Methods III and IV for extracting proton flow

Methods III and IV refer to two alternative methods to extract proton sideward flow with minimum distortion arising from PID uncertainties. For Method III, there are extensive simulations and other tests which address issues of distortion and systematic error other than those arising from PID errors.

Method III

Method III is used in Heng's analysis and minimizes deuteron contamination by discarding the upper half of the proton dE/dx band. We are used to the idea that deuterons misidentified as protons come from further back in y, and so naive expectations lead us to expect that <Px> at forward rapidities is distorted to lower values by deuteron contamination. In contrast, when we examine <Px> vs. Py for protons at some forward rapidities, under conditions where appreciable deuteron contamination is known to be present and is known to be increasing with Py, we observe that <Px> rises at high Py (above Py ~ 0.5 GeV/c). The detailed simulations discussed below confirm that deuterons indeed can have this effect. An important ingredient in the explanation is that contaminating deuterons do indeed come from further back in y when we consider mean Pt, but at high Py, they come from a y region that is really very close to the proton y region which they contaminate.

In order to quantify the effect of deuteron contamination, Heng carried out a simulation featuring an appropriate admixture of protons and deuterons, with realistic dE/dx bands for both species. A crucial feature of the simulation was that the deuteron Pt spectra were based on actual fits to dE/dx data in bins of Pt. An illustration of the final result is shown opposite -- we see that the effect of the remaining deuteron contamination in the lower half of the dE/dx band for protons is small and well within the final systematic error. (Note the zero-suppressed vertical scale. Note also that we have not corrected for this small remaining deuteron contamination, which would lower the proton flow.) Heng has a separate web page dealing with issues of deuteron contamination, and various addition details can be found there.

Keeping the lower half of the proton dE/dx band moves us closer to contaminating positive pions, but the selection of high Py removes most pions. Nevertheless, a small correction is still needed for remaining pi+ contamination at mid to backward rapidities at 6A and 8A GeV. It is relatively easy to generate this correction, because we know that pions misidentified as protons have almost zero flow, and with the help of the negative pions, we can get a good handle on the percentage of pi+ contamination among the selected protons in the rapidity bins in question. This pi+ correction could be avoided altogether by restricting the range of rapidities for fitting the slope F, but we prefer to apply the correction and keep the y range broader. Heng has a separate web page dealing with issues of pion contamination.

Method IV

Method IV relies on UCD PID to identify the best interval of Py and especially the best region of the dE/dx band at any y. UCD PID refers to Jenn's package which gives Pt-integrated probabilities as a function of rigidity. Because of the integration over Pt, this package is not used in UCD's own physics analyses of radial flow and spectra in general, and Daniel & Jenn have always made it clear that UCD PID is not intended for use beyond a limited set of analysis circumstances, and is not intended to describe Pt or Py dependence. The first five bullets on Heng's page entitled "New Analysis at 6 GeV" addresses some of the quantitative differences between a treatment that explicitly fits the dE/dx bands as a function of Pt, compared with one that averages over all Pt.

Beyond the question of Pt and Py dependence, there are indications that UCD PID has some unexpected behavior at forward rapidities at the higher beam energies. This is documented in the third bullet under 4 GeV on Heng's main page for supporting material.

The fairly close agreement between Methods III and IV indicates that the factors mentioned above under Method IV are not very serious sources of distortion or systematic uncertainty. Nevertheless, to the extent that small differences do exist, we can say that Method III has documented quantitative material to address its inherent systematic error, whereas the systematic error associated with Method IV has not been quantified. Some residual deuteron contamination could account for the small extra flow obtained from Method IV.

Note on error bars
The error bars on F in Heng's MS are dominated by systematic uncertainties. There are several contributing factors, such as:
(1) The uncertainty in defining an effective slope near midrapidity.
(2) The uncertainty arising from the assumption that <Px> is independent of Py.
(3) The uncertainty arising from tracker averaging.
(4) Uncertainties inherent in method III, as explained above.
Generally, (1) above is the biggest single factor, especially if we take a conservative approach and run through all conceivably plausible procedures to establish a local slope. The plotted error bars are consistent with a quadrature sum of the various factors, which ends up being a bit bigger than (1) alone.

Originally posted: April 27, 2000
Last Updated: May 5, 2000