2006 Polarizations for RHIC. ---------------------------------------- Final polarization along with absolute stat. and syst. uncertainties in each physics fill are provided in Pol2006_blue_phenix_brahms.dat - PHENIX/BRAHMS Blue Pol2006_yellow_phenix_brahms.dat - PHENIX/BRAHMS Yellow Pol2006_blue_star.dat - STAR Blue Pol2006_yellow_star.dat - STAR Yellow The supporting presentations are RSC_15nov2007_kieran.ppt RSC_15nov2007_carlos.pdf RSC_30nov2007_sasha.ppt ---------------------------------------- All uncertainties below are relative (Delta P/P or Delta A/A). Throughout the 2006 run the hydrogen jet target polarimeter (HJet) was used, alternating blue and yellow beam on the jet. Generally a measurement with one beam extends across many fills (a period). Totally, we obtained 5 periods with blue and 4 periods with yellow beams for 100 GeV running, and 1 period for blue and 1 period for yellow beam for 31 GeV running. Yellow 31 GeV HJet measurements showed a considerably larger background (compared to blue 31 GeV and blue and yellow 100 GeV), the source of which and its effect on polairzation measurements in HJet are not yet well investigated, so was lebeled as unreliable. The statistical uncertainty (deltaP/P) in Run6 was ~8-20% per fill in HJet measurements. The whole collected Run6 HJet statistics allowed to provide pC to HJet normalization on the level ~1.5% for 100 GeV and ~4% for 31 GeV beams. The systematic uncertainty of HJet measurements includes uncertainty on molecular hydrogen contamination in polarized atomic hydrogen jet (2% for deltaP/P) and an upper limit for the effect of "other" background estimated from the asymmetry in "non-signal" strips (uncertainties 1.3% for blue 100 GeV, 1.5% for yellow 100 GeV and 1.9% for blue 31 GeV). With the exception of 31 GeV yellow running, HJet demonstrated very robust performance, from the stability of target asymmetry and low background over periods and over both beams. For details, see Kieran's RSC presentation from Nov.15,2007. In 2006, the pC polarimeters used a new target scan mode, when the measurements were generally performed with vertical targets, stepping, in x (transverse horizontal coordinate) across the beam, with equal measurement time at each step. It allowed to measure horizontal polarization profile in each run separately (with limited stat. precision). Horizontal targets were used in a few measurements (almost all of them in the end of Run6), which provided vertical polarization profile measurements. At the end of a number of fills, measurements were performed in fixed target mode, with the intention to have the target positioned at the intensity peak in x. The strategy is to obtain the normalization for pC measurements using absolute polarization measurements with HJet in the fills for which HJet measurement is available, and after that use the properly normalized pC measurements to define the polarization in each physics fill. On the first step of pC data analysis, two parameters, t0 and dead layer (DL), were extracted for each strip in each measurement (run) from the fit of the "banana" plot, the recoil Carbon time-of-flight (ToF) vs energy. The DL parameter carries the meaning of "effective" dead layer and is used to correct the carbon deposited energy to obtain carbon kinetic energy. t0 is a ToF offset. After quality checks (QA), on the average each fill contained about 5 "good" runs. The list of QA checks was the same as in Run5 pC analysis. It included control of the width and position of the carbon (C) mass peak, as well as C mass peak position vs its kinetic energy (which detects problems with WFD and/or DAQ and/or in the fit of "banana"; only a few strips were masked due to this QA); strip by strip variations of the number of events in the "banana" (4 runs were removed from the analysis); consistency in bunch-by-bunch asymmetry measurements (3 runs were removed from the analysis). All systematic uncertainties from the effects above were estimated to be negligible for the final fill-by-fill polarization measurements, except the energy correction effect (described by DL), which was defined to be 1.2%. After QA checks, it was found that two blue fills (7621 and 7804) and two yellow fills (7654 and 7671) do not contain any