Proton Data

The experiments with the polarized proton target are listed in Table iii with the year of their publication, average and integrated value of ,

  
Table iii: Polarized DIS experiments with polarized proton target.

Here we are going to describe each experiment briefly and summarize into three tables for experimental condition (Table iv), data coverage (Table v), and analysis procedure (Table vi).

• SLAC-E80 [10,11]
  • The SLAC experiment E80 was performed at SLAC using the 6-20 GeV polarized electron beam and the butanol polarized target. They have improved the target polarization after their first publication; from 0.510.06 to 0.850.08.

  • A typical value of the f was 0.11 with a 10% uncertainty. Radiative correction has been made only for the data in the second paper. The nuclear effect on the asymmetry is not considered in the paper, but the effect would be minimum if they used butanol target.

  • In the deduction of the asymmetry , they have neglected the contribution from . They listed the upper limit of estimated taking but did not include the uncertainty into the asymmetry . The depolarization factor was calculated assuming R is constant. This assumption is to be checked.
• SLAC-E130 [12]
  • The SLAC experiment E130 was the successor of the previous experiment E80. The dilution factor f has been estimated using , small correction from radiative processes and Fermi motion effect, and found to be 0.1500.04. If we estimate the f in the same manner as the EMC, we obtain,

  • In the extraction of the asymmetry , they neglect the term . The upper bound for the was estimated as from 0.2 to 0.9 of the error in depending on the kinematic region.
  • The depolarization factor has been estimated assuming the unpolarized structure function to be constant. This assumption is to be checked).

• CERN-EMC [14]
  • They have extended the SLAC measurements to lower-x region, especially using the higher energy polarized muon beams. The target utilized was ammonium target (NH).
  • The dilution factor f was estimated using the following formula,

    

    Here they used phenomenological formulae,

    

    and

    

    represents ``EMC effect'' on nitrogen N which has been assumed to be identical to that of carbon C.

  • The effect of polarized nitrogen on the measured asymmetry has been estimated basing on the measurement + shell model calculation.
  • was systematically lower by 5-25% than which is being used widely. Hence we have re-evaluated the photon depolarization using the value of , and reflected it to the asymmetries listed in the paper.
• CERN-SMC [18]
  • The SMC experiment is the successor of the EMC experiment. The measurements has been further extended to low-x region down to x=0.003. The polarization of the muon beam has been confirmed by the measurements of the energy distribution of decay positron.
  • The dilution factor f was estimated to be 0.12. The depolarization was evaluated using the R expression Ref [15].
  • The effect of has been neglected but included in the systematic uncertainty. The knowledge on the measurement of has been reflected to the analysis.
• SLAC-E143 [19,24]
  • The SLAC experiment E143 is one of the post-EMC experiments, which improves the precision of the measurements of spin-dependent structure functions much.
  • They have measured both and . This allowed to derive and from Eqs. (5),(5) without any assumption. The asymmetries were measured with the polarized electron beam of three energy points. Only the data taken with 29.1 GeV beam has been used to obtain integral after the study of dependence in asymmetries.
  • The nuclear effect on the asymmetry has been evaluated from the measurement on N polarization plus shell model calculation.

  
Table iv: Parameters on experimental condition. As for E143, only 29.1 GeV data are presented in Ref. [19]. The data with the beam energies in the parenthesis are used to confirm the -evolution in Ref. [24]

  
Table v: Statistical issues of each experiment are summarized for proton data.

  
Table vi: Corrections to the measured asymmetries. The effect of was neglected but the uncertainty due to the effect has been estimated and included in the systematic uncertainty.