Longitudinal double-spin asymmetries for inclusive charged pion production opposite a jet

Update 2008-10-03: include the effect on A_{LL} from the uncertainty on the jet pT shift in the total point-to-point systematics.

Comparison to models obtained by sampling a_{LL} and parton distribution functions at the kinematics specified by the PYTHIA event:

Asymmetries are plotted versus the ratio of pion p_{T} and the p_{T} of the trigger jet.

Dataset and Cuts

• Runlist (297 long2 runs)
• BJP1 HW+SW trigger (137221, 137222)
• BBC timebin 6-9
• p_{T}(π) > 2.0
• |η_{π}| < 1.0
• |DCA_global| < 1.0
• nHitsFit > 25
• recalibrated nσ(π) in [-1.0, 2.0]
• trigger jet p_{T} in [10.0, 30.0]
• trigger jet detector η in [-0.7, 0.9]
• trigger jet neutral energy fraction < 0.92
• trigger jet ϕ within 36 degrees of fired jet patch center
• Δϕ(trigger jet-pion) > 2.0

Error bars on each histogram take multi-particle correlations into account when multiple pions from an event fall into the same bin. Here is the Δϕ distribution obtained from the data and compared to Monte Carlo:

Systematic Uncertainties

Systematic uncertainties are dominated by the bias in the subprocess mixture introduced by the application of the jetpatch trigger. Uncertainty in the asymmetry of the PID background also contributes in the two highest z bins. The full bin-by-bin systematic uncertainties are

π- = {9.1, 8.1, 6.1, 11.1} E-3
π+ = {14.8, 11.0, 6.6, 14.8} E-3

π- = {9.6, 9.5, 17.1, 14.9} E-3
π+ = {15.3, 13.0, 17.3, 21.8} E-3

Trigger Bias

I initially tried to estimate the bias from the JP trigger by applying the Method of Asymmetry Weights to PYTHIA. The next three plots show the Monte Carlo asymmetries after applying a) the minbias trigger, b) the jetpatch trigger, and c) the difference between a) and b):

a)

b)

c)

As you can see, the bias from this naïve approach is huge. It turns out that a significant source of the asymmetry differences is the fact that each of these bins integrates over a wide range in jet pT, and the mean jet pT in each bin is very different for MB and JP triggers:

We decided to factor out this difference in mean pT by reweighting the minbias Monte Carlo. This reweighting allows the trigger bias systematic to focus on the changes in subprocess mixture introduced by the application of the trigger. Here’s the polynomial used to do the reweighting:

Here are the reweighted minbias asymmetries and the difference between them and the jetpatch asymmetries:

The final bias numbers assigned using GRSV-STD are 6-15 E-3.

PID Background

I calculate the background in my PID window using separate triple-Gaussian fits for π- (8.6%) and π+ (9.2%), but I assume a 10% background in the final systematic to account for errors in this fit:

Then I shift to a sideband [-∞, -2] and calculate an A_{LL}:

The relation between measured A_{LL} and the “true” background-free charged pion A_{LL} is

so the systematic uncertainty we assign is given by

and is ~9 E-3 in the highest bin, 1.5-4 E-3 elsewhere.

Jet pT Shift

I used the corrections to measured jet pT that Dave Staszak determined by comparing PYTHIA and GEANT jets link to correct my measured jet pTs before calculating z. The specific equation is

p_{T,true} = 1.538 + 0.8439*p_{T,meas} - 0.001691*p_{T,meas}**2

There is some uncertainty on the size of these shifts from a variety of sources; I took combined uncertainties from the 2006 preliminary jet result (table at http://cyclotron.tamu.edu/star/2005n06Jets/PRDweb/ currently lists the preliminary uncertainties). The dotted lines plot the 1σ uncertainties on the size of the jet pT shift:

Next I used those 1σ pT shift curves to recalculate A_{LL} versus z. The filled markers use the nominal pT shifts. The open markers to the left plot the case when the size of the shift is large (that is, the 1σ corrected jet pT is lower lower than the nominal case, which causes some migration from nominally higher z into the given bin). The open markers to the right plot the case where the shift is small (corrected jet pT closer to measured).

In short: low markers represent migration from lower z, high markers represent migration from higher z.

No assignment of systematic at the moment. If I were to assign a systematic based on the average difference between the nominal and min/max for each bin I’d get

I assign a systematic based on the average difference between the nominal and low/high for each bin; this ends up being 3-16 E-3.

Relative Luminosity

Murad’s detailed documentation

A pT-independent systematic uncertainty of 9.4 E-4 is assigned.

Non-longitudinal Beam Components

Analysis of beam polarization vectors leads to tan(θB)tan(θY)cos(ΦB-ΦY) = 0.0102. I calculated an Aσ from transverse running:

The small size of the non-longitudinal beam components mean that even the Aσ in the case of π- leads to a negligible systematic on A_{LL}. A pT- and charge-dependent systematic of 1.4-7.3 E-4 is assigned.

Single Spin Asymmetries

The following are summary results (val ± err and χ2) from straight-line fits to single-spin asymmetries versus fill:

There’s a hint of an excess of uu and/or ud counts for π-, but no systematic is assigned.