Renee has suggested it would be good to get a scan of samples with a few different primordial k_T values. I have produced "high statistics" samples in bins of partonic p_T with primordial k_T of 2, 1.5, 1, and 0.5 GeV/c. For each I have calculated independent sets of fudge factors utilizing the fit function developed for the embedding sample:

• For partonic p_T < 35 GeV/c: c₀ / p_T^c₁
• For partonic p_T > 35 GeV/c: c₀×exp(c₁×p_T)

The fudge factors are calculated such that the 75-∞ GeV/c bin is defined to be unity. My expectation would be that the fudge factors should be independent of primordial k_T.

Figure 1

In Fig. 1 I show the k_T = 2 GeV/c partonic p_T spectra before reweighting and after reweighting. In each case, I show the results for the fits to individual bins of partonic p_T. For the reweighted spectra I have corrected for the generated luminosities, applied the fudge factors, and factored out the p_T bin width.

Table 1: Fudge Factors

In Table 1 I post the fudge factors calculated for the various samples and bins of partonic p_T. For primordial kT between 1 and 2 GeV/c, the numbers are fairly consistent, very slowly decreasing as one moves lower in partonic p_T before dipping for the lowest bins. In the k_T = 0.5 sample, the trend is a bit different, rising to about 1.2 by moderate partonic p_T before tapering low at low partinic p_T. It is not clear to me this is sensible. Thus, for the following, I utilize the fudge factors calculated for the particular bins, save the k_T = 0.5 GeV/c sample, where I also utilize those calculated for the k_T = 1 GeV/c sample.

Figure 2

kT = 2 GeV/c	kT = 1.5 GeV/c
kT = 1 GeV/c	kT = 0.5 GeV/c

In Fig. 1 I overlay the parton jet and particle jet cross sections from PYTHIA with the jet cross section from NLO pQCD, as calcualted by Zilong. The cross section is calculated across a consistent bin width from that of the data and plotted at the bin center, as are the data. Thus, L-W issues should be completely removed. In this case, I have used the k_T = 1 GeV/c fudge factors for both the k_T = 1 GeV/c and k_T = 0.5 GeV/c samples. One can see that in general the shapes match quite well at high jet p_T. At low p_T, particle jets are enhanced relative to parton jets and NLO.

Figure 3

kT = 2 GeV/c	kT = 1.5 GeV/c
kT = 1 GeV/c	kT = 0.5 GeV/c

In Fig. 3 I show the ratios of PYTHIA to NLO pQCD for the different samples of primordial k_T. Again, I use the k_T = 1 GeV/c fudge factors for both k_T = 1 GeV/c and k_T = 0.5 GeV/c samples. One can much more clearly see a divergence from NLO for both particle jets and parton jets for k_T = 2 and 1.5 GeV/c. For the k_T = 1 samples the parton jet cross section is rather close to NLO pQCD, while the k_T = 0.5 GeV/c sample appears to undershoot NLO. In all cases, the particle jet cross sections are enhanced relative to NLO at low jet p_T. This is qualitatively quite similar to that observed by Pibero in the 200 GeV PYTHIA sample. If it is indeed real, this could account for a portion of the low-p_T JP0 enhancement relative to the data I see in the embedding and possibly also the high-p_T divergence seen for several years, now, in both 200 and 500 GeV.

Figure 4

kT = 0.5 GeV/c with kT = 0.5 GeV/c FFs	kT = 0.5 GeV/c with kT = 1 GeV/c FFs

In Fig. 4 I compare PYTHIA/NLO for the k_T = 0.5 GeV/c sample using the independently calculated FFs for the k_T = 0.5 GeV/c sample vs. using those of the k_T = 1 GeV/c sample. The shapes are qualitatively similar, e.g., low-pT enhancement for particle jets. Using the 0.5 GeV FFs there appears to be a vertical offset ~+10% and a bit of an enhancement in the low-p_T, particle-jet divergence relative to the 1 GeV/c FF sample. The 1 GeV/c FF sample seems more consistent with the big picture in Fig. 3, thus, I am inclined to believe the 1 GeV/c FFs are more realistic. This opinion should be taken with a heaping tablespoon of salt.

Table 2: k_T = 2 GeV/c Fudge Factors for Different Fit Functions

Pibero used a different fit function to calculate the fudge factors for the 200 GeV embedding. As a sanity check, I have also recalculated the fudge factors for the k_T = 2 GeV/c sample using Pibero's fit function (exp(pol2)). A comparison is shown in Table 2. The fudge factors differ by ~10% from 2-9 GeV/c and ~5% for partonic p_T > 9 GeV/c (save the highest bin defined to be 1). In general, my current fit procedure gives a better fit probability above 7 GeV/c. Below this, Pibero's fit function has more parameters so that for the current binning, the χ² probability does not really apply. If I adopt a hybrid strategy of Pibero's function below 7 GeV/c and mine above, I find, in order of the low bins to high bins, the following new fudge factors: 0.585, 0.835, 0.937, and 0.973 (different by 6%, 3.7%, 2.8%, and 2.5% compared to my previous values). I conclude this will not make a qualitative difference from the current version.