Kevin has observed significant non-zero Collins asymmetries in the Run-12 data. It is useful to verify this with an independent analysis. Here, I parallel what he did, looking at Collins asymmetries for the following:

• events
  • Kevin's 488 "good" runs (NOTE: it turns out, I allowed 54 extra runs to slip through. This should explain the slightly smaller uncertainties I see when compared to Kevin's)
  • Bunch-crossing ID outside the abort gaps (30-38 and 110-118, note these are shifted one from the typical due to a "slip" in the counter for Run-12)
  • Good spin-4 bit
  • Vertex rank > 0 and |z| < 60 cm.
• Jets
  • Geometric matching to JP0, JP1, JP2, or AJP trigger or VPDMB/VPDMB-nobsmd "did fire"
  • No charged-particles with p_T > 30 GeV/c
  • R_T < 0.95
  • ∑p_T,ch > 0.5 GeV/c
  • |η_det - 0.1| < 0.8
  • |η_jet| < 1
  • 5 < p_T,jet < 55 GeV/c
• Pions
  • ΔR > 0.1
  • -1 < n_σ(π) < 2.5
  • N_hits,dE/dx > 5

For the Collins analysis, I focus on jets with p_T > 9.9 GeV/c. For Collins-like I focus on the range p_T < 9.9 GeV/c.

I note some differences from Kevin's analysis. First, I do include a geometric trigger match. Second, I consider vertices below 10⁶ but above 0. These, I believe, are single-track vertices. My detector-η cut is a bit different. I also have a slightly-tighter n_σ(π) cut. I do not cut on the total N_hits (that is above the nominal 12 hits), but rather on N_{hits, dE/dx}. I chose 9.9 GeV/c rather than a flat 10 GeV/c as it correlates with the binning I use for the p_T-dependence.

For polarization correction, Kevin takes the event-weighted average of the polarization and divides from the raw asymmetries. Here, I adopt the same approach I used for the Run-11 analysis. I calculate the weighted-average of the various triggers, detector halves, etc., on a fill-by-fill basis. I use the polarization values from the CNI Polarimetry page.

Collins Asymmetries

Figure 1

It is quite clear there are charge-dependent Collins asymmetries for forward scattering. The effects are muted for backward scattering, which is consistent with the expectation for damped polarization-transfer at backward angles. This is qualitatively consistent with Kevin's parallel analysis.

It does appear the asymmetries, here, are larger than what Kevin sees. For a constant fit I find

for π⁺

****************************************
Minimizer is Linear
Chi2                      =      22.5218
NDf                       =            6
p0                        =   0.00376381   +/-   0.000505535 

for π^-

****************************************
Minimizer is Linear
Chi2                      =      10.5762
NDf                       =            6
p0                        =  -0.00394722   +/-   0.000514243 

So, the constant fits are not great. The statistical uncertainties are about 9% larger than Kevin's. The asymmetries appear to be larger, as well, by a factor of 4.8 in π⁺ and 1.7 in π^-. On the other hand, the constant fits are constistent with asymmetries of equal-magnitude and opposite charge-sign for π⁺ and π^-. For linear fits through the origin I find

for π⁺

****************************************
Minimizer is Linear
Chi2                      =      7.04447
NDf                       =            5
p0                        =            0                      	 (fixed)
p1                        =    0.0356633   +/-   0.00423519  

for π^-

****************************************
Minimizer is Linear
Chi2                      =      8.46514
NDf                       =            5
p0                        =            0                      	 (fixed)
p1                        =   -0.0322351   +/-   0.0041263   

The fits are not bad (both better than 1.6σ). The linear dependences are, again, perfectly consistent in magnitude and opposite in sign. Moreover, the significance is tremendous, ~8σ.

Figure 2

In Fig. 2 I show the χ² distribution for the Collins fits. There do appear to be statistically significant (~3.6σ and ~3.0σ) shifts to higher ν for x_F > 0. So, it is possible there are some hidden systematics present.

Figure 3

In Fig. 3 I post the p₀ residual distribution, assuming a null result. The residual distribution appears to be centered reasonably close to zero (within 2.3σ). However, the width of the distribution is ~10σ from 1. The raw width of the distribution is wide by about 15%.

Figure 4

In Fig. 4 I show the asymmetries as a function of j_T in different windows of z. There appears to be something of an interesting j_T dependence present. It appears consistent with a 1/j_T-dependence. Such a fit for the 0.1 < z < 0.8 bin returns

for π⁺

 Chi2                      =      6.03665
 NDf                       =            5
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0           2.60737e-03   3.12981e-04   3.00000e-06  -1.54922e-09

for π^-

 Chi2                      =      10.3829
 NDf                       =            5
  EXT PARAMETER                                   STEP         FIRST   
  NO.   NAME      VALUE            ERROR          SIZE      DERIVATIVE 
   1  p0          -1.97587e-03   3.33053e-04   5.48669e-07   9.79204e-05

Again, the dependence is consistent with equal magnitude (within 1.4σ) and opposite sign for π⁺ and π^-.

Figure 5

In Fig. 5 I show the p_T-dependence for different windows of z. The asymmetries tend to grow with p_T, at least, to a certain point. This seems consistent with the expectation that the low-p_T range involves more gluonic subprocesses.

Collins-like Asymmetries

As a reminder, I focus on the lower range of pT < 9.9 GeV/c for the Collins-like asymmetry, which is a gluonic effect.

Figure 6

The Collins-like moment is quite tiny in both forward and backward scattering.

Sivers Asymmetries

Figure 7

Figure 8

The Sivers moment is, again, quite tiny in both forward and backward scattering. Generally, the recent twist-3 prediction expects the Sivers asymmetry to increase going from forward to backward scattering (a bit counter-intuitive to me). It is difficult to say we observe this in any of the results.