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
 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


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: