Extracting A_LL and DeltaG
Determining state of beam polarization for Monte Carlo events
While Pythia does a pretty good job of simulating prompt photon production
in p+p collisions, it does not include polarization for the colliding protons
nor partons. A statistical method for assigning polarization states for each
event based on ALL [1] is demonstrated in this section.
For an average number of interactions for each unpolarized bunch crossing,
Neff, the occurence of an event with a particular polarization
state obeys a Poisson distribution with average yield of events per bunch
crossing:
For simplicity, the polarizations of the blue and yellow beams are assumed
to be PB=PY=0.7 and Neff=0.01. The "+" spin
state defines the case where both beams have the same helicities and the "-"
spin state for the case of opposite helicities. The asymmetry
ALL is calculated from the initial states polarized and unpolarized
parton distribution functions and parton-level asymmetry:
The algorithm then consists in alternatively drawing a random value
Nint from the Poisson distributions with mean μ+
and μ- until Nint>0 at which point an interaction
has occured and the event is assigned the current spin state. The functioning
of the algorithm is illustrated in Figure 1a where an input ALL=0.2
was fixed and Ntrials=500 different asymmetries were calculated.
Each trial integrated Ntotal=300 events. It is then expected that
the mean ALL~0.2 and the statistical precision~0.1:
Indeed, both the ALL and its error are reproduced. In addition,
variations on the number of events per trial were investigated
(Ntotal) in Figure 1b. The extracted width of the Gaussian
distribution for ALL is consistent with the prediction for
the error (red curve).
- ROOT macro used to generate Figure 1a SimALL.C
- ROOT macro used to generate Figure 1b SimALL2.C
Figure 1a |
Figure 1b |
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Event reconstruction
For this study, the gamma-jets Monte Carlo sample for all partonic
pT were used. As an example, the prompt photon processes
for the partonic pT bin 9-11 GeV and their total cross
sections are listed in the table below. Each partonic pT
bin was divided into 15 files each of 2000 events.
==============================================================================
I I I I
I Subprocess I Number of points I Sigma I
I I I I
I----------------------------------I----------------------------I (mb) I
I I I I
I N:o Type I Generated Tried I I
I I I I
==============================================================================
I I I I
I 0 All included subprocesses I 2000 9365 I 3.074E-06 I
I 14 f + fbar -> g + gamma I 331 1337 I 4.930E-07 I
I 18 f + fbar -> gamma + gamma I 2 8 I 1.941E-09 I
I 29 f + g -> f + gamma I 1667 8019 I 2.579E-06 I
I 114 g + g -> gamma + gamma I 0 1 I 1.191E-10 I
I 115 g + g -> g + gamma I 0 0 I 0.000E+00 I
I I I I
==============================================================================
The cross sections for the different partonic pT bins has
been tabulated by Michael Betancourt
and is reproduced here for convenience.
Partonic pT [GeV] | Cross Section [mb] |
3-4 | 0.0002962 |
4-5 | 0.0000891 |
5-7 | 0.0000494 |
7-9 | 0.0000110 |
9-11 | 0.00000314 |
11-15 | 0.00000149 |
15-25 | 0.000000317 |
25-35 | 0.00000000990 |
35-45 | 0.000000000449 |
These events were processed through the
2006 pp200 analysis chain, albeit without any cuts on the SMD.
The simulated quantities were taken from the Pythia record and the
reconstructed ones from the analysis.
Figure 2 |
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Figure 3 |
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Figure 4 |
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Figure 5 |
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Figure 6 |
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Figure 7 |
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Figure 8 |
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Figure 9 |
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Partonic kinematics reconstruction
Figure 10 |
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Figure 11 |
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Figure 12 |
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Figure 13 |
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Figure 14 |
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Figure 15 (a) |
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Figure 15 (b): quark from proton 1 (blue beam, +z direction) |
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Figure 15 (c): quark from proton 1 (blue beam, +z direction) and q + g -> q + gamma subprocess (29) |
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Figure 15 (d): quark from proton 1 (blue beam, +z direction) and q + qbar -> gamma + g subprocess (14) |
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Predictions for A_LL and direct determination of DeltaG(x)
Figure 16 (a) |
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Figure 16 (b): quark from proton 1 (blue beam, +z direction) |
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Figure 16 (c): quark from proton 1 (blue beam, +z direction) and q + g -> q + gamma subprocess (29) |
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Figure 16 (d): quark from proton 1 (blue beam, +z direction) and q + qbar -> gamma + g subprocess (14) |
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References
- Appendix Simulation Studies of Direct Photon Production at STAR
- DeltaG(x,mu^2) from jet and prompt photon production at RHIC
arXiv:hep-ph/0005320
Pibero Djawotho
Last updated Wed Jul 16 10:29:22 EDT 2008