Determination of ΔG from pp -> π 0 production at PHENIX

Determination of ΔG from pp ->π0 production at PHENIX Pre-Spin2008 RHIC Spin Meeting • Swadhin Taneja • SUNY Stony Brook University SwadhinTaneja Pre- Spin2008 RHIC Spin Meeting

Outline • PHENIX Double helicity asymmetry (ALL) in π0 measurement. • Theory interpretation of ALL . • Sensitivity of π0 ALL to the gluon spin, ΔG. • Theoretical uncertainties in the extraction of ΔG. • Results and Conclusions. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

PHENIXπ0 ALL from Run-5 and Run-6 • New Run 6 PHENIX data. • 13% CL with Run 5 • Systematic Uncertainty: • - Relative luminosity (ΔR) • - Beam polarization (ΔP) • NLO pQCD expectation(GRSV) • - ΔG =0.24 , std. • - ΔG = 0 , zero • - ΔG = -1.05, negative The measurements are more consistent with ΔG = 0 . SwadhinTaneja Pre- Spin2008 RHIC Spin Meeting

Theory interpretation of ALL • fa and fb are both quarks (qq). • fa is quark and fb is gluon(qg). • fa and fb are both gluons(gg). Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Sensitivity of π0 ALL to ΔG • Vary ΔG and refit to pDIS data • (Fit by GRSV Group) • Calculate χ2 with PHENIX data, • χ2 profile is : • - non- parabolic so both • Δχ2 =1 and 9 (1σ and 3σ) are important • - wider on the negative side • From just the statistical uncertainty : Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Sensitivity of π0 ALL to ΔG • The two primary systematic uncertainties are from polarization and relative luminosity. • The polarization uncertainty is insignificant when extracting ΔG. • Relative luminosity while small is significant. • Systematic uncertainty gives an additional +/- 0.1 Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting 6

Theoretical uncertainties • PDF model dependence as a function of x. • Fragmentation functions model dependence. • Theory energy scales, μ (factorization scale, fragmentation scale and renormalization) dependence. • Strong coupling constant uncertainty dependence. • Unmeasured x range dependence. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

PDF models from pDIS • The gluon polarization distribution as a function of x for five fits to polarized DIS data. • Notice the 1σ experimental uncertainty (hatched band) from pDIS (Calculated by BB). Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

ALL for different models • Small ΔG in our measured x region 0.02 to 0.3 gives small ALL (DSSV and GS-C). Large ΔG gives comparatively larger ALL . • Note small ALL (GS-C) does not necessarily mean small ΔG in the full x range. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Shape uncertainty • Obtain different ΔG’s by varying the size of a gluon distribution. • Do not re-fit to the pDIS data. • Plot the χ2 profile. The constraint at 3σ is nearly shape independent • Variation in ΔG due to shape in our x region is minimal. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting 10

Re-fit vs no refit • The two curves are consistent on the positive ΔG side. • On the negative side the • two are consistent. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Theory scale (μ) uncertainty • Uncertainty from scale is small for the positive values of ΔG but is sizable for negative values. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Results & Conclusions • We presented the results for the double helicity asymmetry (ALL ) in p0 from PHENIX for Run 6. • We studied the effects of theoretical uncertainties on the extraction of gluon spin, ΔG . • Based on our analysis we conclude that PHENIX Run5 and Run6 combined data for π0 ALL gives for DG in the x range (0.02- 0.3) , at μ2 = 4 GeV2 : • For a variety of DG shapes we find at 3σ • Caution: This is not the entire gluon spin, x range below 0.02 and above 0.3 is yet to be explored. Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

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Swadhin Taneja Pre- Spin2008 RHIC Spin Meeting

Determination of ΔG from pp -> π 0 production at PHENIX