1. 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-1999-03, September 1999 1 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. 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-1999-03, September 1999, Page248

3. 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-1999-03, September 1999, Page248 [1]A. Deshpande et al., Polarized HERA Workshop Proceedings, DESY-Proceedings-1998-01

4. 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 10 -4 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  10 -2 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-1999-03, September 1999, Page248

5. 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] -- 50 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-1999-03, September 1999, Page248 [2] J. Contreras, Tools for fast detector simulation, http://www.desy.de:8888/~gehrt/heraspin

6. 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-1999-03, September 1999, Page248 10 bins to the left of green line 4 extra bins between the green and the purple line

7. 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-1999-03, 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. 8 Close up of migration effects Small migration for high y kinematics Large migration for low y kinematics C. Aidala et al, DESY-PROC-1999-03, September 1999, Page248 Bin 6 Large y~1 Bin 7 Small y 58 9 6 7 85 4

9. 9 Efficiencies (left) and Purities (right) This is the default font C. Aidala et al, DESY-PROC-1999-03, September 1999, Page248

10. 10 Re-Calculate Asymmetries This is the default font C. Aidala et al, DESY-PROC-1999-03, September 1999, Page248 -- 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. 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-1999-03, September 1999, page 252) using HECTOR 1.11 -- 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-1999-03, September 1999, Page248