# MC Asymmetry Rescaling

In Pythia ♥s Kretzer we looked at the contributions to charged pion production from different partonic subprocesses as a function of pion p_{T}. We discovered that the distributions coming out of Pythia match much better with Kretzer fragmentation functions than with the more modern DSS set.

Tuning Pythia using independent fragmentation can be a tricky business, and even if we did get a better tune we’d still need to run it through GEANT. That’s not a viable option for evaluating systematic uncertainties in the Run 5 charged pion A_{LL} measurement. Instead, we propose the following:

- Take the ratio of DSS and Kretzer subprocess fractions to get pion p_{T}-dependent scaling factors for gg, qg, and qq scattering.
- Split the Monte Carlo distributions into gg, qg, qq, and other processes. Rescale the gg, qg, and qq by DSS/Kretzer, then recombine. At this stage we’re still dealing with individual partonic p_{T} samples.
- Plug the recombined samples into the usual MC Asymmetry workflow for assigning trigger+reconstruction bias systematics.

The charge-independent scaling factors I obtained in Step 1 are

`gg_scale = [2.2040, 2.4842, 2.7525, 3.0736, 3.5487]`

qg_scale = [1.1026, 1.0804, 1.0356, 0.9775, 0.9145]

qq_scale = [0.5162, 0.5249, 0.5337, 0.5430, 0.5571]

Here’s a qualitative plot showing the effect of the rescaling:

We get a nice improvement at high p_{T}, particularly in scenarios like pi+ GRSV-MIN, where the difference between gg asymmetries and qg asymmetries is really pronounced. To get more quantitative, we can calculate χ2 statistics comparing the Monte Carlo histograms to the actual NLO predictions. Unfortunately, the huge difference in precision at low and high p_{T} obscures the big picture in my opinion. Instead, here are χ2 values given separately for the low 2 p_{T} bins and then the upper 3 ones:

[2.00 - 4.56]

`Scenario (-) | Chi2 (raw) | Chi2 (scaled)`

MAX | 37.86 | 118.06

MIN | 30.08 | 141.29

STD | 105.36 | 70.72

ZERO | 68.19 | 233.78

Scenario (+) | Chi2 (raw) | Chi2 (scaled)

MAX | 73.46 | 130.63

MIN | 74.85 | 226.24

STD | 166.92 | 199.31

ZERO | 42.58 | 188.73

[4.56 - 12.84]

`Scenario (-) | Chi2 (raw) | Chi2 (scaled)`

MAX | 194.71 | 37.41

MIN | 78.74 | 9.96

STD | 166.84 | 62.02

ZERO | 6.62 | 1.56

Scenario (+) | Chi2 (raw) | Chi2 (scaled)

MAX | 23.16 | 6.86

MIN | 78.61 | 4.88

STD | 30.68 | 34.48

ZERO | 39.86 | 19.09

At low p_{T} the agreement between NLO and Pythia actually gets worse. The absolute change in the value of A_{LL} is small, though. At higher p_{T} we see a significant reduction in χ2 everywhere except for pi+ STD.

- kocolosk's blog
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