A_LL Details

Details on the A_LL result and the systematic studies:

The result in numbers:

Bin <p_T> [GeV] in bin A_LL stat. error syst. error
1 4.17 0.01829 0.03358 0.01603
2 5.41 -0.01913 0.02310 0.01114
3 7.06 0.00915 0.03436 0.01343
4 9.22 -0.06381 0.06366 0.01862


A_LL as separated by trigger:

Figure 1: A_LL as a function of p_T for HT1 (black) and HT2 (red) triggers separately. HT1 here is taken as all triggers that satisfy the HT1 requirement, but not HT2. Since the HT2 prescale is one, there are very little statistics for HT1 at the highest p_T. The highest p_T point for HT1 is outside the range of the plot, and has a large error bar. The high p_T HT1 data is used in the combined result. 


Systematics: Summary


  Bin 1 Bin 2 Bin 3 Bin4
relative luminosity 0.0009 0.0009 0.0009 0.0009
non-longitudinal pol. 0.0003 0.0003 0.0003 0.0003
beam background 0.0012 0.0084 0.0040 0.0093
yield extraction 0.0144 0.0044 0.0102 0.0116
invariant mass background 0.0077 0.0061 0.0080 0.0108
total 0.01603 0.01114 0.01343 0.01862

The first two systematics are common to all spin analyses. The numbers here are taken from the jet analysis. No Pi0 non-longitudinal analysis has been performed due to lacking statistics. These systematics are irrelevant compared to the others.

The analysis specific systematics are determined from the data, and as such are limited by statistics. The real systematic limit of a Pi0 analysis with a very large data sit will be much lower.

For the yield extraction systematic the invariant mass cuts for the pion yield extraction are varied. The systematic is derived from the maximum change in asymmetry with changing cuts.

For the beam background, the systematic is derived by studying how much A_LL changes when the beam background is removed. This is a conservative estimate that covers the scenario that only half of the background is actually removed. The asymmetry of the background events is consistent with zero.

For the invariant mass background systematic, A_LL is extracted in three invariant mass bins outside the signal region. The amount of background under the invariant mass peak (includes combinatorics, low mass and others) is estimated from the invariant mass distribution as shown below. For all three bins, the background A_LL is consistent with zero, a "worst case" of value + 1 sigma is assumed as deviation from the signal A_LL.

Invariant mass distribution:

Figure 2: Invariant mass distribution for HT1 events, second p_T bin. The red lines are the MC expectations for Pi0 and Eta, the green line is low mass background, the magenta line is combinatoric background, the thick blue line is a pol2 expectation for the other background, the blue thinner line is the total enveloppe of all contributions, compared to the data. At low mass, the background is overestimated.


Other systematic studies: False Asymmetries


False asymmetries (parity-violating single spin asymmetries) were studied to exclude systematic problems with spin asignments and the like. Of course the absence of problems in the jet analysis with the same data set makes any issues very unlikely, since jet statistics allow much better verifications than Pi0s. Still, single spin asymmetries were studied, and no significant asymmetries were observed. For both triggers, both asymmetries (yellow and blue) and for all p_T bins the asymmetries are consistent with zero, in most cases within one sigma of zero. So there are no indications for systematic effects. The single spin asymmetries are shown below:

Figure 3: Single spin asymmetry epsilon_L for the blue beam.

Figure 4: Single spin asymmetry epsilon_L for the yellow beam.