Kaon-kaon fitting with momentum resolution
Fitting kaon-kaon correlation functions with momentum resolution
In this page I will show the results of the fit of the experimental kaon-kaon correlation functions (binned directly in spherical harmonics). The difference to the previous study ( www.star.bnl.gov/protected/hbt/kisiel/081009/KKSHAnalysis.php) is that this time the momentum resolution is taken into account. For the detailed description of the method, see here: www.star.bnl.gov/protected/hbt/kisiel/081010/KKSHMomentumResolution.php.
Again I have fitted the identical kaon correlation functions. They were calculated in two kT bins (0.2-0.45) GeV/c and (0.45-0.9) GeV/c. The bins correspond to the average pT of 0.36 and 0.545 respectively. The main motivation for the study was to see whether the momentum resolution is able to explain the low values of lambda parameter seen in the experiment. Below I give the results.
| not-MR aware fit | MR aware fit | ||
| kt1 | lambda | 0.448 +/- 0.04 | 0.543 +/- 0.05 |
| Rout | 6.94 +/- 0.23 | 7.15 +/- 0.25 | |
| Rside | 5.42 +/- 0.2 | 5.54 +/- 0.21 | |
| Rlong | 6.38 +/- 0.2 | 6.54 +/- 0.22 | |
| kt2 | lambda | 0.361 +/- 0.06 | 0.403 +/- 0.07 |
| Rout | 7.99 +/- 0.58 | 8.50 +/- 0.69 | |
| Rside | 4.20 +/- 0.34 | 4.23 +/- 0.33 | |
| Rlong | 4.65 +/- 0.43 | 4.55 +/- 0.45 |
Please note that the fit is done simultaneously to four correlation functions (K+K+ and K-K-, Reversed Full Field and Full Field). I use 20 points (0.0-0.1 GeV/c in k*) x 3 Ylm components (00, 20, 22) x 4 pair/field combinations giving me the total ndof of 240-5 = 235. The chi2 of the fits are all aroung 400, giving chi2/ndof of 1.8, so the above errors should be increased by 30%.
The results of non-MR-aware and MR-aware fits seem to be in agreement, but some trends are visible. Lambda is increased for MR-aware fit, as expected, but only moderately (by 10%). Radii do not change much, they grow some but well within the statistical error.
You can judge the quality of the fit on this figure:
where the colored points are data (for the second kt bin) and the red line is the fit (to all of them simultaneously). The fits seems to work very well, capturing the main features of all the Ylm components.
Summary
We have employed momentum resolution aware fitting to kaon-kaon correlation functions from STAR. The fit works very well, and gives lambda values which are up to 10% higher than non-MR aware fit. This is however insufficient to explain the low values of lambda.