reliable "good" runs. Polarization values for them was borrowed from the other beam, and an additional systematic uncertainty (~10%) was assigned for those fills from the width of the correlation between blue and yellow beam polarization in a fill as measured from "good" fills. For details, see Carlos's RSC presentation from Nov.15,2007. To obtain average polarization over the beam intensity distribution in the transverse plane, the knowledge on the polarization profile (polarization vs x and y in transverse plane) is necessary. The correction due to pol. profile depends on the ratio of width of the beam intensity profile and beam polarization profile. It can be obtained from the direct measurements of the widths of the profiles, which requires good target positioning during the scan. Another way, which excludes the necessity of the precise target positioning, is a fit of polarization vs event rate (which is proportional to beam intensity) in a scan, by a function P/Pmax=(I/Imax)^R; here it is assumed that both intensity and polarization profiles have gaussian shapes with widths sigma_I and sigma_P, correspondingly, and at least one point in the scan corresponds to beam maximum intensity; Pmax and Imax are polarization and event rate at beam maximum intensity; R is (sigma_I/sigma_P)^2. Since many of the pC measurements (about half) showed non-gaussian intensity profiles, which may be due to target positioning problems, this latter approach was used to extract Pmax and R parameters for each fill, which were used to calculate the average beam polarization for fixed target mode (when doing normalization to HJet measurements) and for colliding beams:

=Pmax/sqrt(1+R) and

=Pmax/sqrt(1+R/2), correspondingly, for one dimensional case. Six fills in yellow beam measurements were found to be unfinished scans, where the maximum intensity point was not reached. To correctly extract Pmax and R parameters for those fills, the measurement of Imax was obtained from neighboring fills, assuming that pC event rate normalized by beam intensity (from WCM) at maximum intensity should be about the same for all measurements with the same target. The uncertainty of this approach was found to be about 10% which comes from beam and carbon target stabilities (i.e. beam emittance stability, target vibration, etc.). To relate HJet measurements to pC measurements, only R parameter in one direction (vertical or horizontal) is necessary, because the carbon target automatically averages polarization in the other direction. Fills with unfinished scans as well as fills with unreliable measurements were excluded from calculation of pC to HJet normalization. The normalization was obtained separately for "golden" fills (with gaussian shape of intensity profiles) and for "other" fills. The difference of ~11% (~3 sigma_stat) was found in blue 100 GeV fills, and no difference in yellow 100 GeV and blue 31 GeV was found. The decision was made to use separate normalization for "golden" and "other" fills, for both beams and both energies. The stat. uncertainty was taken as a maximal of two, "golden" fills vs "others" - a safe decision no matter what set of fills experiments will use for the analysis. The obtained normalization corrections were in the range 1.14-1.27, with initial normalization based on Run4 results (1.013 and 1.016 in Run5). The source of such a shift in normalization is not yet clear. One reason could be an improper energy correction. An incorrect energy correction doesn't affect the average measurements in pC, due to normalization to HJet, but it may give a fill-to-fill relative effect due to drift in energy correction (DL), which was about 8mkg/cm^2 from the beginning to the end of Run6. So this +/-4mkg/cm^2 variation from the average over Run6 DL may introduce +/-2.4% relative effect on polarization. It was taken as an upper limit of global uncertainty due to DL drift. Since yellow 31 GeV HJet measurements appeared to be unreliable, the normalization for 31 GeV yellow pC measurements was obtained from the simple assumption: A_N(31GeV)/A_N(100GeV) is the same for both blue and yellow polarimeters. The reliability of this assumption was estimated to be <2% for "golden" measurements, for the range of DL parameters and energy