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# Run12 Collins Analysis: Addressing PWG Comments

During the weekly meeting on 9/25/2014, a few concerns were expressed about the run12 Collins analysis that should be addressed before preliminary. Those discussed in this post are:

1.) Use a larger input Sivers asymmetry for weighting to get a scale of the leak through effect (i.e. what value to scale the true Sivers asymmetry by).

2.) Measure the Collins asymmetry when our pion sample is dominated by kaons,protons and electrons. Namely, switch the nSigmaPion cut from -1 < nSigmaPion < 2.5 to (nSigmaPion < -1 || nSigmaPion > 2.5) The size of the asymmetry will determine whether we should correct the pion asymmetry points by a dilution factor, or assign a systematic error bar.

3.) Measure the sin(phi_S + phi_H) moment, and show that it's consistent with zero. Maybe release with the Collins moment preliminary?

Let's go through one at a time...

1.) **Disclaimer: **I double checked the yields for each bin in the Collins asymmetry. It turns out that a simple rebin won't fix the problem of having some empty bins for the yields. It turns out that there are several fills with only one or two runs in them, and we don't get good counts. This is messing with the fits, so I threw out all fills that have zero counts. This had little effect on the Collins measurement (slight increase in statistical error), but the Sivers asymmetry did increase from this. The output measured previously was ~1e-5, now it's 2e-4. Filling jet-by-jet (and not track-by-track) for Sivers, I believe there were several empty bins. This is noted as I will quote a different number below than what I gave in the talk on 9/25/2014.

I went with a 0.1 input Sivers asymmetry for the leak through calculation. This asymmetry is large enough so that when we measure the output from the Collins asymmetry, we should be able to get a scale value that isn't consistent with zero. With a statistically significant value, we can get a scale value from the output to scale the true Sivers asymmetry by. Using this input weight, we return the plots attached below as CollinsAsymmetry*_SiversWt_H2H1.pdf (apparently PDF files aren't accepted to put inline, lesson learned). At the particle level, these asymmetries are consistent with zero when fit with a constant fit, as expected. At the detector level, we return the following parameters for a constant (pol0) fit

Charge | Z | p_{T} |
j_{T} |
|||

Value | Error | Value | Error | Value | Error | |

+ | -0.00471 | 0.00099 | -0.00436 | 0.00072 | -0.00432 | 0.00099 |

- | -0.00618 | 0.00101 | -0.00504 | 0.00074 | -0.00598 | 0.00097 |

At the detector level we see that pi+ shows an asymmetry of about 0.005, or 5% of the input asymmetry. For pi-, we return about 6% of the input asymmetry. Taking these two values, and applying it to the true Sivers asymmetry from data (2.2e-4 +/- 4.3e-4) we get a leak through value of 1.1e-5 for pi+ and 1.3e-5 for pi- (or ~2e-5 if we use the error bar instead of the average value). For the Collins asymmetry from data, we have asymmetries on the order of 0.5-1%, where these won't contribute. It seems safe enough to ignore these as systematic errors.

2.) If we change up the nSigmaPion cut for the data, and measure the Collins asymmetry we will be getting an asymmetry which includes from kaons, protons, and electrons. These asymmetries are significant, as it turns out, and can be found attached below named KpeAsymmetry*.pdf. Fitting with a pol0 constant to get an idea of how significant these are, we get the following output:

Charge | Z | p_{T} |
j_{T} |
|||

Value | Error | Value | Error | Value | Error | |

+ | 0.00209 | 0.00142 | 0.00222 | 0.00142 | 0.00216 | 0.00142 |

- | -0.00295 | 0.00148 | -0.00308 | 0.00148 | -0.00294 | 0.00148 |

We have about a 1.5 sigma asymmetry for pi+, and about a 2 sigma asymmetry for pi-. The assumption that these are zero wasn't a good one, and we shouldn't make a correction to our asymmetry points. Rather, I propose instead we add a systematic error bar as an asymmetry increase (i.e. one sided error). If the K/p/e were really pions, we would measure a larger asymmetry, so these are dragging the result down. Hence, a one sided error bar on the upper side.

3.) Finally, measuring the sin(phi_S + phi_H) moment was simple enough in the code. These asymmetries can be found below labeled as OtherMoment*.pdf, and they're very small. Fitting again with a pol0 to get a handle on the size, we get the following output from the code

Charge | Z | p_{T} |
j_{T} |
|||

Value | Error | Value | Error | Value | Error | |

+ | 0.00043 | 0.00094 | 0.00041 | 0.00094 | 0.00042 | 0.00094 |

- | 0.00158 | 0.00097 | 0.00164 | 0.00097 | 0.00159 | 0.00097 |

Here we see a signal consistent with zero for pi+, but a 1.5 sigma effect for pi-. I'm not particularly sure what the proper sign of these asymmetries should be, I can't find any projection plots. Regardless, they're small and zero for the most part. I think it's still up in the air right now whether these are going to be released for SPIN 2014, but the systematics should be the same for this as well as the Collins measurement, so there shouldn't be a lot of extra work to get it ready if there's a strong opinion in favor of showing this at SPIN.

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