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Review of Transversity and Rellum Systematics
This is a summary of methods used at estimating systematic uncertainties for previous A_LL measurements. The information was obtained from the following theses:
- Leight: STAR 2009 pi0 A_LL
- Betancourt: STAR 2009 direct photon A_LL
- Staszak: STAR 2006 jets A_LL
- Boyle: PHENIX 2005-06 pi0s A_LL
- Kocoloski: STAR pi+/- A_LL
- Fukao: PHENIX 2005 pi0 A_LL
Transverse Polarization | Relative Luminosity | |
Leight | A_sigma too small from pi0 analysis; used A_sigma from 2009 inclusive jets; ~2.5 e-4 (pT-independent) |
difference between pi0 A_LL computed using ZDC vs. BBC for rellum; ~1.7 e-4 (pT-dependent) |
Betancourt | Approximated as 0.02 * A_LL ~10 e-4 (pT-dependent) |
difference between photon A_LL computed using ZDC vs. BBC for rellum; ~1.5 e-3 (pT-dependent) |
Staszak | via A_sigma; used STAR scaler polarimetry to obtain polarization angles. A_TT was consistent with zero Ranges from ~0.09 e-3 to 1.28 e-3 (pT-dependent) |
Compare rellum using two different detectors; uncertainty contribution given by Equation 5 below deltaR ~ 9.4 e-4 |
Boyle | A_TT measured in 2005 for 4 fills with spin rotators disabled; used local polarimetry to obtain polarization angles ~negligible contribution |
deltaR obtained from ZDC to BBC rellum comparison; deltaR propagates to deltaA_LL via equation 6 below (eq. 4.7-8 from thesis) ~5 e-4 Followed up with bXing-by-bXing analysis which is then width corrected and rate corrected Asymmetry of scalers ratio plus its uncertainty is the contribution to A_LL systematic |
Kocoloski | Extracted A_sigma from 2005 data set | |
Fukao | Size of A_TT term in "A_meas" equation below used as systematic ~5 e-3 from A_TT ~5 e-4 from A_L |
deltaR obtained from ZDC to BBC rellum comparison; followed up with bXing-by-bXing BBC/ZDC trigger ratio via MLM (see eq A.34-A.36) Contribution to A_LL systematic given by equation 6 below deltaR / R ~ 2 e-4 for longitudinal |
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Some relevant equations:
EQUATION 1: If the supposedly longitudinal proton beam polarization makes an angle Theta w.r.t. proton momentum, the yield is given in terms of asymmetries as:
EQUATION 2: If the beams are transversely polarized, the yield is written i.t.o. azimuthal dependence as:
EQUATION 3: The systematic uncertainty of A_LL due to A_sigma is given by:
EQUATION 4: The systematic uncertainty of A_LL due to A_TT is given by:
EQUATION 5: For relative luminosity, Staszak's thesis uses
EQUATION 6: Boyle's thesis uses, where the approximation N^{++} \approx R N^{+-} is used:
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