slopes, in pC blue and yellow measurements. The major uncertainty for this assumption comes form the possibility of having different normalization for "golden" fills and "others". The normalization for pC yellow 31 GeV measurements was obtained from A_N(blue31GeV)*A_N(yellow100GeV)/A_N(blue100GeV), where all A_Ns are simple averages between "golden" fills and "others". For the uncertainty, half of the maximal shift in normalization between "golden" fills and "others", among A_N(blue31gev), A_N(yellow100gev) and A_N(blue100gev), was taken, which was 11%/2=5.5%. Another uncertainty should be taken into account here - the one connected with DL drift. DL in 31 GeV period changed differently compared to 100 GeV period, in blue and yellow, with difference by about 5 mkg/cm^2, which may results in the additional shift in A_N in one beam relative to the other by ~3%, for 31 GeV running. So the final uncertainty for pC yellow 31 GeV measurements normalization was 8.6% (see summary below). After normalization for pC measurements is obtained, the last step is to provide polarization values for experiments which are averages obtained weighting with a product of two beam intensities in both x and y transverse dimensions. For the simple case when the transverse size (sigma_I) is about the same in yellow and blue beams:

=Pmax_2/sqrt(1+R_x/2)/sqrt(1+R_y/2), where R_x and R_y are (sigma_I/sigma_P)^2 in horizontal and vertical direction respectively, and Pmax_2 - is polarization at the intensity peak in two dimensional transverse plane, which is equal to Pmax*sqrt(1+R), where Pmax is polarization at the intensity peak in one dimensional case (integrated over the perpendicular direction; this is what we get from pC). So the knowledge on pol. profile in both transverse directions is necessary. pC in Run6 provided vertical pol. profile measurements only in a few runs taken at the end of the 100 GeV running, which showed R_y in about the same range as R_x. So the possible range in R_y was obtained as a maximal variation (+/-RMS) from mean R_x in both blue and yellow beams: 0.085+/-0.085 for 100 GeV beams and 0.11+/-0.11 for 31 GeV beams. These ranges were considered as a possible range in the average over fills vertical profile (which appears in global uncertainties), as well as a possible fill from fill fluctuation in vertical profile (which appears as non-correlated from fill to fill uncertainty). They give 2.0% and 2.6% uncertainties in 100 GeV and 31 GeV polarization measurements for experiments, correspondingly. Below is a summary of systematic uncertainties for fill-by-fill (non-correlated) measurements, discussed above. From vert profile: 2.0% for 100 GeV and 2.6% for 31 GeV Energy correction: 1.2% Below is a summary of global systematic uncertainties (considered as correlated from fill to fill), discussed above. blue-100 yell-100 blue-31 yell-31 Jet normalization, stat: 2.3% 2.4% 5.9% - Jet normalization (horiz. profile): 1.1% same same same Jet normalization, syst (molecular): 2.0% same same same Jet normalization, syst (other): 1.3% 1.5% 1.9% 8.6%* Pol. profile (vert. for exp): 2.0% 2.0% 2.6% 2.6% Energy correction: 2.4% 2.4% 1.2% 1.2% * breakdown of yell-31 systematic error for jet normalization: (8.6%)^2 = (7.9%)^2 + (1.9%)^2 + (2.9%)^2 with 1.9% - correlated with blue-31: " Jet normalization, syst (other)", copied from blue-31 2.9% - correlated with blue-31: half of "Jet normalization, stat" from blue-31 7.9% - uncorrelated with blue-31: includes 100 GeV non-correlated between blue and yellow normalization uncertainties (stat, syst-molecular and vert. profile), 3% due to DL drift and 5.5% due to possible shift in normalizations between "golden" fills and "others". So the final global uncertainties, deltaP/P, are: Blue-100GeV: 4.7% Yellow-100GeV: 4.8% Blue-31GeV: 7.2% Yellow-31GeV: 9.3% Considering that "Jet normalization, syst." as well as "Energy correction" uncertainties are mostly correlated between blue and yellow, the final global uncertainties for a product of two beams, delta(P_B*P_Y)/(P_B*P_Y): 100 GeV: 8.3%, which is sqrt{2.3^2+2.4^2+1.1^2+1.1^2+(2.0+2.0)^2+(1.3+1.5)^2+2.0^2+2.0^2+(2.4+2.4)^2} 31 GeV: 13.9%, which is sqrt{(5.9+2.9)^2+1.1^2+1.1^2+(2.0+2.0)^2+(1.9+1.9)^2+7.9^2+2.6^2+2.6^2+(1.2+1.2)^2}