<z> Details

<z> Details

 

The goal of this analysis is to relate the neutral pions to the jets they are embedded in. The analysis is done using the common spin analysis trees, which provide the necessary tools to combine the jet and neutral pion analysis.

A neutral pion is associated to a parent jet if it is within the jet cone of 0.4 in eta and phi. To avoid edge effects in the detector, only neutral pions with 0.3 < eta < 0.7 are accepted. 

 

Cut details:

E_neutral / E_total < 0.95

higher energy photon of Pi0 > 2.8 GeV (HT1 trigger); > 3.6 GeV (HT2 trigger)

combination HT1/HT2: below 5.7 GeV only HT1 is used, above that both HT1 and HT2 are accepted

 

The final result uses both HT1 and HT2 triggers, but a trigger separated study has also been done, as shown below. There, HT2 includes only those HT2 triggers that do not satisfy HT1 (because of prescale).

Figure 1: <z> for Pi0 in jets as a function of p_T for HT1 and HT2 triggers. Also shown is the mean jet p_T as a function of pion p_T.

 

Bin-by-Bin momentum ratio

Figure 2: Bin-by-bin ratio of pion to jet p_T. The <z> is taken from the mean of these distributions, the error is the error on the mean. A small fraction of all entries have higher Pi0 p_T than jet p_T. Similar behavior is also observed for Pythia MC with GEANT jets. This obviously increases the <z>. An alternative would be to reject those events. The agreement with MC becomes worse if this is done.

 

Here is the data - MC comparison for 3 of the above bins. For the simulation, the reconstruction of the Pi0 is not required to keep statistics reasonable, so the true Pi0 pt is used. However, the MC jet finding uses all momenta after Geant, this is why the edges are "smoother" in the MC plot than in the data plots. Since <z> is an average value, this is not expected to be affected by this, since on average the Pi0 pt is reconstructed right.

Figure 3: Data / MC for Bin 5: 6.7 to 8 GeV

Figure 4: Data / MC for Bin 6: 8 to 10 GeV

Figure 5: Data / MC for Bin 7: 10 to 12 GeV

 

 

 

 

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.