# Run-12 Transverse Jets: Collins in Eta Bins

I found that in my previous updates I used about 50 or so more runs than did Kevin in his measurement. This should account for much of the uncertainty difference we see. I have, now, removed those runs from my list for a more direct comparison. The results, here, still include the geometric trigger which will grow my statistical uncertainties relative to Kevin's. Additionally, I now examine the effect of binning in pseudorapidity. I use the same bins as for the Sivers measurement: |η| < 0.5 and 0.5 < |η| < 1. Now, the asymmetries are calculated fill-by-fill and the weighted averages are performed over fill, trigger, beam, and eta. This will add an additional increase to the over-all uncertainty, since I will lose a few events from splicing the data and requiring all 12 azimuthal bins be filled for each detector half and each spin state.

# pT > 9.9 GeV/c

The higher pT jets are more sensitive to quark effects. Thus, one expects the largest Collins signal to come from the high-pT jets. I have chose 9.9 to correlate with my definition of jet-pT bin edges. This is also a slight departure from Kevin's analysis where he places the cut-off at the more nicely round number of 10 GeV/c.

## Table 1: π+

 xF > 0 xF < 0 η Range Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν |η| < 1 0.0357 0.00458 5.430/5 0.00368 0.000537 19.34/6 0.0119 0.00457 8.510/5 0.00134 0.000537 9.095/6 |η| < 0.5 0.0324 0.00573 5.036/5 0.00317 0.000673 14.76/6 0.0105 0.00566 7.393/5 0.00113 0.000666 7.962/6 0.5 < |η| < 1 0.0415 0.00760 4.441/5 0.00457 0.000891 7.961/6 0.0146 0.00776 3.357/5 0.00173 0.000907 3.273/6

## Table 2: π-

 xF > 0 xF < 0 η Range Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν |η| < 1 -0.0335 0.00476 10.02/5 -0.00375 0.000546 12.27/6 -0.00206 0.00475 5.163/5 -0.000510 0.000546 4.477/6 |η| < 0.5 -0.0248 0.00595 10.60/5 -0.00327 0.000684 5.149/6 -0.0101 0.00588 6.650/5 -0.00110 0.000677 6.960/6 0.5 < |η| < 1 -0.0489 0.00794 3.309/4 -0.00461 0.000908 15.54/5 0.0131 0.00806 6.075/5 0.000590 0.000924 8.314/6

The numbers for the full η range are very similar to those I had before. The linear fits are quite reasonable. The magnitudes are consistent for π+ and π- with opposite charge-sign. The slopes are of 7.8σ and 7.1σ significance, respectively. For the η bins, the asymmetries are also consistent in magnitude with opposite sign between the two charge-states. For central pseudorapidity I find an asymmetry of 6.8σ and 6.9σ, respectively. There is a hint of increase in the z-dependence as one moves forward in η, but the statistical significance is quite small (< 1σ for π+ and 2.43σ for π-). Similarly, when one integrates over all bins one finds hints--but nothing more--of an increase in the asymmetry as one moves forward in η (1.25σ for π+ and 1.18σ for π-).

# pT < 9.9 GeV/c

While low-pT jets are more sensitive to gluonic subprocesses we benefit from a tremendous amount of statistics. Additionally, they may be quite useful in comparison to the Run-11 results. Kevin has already posted low-pT Collins asymmetries; and I, now, post my independent analysis.

## Table 3: π+

 xF > 0 xF < 0 η Range Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν |η| < 1 0.00629 0.00276 13.26/5 0.000908 0.000401 13.31/6 0.00401 0.00276 1.497/5 0.000320 0.000400 2.972/6 |η| < 0.5 0.00474 0.00348 9.694/5 0.000793 0.000506 9.092/6 0.00102 0.00343 2.076/5 -0.000159 0.000499 2.062/6 0.5 < |η| < 1 0.00892 0.00455 10.92/5 0.00110 0.000658 11.97/6 0.00944 0.00462 5.446/5 0.00118 0.000667 6.500/6

## Table 4: π-

 xF > 0 xF < 0 η Range Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν Linear Fit Uncertainty χ2/ν Constant Fit Uncertainty χ2/ν |η| < 1 -0.00761 0.00283 3.581/5 -0.000670 0.000408 8.111/6 -0.00392 0.00282 16.83/5 -0.000473 0.000406 17.41/6 |η| < 0.5 -0.00736 0.00354 4.662/5 -0.000894 0.000514 5.945/6 -0.00130 0.00350 12.81/5 -5.09e-05 0.000507 12.93/6 0.5 < |η| < 1 -0.00805 0.00470 8.575/4 -0.000288 0.000671 11.33/5 -0.00877 0.00475 8.380/5 -0.00123 0.000679 8.504/6

Thus, for the full η range the charge-sign-dependence is still quite significant (3.5σ), however, the size of the effects and significance of the z-dependence is quite reduced relative to high-pT jets. The integrated asymmetry returns a charge-sign-dependence of 2.76σ. The quality of the constant fit is also much better than in the high-pT case. There are hints of an η-dependence, but nothing significant.

# Summary

## Figure 7

 pT > 9.9 GeV/c pT < 9.9 GeV/c

Anselm asked for a plot of the slopes as a function of η. In Fig. 7 I show the slope dependence on η. There does appear to be a fairly linear dependence on η which seems to scale with pT. I'm bothered a bit by the high-η behavior, but perhaps it is not statistically significant. A double-check by Kevin will be quite useful, here.

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