From: jwqiu@qcd.phy.bnl.gov (Jianwei Qiu)
Date: Wed, 22 Oct 1997 18:21:15 -0400
Subject: Notes on discussion of single spin asymmetries

	Weekly Spin Physics Discussion Meeting at BNL
Notes on the discussion of single spin asymmetries on October 21, 1997.
		by Jianwei Qiu

1) Informal presentation on single transverse-spin asymmetries
   by Jianwei Qiu (based on work done with G. Sterman):
   
   * strong single transverse-spin asymmetries (as large as 30%) were 
     observed in forward region of pion production in p-p and pbar-p
     collisions.  Fermilab data show
     > Asymmetries for pi(+) and pi(-) have about the same magnitude,
       but opposite sign; 
     > Magnitude of asymmetries for pi(0) is smaller than that of pi(+); 
     > Magnitudes of symmetries for all types of pions increases 
       as xF increases;
     > Asymmetries for pi(+) and pi(-) change sign when polarized 
       proton is replaced by polarized antiproton;
     > Asymmetries for pi(0) remains the same when the polarized 
       p is replaced by p-bar.

   * Pointed out by G. Kane et al. in 1978, pQCD predicts that single 
     transverse-spin asymmetries in hadronic pion production vanish 
     in asymptotic limit.

   * Single transverse-spin asymmetry (A_N) in pQCD should be a twist-3 
     effect.  For pion production, A(p,s_T) + B(p') => pion(k) + X,
     dominant contribution to A_N has following factorized form,
          A_N(s_T) ~ (d/dx)T(s_T)_3 * f_2 * D_2 
     where f_2 and D_2 are normal twist-2 parton distribution and 
     pion fragmentation function, respectively, and T(s_T)_3 is a new 
     twist-3 correlation function.  Because of symmetries and kinematics, 
     only one twist-3 correlation function contributes to A_N at leading 
     power.

   * It is the derivative, d/dx, of T(s_T)_3 that makes the asymmetries 
     increases as xF increases.

   * With a simple model for T(s_T)_3 including one parameter 
     (normalization), theoretical calculation reproduces all features 
     of the Fermilab data.

   * Just as all twist-3 effect, A_N in pion production decreases at 
     higher energies.  With root(s)~200 GeV and p_T~20 GeV, A_N is only 
     a few percents, while it was ~30% shown in Fermilab data.

2) Discussions:

   * AGS data on A_N with 18 GeV polarized beam show features slightly 
     different from Fermilab data.  But, Argonne's data with 12 GeV beam 
     have features similar to Fermilab's data.

   * Existing Data on A_N have relatively small p_T (1~4 GeV).  Is this 
     p_T too small for application of pQCD?

     pQCD works well for spin-averaged pion production with p_T as low as
     a few GeV.  Theoretical predictions shown by Qiu were evaluated at
     p_T = 4 GeV.  Although pQCD prediction may have a larger error when 
     p_T becomes smaller, we do not expect any dramatic change of features
     when p_T is reduced by one GeV or so. 

   * Since leading power pQCD (twist-2) predicts vanishing A_N, 30% 
     asymmetries shown in Fermilab data itself is very interesting.  
     Next to leading power pQCD (twist-3) predicts decrease of A_N as 
     energy increases.  A measurement of large A_N at RHIC energies 
     will be even more interesting.

   * Since asymmetry measurement for pion production is relatively 
     easier to do, the 30% asymmetries provide us real opportunities 
     to study QCD dynamics beyond "leading twist".    

   * At beginning of RHIC running, no spin rotators will be in place, and
     luminosity will be too low to do Drell-Yan measurement with two
     transversely polarized beams.  It might be the ideal time to measure
     the single transverse-spin asymmetries.  There should be enough
     rate for pions with p_T as low as 5 GeV at root(s) ~ 200 GeV.
     > need to estimate errors on A_N for pion productions;
     > need to find out the optimal kinematics for large A_N.

   * A_N is large in the forward region.  Both Phenix and Star detectors
     have very limited coverage in rapidity.
     > explore the possibilities at BRAHMS detector, which has a rapidity
       coverage 0 < |y| < 4, and p_T < 3 GeV.
     > do theoretical calculations to see what kind signals for 
       Phenix and Star.

3) What is next?

   * Come back to meet again in three weeks.

   * Experiment: 
     > feasibility and errors.

   * Theory: 
     > estimate signals for Phenix and Star with limited rapidity
       coverage;
     > find out the optimal kinematics for the largest asymmetries.