In order to estimate the order magnitude of the single spin Collins asymmetry at midrapidity I calcuated the following partonic components from jet reconstruction using the STAR PYTHIA + GEANT simulation and the most recent global analysis of the Collins functions and transversity distributions.  Software triggers used in the existing 2006 transverse analyis by Murad were applied.  In order to mock up the single spin asymmetry, I assigned the polarization to only one proton and assumed it was always the parton associated with flavor1 and x1 in PYTHIA that originated from the polarized proton.  The following plots are integrated over jet pT > 11.44 GeV with |zVer| < 60, 0.05<R<0.9, 0.0<detEta <1 and a software+geometric trigger applied.

The single spin asymmety is estimated using the following fomula:

    A_N=δf(x)/f(x)  x  dNN(s,t,u) x H₁(z)/D(z)

where each component is defined as:

     δf(x) -  quark transversity distibution

     f(x)   -  quark momentum distribution

     dNN(s,t,u) - spin transfer coefficient

     H₁(z) - Collins Fragmentation Function

     D(z) - unpolarized Fragmentation Function

There is an additional factor of sin(φ_S - φ_H) where φ_S (φ_H) is the angle the proton spin (hadron pT WRT jet axis) makes with the reaction plane. This will produce a phi modulation to the asymmetry and therefore the above equation is the maximal scenario, ie sin(90) =1. Note the reaction plane is defined by the incoming proton momenta an the outgoing jet thrust axis. (See figure 1 in Feng's PRL - attached below).

FIG 1:  dNN(s,t,u)

The histogram of the partonic spin transwer dNN was filled for all jet which fullfilled the above conditions.  Only one jet per event can contribute to the final asymmetry.  Therefore, this histogram was incremented with a dNN==0 for all non-leading jets in the event. 

FIG 2: <x1>

This histogram was incremented only once for each event which had at least one jet which passed the above jet cuts. It includes contributions from events in which dNN==0 so it is an underestimate. 

FIG 3: <x2>

This histogram is incremented once per event for every event which has at least one jet which fullfills the above conditions.

FIG 4: <z>

 An estimate of <z> from Adam's pi+/pi- analysis. The value of 0.25 = <z> was used.

Looking  at the most recent global analysis of transversity by Anselmino et. al. (paper attached) in combination with the unpolarized distributions I estimate the following ratios for a given x:

Again using the global analysis paper I estimated the ratio of H1(z)/D(z) to be +0.2 (-0.4) using <z> = 0.25 for the favored (unfavored) Collins function and the ratio unfavored/favored = 0.6 for <z>=0.25 for EMC data.  Putting it all together the asymmetry will be of the following order of magnitude:

A_N  = δf/f  * d_NN  * H₁/D

A^pi+_N = A^π+_N(favored) + A^pi+_N(unfavored) =1/1.6*(0.3 * 0.5 * 0.2) + 0.6/1.6*(-0.2*0.5*-0.4) =+0.034

A^pi-_N  = A^π-_N(favored) + A^π-_N(unfavored) = 1/1.6*(-0.2 * 0.5 * 0.2) + 0.6/1.6*(+0.3*0.5*-0.4) = -0.035

Looking at the A_N  calculated by Murad for the PRD 2006 data  (Fig. 10):

     http://cyclotron.tamu.edu/star/2005n06Jets/PRDweb/

If we assume we will calculate A_N(0<detEta<1) for the polarized blue beam and A_N(-1<detEta<0) for the yellow, and we combine the error bars in two forward (backward) regions then we need to divide the A_TT statistical error bars by sqrt(2).  But the asymmetry is proportional to sin(phi_S- phi_H) resulting in roughly half of the jets contributing nothing to asymmetry.  We then multiply back again by sqrt(2)  to achieve a statistical precision of:

pT=10,  err ~0.005

pT=20,  err ~0.010

pT=30,  err ~0.030

pT=40,  err ~0.090

Therefore we become statistically limited at pT=30 GeV.  Carl estimated that the Run 2008 data may be able to reduce statistcal errors by ~15%.