10%
25-30 GeV	1.0 +/- 10%
30-35 GeV	0.8 +/- 10%
35-40 GeV	0.7 +/- 10%
40-45 GeV	0.6 +/- 10%

Formulas:

Theory yields : unpol=sig0(PT) & pol=del(pt) , S1=(sig0+del)/2, S2=(sig0-del)/2
Measured yields N1, N2 , for 2 helicity states
- N1(PT)= eff*[ sig0+del + sig0 * w) /2
- N2(PT)= eff*[ sig0-del + sig0 * w) /2
- A_L^raw(PT)= P* (N1-N2)/ (N1+N2)
- V(A_L^raw(PT))= 1/(N1+N2) <-- variance
- A_L^sig(PT)= (1+w(PT))* A_L^raw(PT)
- V(A_L^sig)= (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

Fig 3, Results for W + GRSV-VAL (maximal W polarization)

Left : N1(PT)=red, N2(PT) blue. Right: reconstructed signal AL

ipt=0  y-bins=[41,50] unpol=1826.5 pol=-327.3  AL=-0.125 +/- 0.0234   QA=1.8
   B2S=5.0 , N1=3721 N2=3950 ALraw=-0.021 +/- 0.011, dil=6.00  ALsig=-0.125 +/- 0.069

ipt=1  y-bins=[51,60] unpol=1403.0 pol=-265.8  AL=-0.133 +/- 0.0267   QA=2.9
   B2S=1.0 , N1=889 N2=1075 ALraw=-0.066 +/- 0.023, dil=2.00  ALsig=-0.133 +/- 0.046

ipt=2  y-bins=[61,70] unpol=1233.7 pol=-384.7  AL=-0.218 +/- 0.0285   QA=4.7
   B2S=0.8 , N1=643 N2=912 ALraw=-0.121 +/- 0.025, dil=1.80  ALsig=-0.218 +/- 0.047

ipt=3  y-bins=[71,80] unpol=1811.9 pol=-1041.9  AL=-0.403 +/- 0.0235   QA=10.0
   B2S=0.7 , N1=713 N2=1443 ALraw=-0.237 +/- 0.022, dil=1.70  ALsig=-0.403 +/- 0.040

ipt=4  y-bins=[81,90] unpol=808.8 pol=-525.2  AL=-0.455 +/- 0.0352   QA=8.1
   B2S=0.6 , N1=269 N2=637 ALraw=-0.284 +/- 0.033, dil=1.60  ALsig=-0.455 +/- 0.056

sum2=7084.000000 sum3=-2544.850098 asy=-0.251

Fig 4, Results for W - GRSV-VAL (maximal W polarization)

ipt=0  y-bins=[41,50] unpol=1239.1 pol=490.8  AL=0.277 +/- 0.0284   QA=3.2
   B2S=5.0 , N1=2774 N2=2430 ALraw=0.046 +/- 0.014, dil=6.00  ALsig=0.277 +/- 0.086

ipt=1  y-bins=[51,60] unpol=1452.7 pol=641.2  AL=0.309 +/- 0.0262   QA=6.6
   B2S=1.0 , N1=1241 N2=792 ALraw=0.154 +/- 0.022, dil=2.00  ALsig=0.309 +/- 0.047

ipt=2  y-bins=[61,70] unpol=1426.5 pol=689.9  AL=0.339 +/- 0.0265   QA=7.5
   B2S=0.8 , N1=1140 N2=657 ALraw=0.188 +/- 0.024, dil=1.80  ALsig=0.339 +/- 0.045

ipt=3  y-bins=[71,80] unpol=1135.3 pol=596.1  AL=0.368 +/- 0.0297   QA=7.6
   B2S=0.7 , N1=884 N2=467 ALraw=0.216 +/- 0.027, dil=1.70  ALsig=0.368 +/- 0.049

ipt=4  y-bins=[81,90] unpol=313.8 pol=166.4  AL=0.371 +/- 0.0565   QA=4.3
   B2S=0.6 , N1=234 N2=117 ALraw=0.232 +/- 0.053, dil=1.60  ALsig=0.371 +/- 0.086

sum2=5567.280273 sum3=2584.398926 asy=0.325

Another set of results for W+, W- with 2 x worse B/S (the same PT dependence).

Fig 5. W+ GRSV-VAL (maximal W polarization)

Fig 6. W- GRSV-VAL (maximal W polarization)