1 Detector effects on the asymmetry A 1 : The measurability of the polarized structure function g 1 C. Aidala 1,2, A. Deshpande 1,3, V. W. Hughes 1 DESY-PROC , September Yale University, New Haven, CT 2 Now at Columbia University, New York, NY 3 Now at RBRC at BNL, Upton, NY Abhay Deshpande RIKEN BNL Research Center HERA III Workshop Munich, December 2002

2 The Outline Status of g1 structure function measurement Need for new low x measurements of g 1 to go beyond what has already been measured Polarized DIS experiment at HERA Expectations from present data regarding g 1 at low x  from pQCD fits of “present” real data Measurement of g 1 at low x  small asymmetries  Measurement of small asymmetries & statistical uncertainties event migration (x,Q 2 )  Detector effects: event migration (x,Q 2 )  Purities and asymmetries bin-by-bin  Effect on A 1 measurement… hence g1 measurement radiative corrections  Comment on effect of radiative corrections C. Aidala et al, DESY-PROC , September 1999, Page248

3 On g 1 study for HERA Previous fixed target experiments HERA covers at least 2 decades more in x-Q 2 Predictions of g 1 spin structure function measurements: -- pQCD fit of “present” g 1 data -- Low x behavior extracted from best pQCD fit[1] -- Reverse calculations to get the asymmetry A 1 p -- One more step to go back to the measured asymmetry A m C. Aidala et al, DESY-PROC , September 1999, Page248 [1]A. Deshpande et al., Polarized HERA Workshop Proceedings, DESY-Proceedings

4 The Method: Background The values of g 1 predicted by the pQCD fits extrapolated to the low x (where there is no data x<0.003) indicate that the corresponding A 1 s and hence A m should be very small: A m ~ a few X Events rates in those bins give you the  A m =1/(N1+N2) where N1 and N2 are number of events in each bin with parallel and anti-parallel orientation of leptons and nucleons in l-N collision X=10 -5  from the paper Deshpande et al. [1] was taken Statistical uncertainties calculated for luminosity: 500 pb -1 Detector acceptance taken in to account Pe = Pp = 70% assumed Ee=27 GeV Ep=820 GeV C. Aidala et al, DESY-PROC , September 1999, Page248

5 Detector Simulation The values of N 1 and N 2 referred to previously were calculated from A 1 and  A 1 g1 = A1*F1; A1=Am/[f*Pe*Pp*D]; Am=(N1-N2)/(N1+N2) Events (N1, N2) were put through a HERA fast detector simulation[2] times 500 pb-1 luminosity simulated in this way The Simulations includes/considers in its parameterizations: -- detector acceptance -- vertex distribution -- dead material -- energy and angle smearing -- NO trigger or selection efficiencies included C. Aidala et al, DESY-PROC , September 1999, Page248 [2] J. Contreras, Tools for fast detector simulation,

6 Method (continued….) Given a combination of E, polar angle  azimuthal angle  the code returned: E’,  ’,  ’    From this events were re-constructed based on the scattered electron: y’ = 1 – (E’/2Ee)(1-cos  ’) x’ = E’(1+cos  ’)/2Epy’ (Q 2 )’= 2EeE’(1+cos  ’)  Efficiency and Purity were calculated for each of the 10 bins considering migration to and from 14 bins. C. Aidala et al, DESY-PROC , September 1999, Page bins to the left of green line 4 extra bins between the green and the purple line

7 Efficiency and Purity Efficiency = (No. measured within bin that were generated in the same bin)/(No. generated within bin) Purity = (No. of events measured within bin that were generated within bin)/(No. events measured in the bin) C. Aidala et al, DESY-PROC , September 1999, Page248 Trend Observed: 1. Event migration rate 5-15% OUT of the bin for y~1 Direction of migration along lines of constant y 2. Event migration rate 40-80% for bins away from y~1 Direction primarily to LOWER x values bins. Event migration can be controlled much better using hadronic event reconstruction method [3]  How much is this reduction of migration by use of hadronic migration has NOT been studied [3] U. Bassler & G. Bernardi, Nucl. Inst. Methods A 426 (1999)

8 Close up of migration effects Small migration for high y kinematics Large migration for low y kinematics C. Aidala et al, DESY-PROC , September 1999, Page248 Bin 6 Large y~1 Bin 7 Small y

9 Efficiencies (left) and Purities (right) This is the default font C. Aidala et al, DESY-PROC , September 1999, Page248

10 Re-Calculate Asymmetries This is the default font C. Aidala et al, DESY-PROC , September 1999, Page Recalculate asymmetries and compare with the statistical uncertainties pre-detector migration studies -- FOR ALL BINS, CALCULATED A1 AFTER DETECTOR EFFECTS WAS WITHIN 1-SIGMA OF THE VALUES CALCUALTED FROM PQCD FITS

11 Conclusions Although at low x asymmetries are small, the effect of detector migration DOES NOT destroy measurement -- This effect was later studied using detailed detector MC of H1 and the above result was confirmed The other potential danger: RADIATIVE CORRECTIONS -- Studied by G.Radel and A. De Roeck, (DESY-PROC , September 1999, page 252) using HECTOR Conclusions similar… measurability of small asymmetries is preserved Hadronic final state reconstruction methods will reduce further the event migration effects Spin structure function is measurable all the way up x~10 -5Spin structure function is measurable all the way up x~10 -5 C. Aidala et al, DESY-PROC , September 1999, Page248