Comparison of yields for gamma jet

Jason produced a simple program to look at gamma-jet yields in pythia 8.1.  I modified it to look at specific solid angle regions to compare to predictions and yields in our analyses.  The code started as an example provided with the pythia code.  It is at  my rcf account ~gamJet/pythia8100/examples/main05.cc.   It compiles with >make main05.cc.  With this code I not only look at yields but the x's and flavors of the contributing partons to gamma-jet yeilds.

I divided up eta space as follows:

float min_eta_gamma = -0.9;
float max_EBMC_eta_gamma = 0.0;
float max_WBMC_eta_gamma = +1.0;
float min_EMC_eta_gamma = +1.05;
float max_eta_gamma = +2.0;

float min_eta_jet   = -0.9;
float max_EBMC_eta_jet = 0.0;
float max_WBMC_eta_jet = +1.025;
float max_eta_jet   = +1.9;
 

Then I get the following yields for 4.9pb-1 of integrated luminosity.            (calculated from pythia.statistics(); accepted/sigma = 762952/1.555e-04/1e9 = 4.9pb-1).

With pT_gamma>10 GeV and counting jets in jetfinder pT>5 GeV

drupal.star.bnl.gov/STAR/system/files/yields10GeV.gif

and pT_gamma>7 GeV

 drupal.star.bnl.gov/STAR/system/files/yield7GeV.gif

 Extracting yields for comparison to our ongoing data analyses from 2006:

I checked these made sense in two ways.  First compare to old plot from our proposal generated by Les.

drupal.star.bnl.gov/STAR/system/files/dgOverG.png

In above table I got 180k events at 320pb-1 and for gammas in endcap and jets in full acceptance including endcap.  I could not find a definitive statement about the solid angle included in the above plot but judging from the x range I believe it is just endcap gammas. 

In 1997 an NLO calculation of gamm-jet was published by Chang, Coriano and Gordon PRD 58 (1997) 074002.  arxiv.org/abs/hep-ph/9709496  They calculated cross sections and A_LL for two combinations of the jet and gamma acceptance and pT=10 GeV see figures 2a and 2b.

For figure 2a the jets are in -.5<eta_jet<0.5.   For -1<eta_gamma<1 I read off a cross section of ~200pb/GeV.  With 2 units of eta and a 1 GeV bin I get 200pb/GeVx2x1GeVx50pb-1 = 20,000 events.  I ran the pythia code with altered boundaries to match this and got 30k events (scaled again from 4.9pb-1).  Given that I took only a 1 GeV bin for the paper and didn't integrate over pT this is reasonable agreement.   In the pythia pT spectra only about 1/3 of the counts are in the first 1 GeV bin above 10 GeV.  That would give 60k estimate from the paper, or twice the pythia yield.

Similar for fig. 2b.  Here 0.5<eta_jet<1.5.  For 1<eta<gamma<2 I read off ~60pb/GeV.  For a 1GeV bin width this gives and estimate of 3000 events.  Pythia gives me 1350 events for 4.9pb-1 or 13,800 at 50 pb-1.   Using the same factor of 3 for the calculation to integrate over pT that would give 9k events, within 50% of the pythia value.  Could the differences be gluon distribution functions or more?

We will need to do further comparisons with data and full simulations of the efficiency.

 Estimates of A_LL based on statistics from above

Using the paper cited above we can make some estimates of the impact on deltaG/G and A_LL.

 Looking at the figure 2a in the above paper for central rapidity we found 30k or more events.  Combining 30K into an error on A_LL ,  dA_LL = 1/sqrt(30k)/.65/.65 = 0.014.  Comparing to figure 2c we see that we should get pretty clear discrimination between GRSV-std and GRSV=0 but not between 0 and GS-C.  This is about how well we do with current inclusive jets.   

At forward angles corresponding to figure 2b and 2d we had fewer counts, we'll pick the lower or 9k.   This gives an error dA_LL~0.025 or closer to the spacing between the A_LL curves but we will have more points vs eta_gamma.

I think this indicates we start doing something interesting at 50pb-1.  It can add meaningful confirmation of results to date in another channel.

Estimates of dG/G

We can also go on and use pythia to make estimates of dG/G precision we might get.   This is based on a writeup I made earlier: drupal.star.bnl.gov/STAR/system/files/LOanal.pdf

From the pythia analysis I have also extracted the x and id of the partons involved in the scattering that produced the events.  These are divided by approximately equal regions of deta=1, east barrel(E), west barrel(W) and endcap(C) and all combinations of gamma - jet by region are shown.

drupal.star.bnl.gov/STAR/system/files/x1x210GeV.gif

drupal.star.bnl.gov/STAR/system/files/parton10GeV.gif

 In the following spread sheet

drupal.star.bnl.gov/STAR/system/files/gammaJetALL.xls

I collected the number of gamma jets by calorimeter region pair, the average and rms x1 and x2 and the number of times the g was parton 1 or parton 2 and the number of times u or d quarks participated in qg-gamma jet.  I ignored the small numbes of events that came from other processes or other quarks (s,c,b).  I also collected a histo of cos(thtHat), not shown, and read off the typical values for each sector pair.  I used the central x value for the quarks to read off the polarization of (u+ubar) and (d+dbar) from Bourelly et al. (Eur. Phys. Jour. C41 2005 p321)   Fig. 5.   The figure is for Q^2 = 100 GeV but the evolution of g_1^p at valence values of x is pretty flat with Q^2.  With these I could calculate the avg polarization of the quarks in the qg process.  The one thing I noticed was that pythia seemed to have a smaller ration of d/u (.1-.1) than I expected and graphed in fig. 4 of the Bourelly paper.  This should be explained by the charge coupling of the q charge to the outgoing gamma.  (2/3 charge of u enhances its contribution over d which helps us.)  I have calculations of a_LL hat vs cos(tht*) from LO (t,u,s) that are basically what is in the standard figures for this.  I read those off and entered those as well.   Using the number of jets I could calculate the error bar on A_LL for each region combination as dA_LL=1/sqrt(Njets)/.65/.65.   By dividing this by the avg quark pol and the appropriate a_LL hat I could then get an error on dG/G, the pol of the quarks, for each region combo.

 Summarizing from the spread sheet:

of course these will increase by background subtraction systematic errors and be reduced by efficiencies.  Note that EW and WE are ~2/3 with x_min=x_gluon and ~1/3 x_min=x_q.

Steve Trentalange  provided me with plots of dg/G at the appropriate scales for pT=10 GeV and pT=7 GeV.

I need to do this for lower pT as well.  This will increase the number of events and decrease the x range for both the quarks and the gluons.  The former will lower the net polarization of the quarks, so there is some tradeoff.  The plot of dG/G at 40 GeV^2 is not so different as seen below.

Refs.

An extensive compilation of experimental data on photon yields was compiled by Vogelsan and Whalley in 1997,  W. Vogelsang and M.R. Whalley, J. Phys. G. 23 (1997) A1.