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# Updated Plots and Tables

First, plots: Figure 1 shows my result, Figure 2 shows my result compared to Alan's (using the same pT bins), and Figure 3 shows the combined result (statistical errors only).

Figure 1:

Figure 2:

Figure 3:

I only showed statistical errors on Figure 3 because there was some question about how to combine the systematics. Here's the breakdown of them, 2006 first:

Table 1: Systematic Errors for the 2006 Result.

Error | Pt Bin 1 | Pt Bin 2 | Pt Bin 3 | Pt Bin 4 |

Low Mass Background | .001 | .0011 | .0038 | .001 |

Combinatorial Background | .001 | .0086 | .0016 | .0003 |

Photon Energy Uncertainty | .0015 | .0034 | .0017 | .0015 |

Non-Longitudinal Components | .0094 | .0094 | .0094 | .0094 |

And now 2009:

Table 2: Systematic Errors for the 2009 Result.

Error | Pt Bin 1 | Pt Bin 2 | Pt Bin 3 | Pt Bin 4 |

Mass Window | .0058 | .0013 | .012 | .018 |

Relative Luminosity | .0015 | .0015 | .0015 | .0015 |

Trigger Bias | .00028 | .00059 | .00097 | .0017 |

Finally, there were some questions about how my result ended up so close to Alan's (the calculated chi-square value is .19). Here are some tables of data, as requested, with 2006 first (note that I had to back the epsilon out of the final A_LL, the background fractions, and the background A_LL's: see here for A_LL and statistical errors):

Table 3: Information on the 2006 result

Pt Bin 1 | Pt Bin 2 | Pt Bin 3 | Pt Bin 4 | |

++ Yield | 20209 | 14088 | 7224 | 2505 |

+- Yield | 20088 | 14057 | 7080 | 2470 |

-+ Yield | 19961 | 13645 | 7107 | 2552 |

-- Yield | 20231 | 13825 | 7204 | 2491 |

Combinatorial Background Fraction | 5.8% | 5.9% | 5.3% | 5.9% |

Split-photon (Low-mass) Background Fraction | 3.6% | 3.9% | 9.3% | 8.6% |

Raw Asymmetry | .0065 | .0007 | .022 | -.0065 |

Raw Asymmetry Statistical Error | .01 | .0125 | .0164 | .0268 |

A_LL | .008 | .0058 | .0203 | -.0084 |

A_LL Statistical Error | .0115 | .0136 | .0189 | .0306 |

A_LL Total Systematic Error | .0023 | .0038 | .0043 |
.002 |

And the same for 2009:

Table 4: Information on the 2009 result

Pt Bin 1 | Pt Bin 2 | Pt Bin 3 | Pt Bin 4 | |

++ Yield | 42142 | 73951 | 57713 | 24689 |

+- Yield | 41679 | 72765 | 55676 | 24856 |

-+ Yield | 41509 | 72286 | 55967 | 24157 |

-- Yield | 42049 | 73346 | 56401 | 25043 |

Combinatorial Background Fraction | .064 | .056 | .116 | .203 |

Split-Photon (Low-mass) Background Fraction | .055 | .078 | .044 | .072 |

Epsilon | .0018 | .0022 | .0064 | .00064 |

Epsilon Statistical Error | .0037 | .0029 | .0036 | .0056 |

Raw Asymmetry | .0057 | .0052 | .017 | -.00078 |

Raw Asymmetry Statistical Error | .011 | .0088 | .011 | .017 |

A_LL | .0077 | .0072 | .023 | .0037 |

A_LL Statistical Error | .013 | .01 | .013 | .024 |

A_LL Total Systematic Error | .006 | .002 | .012 | .018 |

Figure 4: Comparison of raw asymmetries (that is, asymmetries before accounting for background)

PS: If you compare my statistical uncertainties to Alan's, it seems like mine should be smaller, given the ratio between the yields I get and the yields Alan gets. As far as I can tell, my statistical errors are larger than expected due to taking pion multiplicity into account (by filling histograms once per event, with the number of pions falling into a given pt bin for an event as the weight). Unfortunately, I don't quite understand how Alan calculated his statistical uncertainties: it appears to be in code linked to here, but I don't understand why the formula given in this code is correct. In his thesis, he says that he's accounting for the effect of pion multiplicity, and that it changes the statistical uncertainties by a few percent only: since he doesn't give a plot of the number of pions per event, I can't figure out whether this means that we're using different methods or if the multiplicities are genuinely different, although I don't think that my pion multiplicity should be so much larger than his, even with an expanded trigger mix.

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