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Determining Centrality at PHENIX

Determining Centrality at PHENIX. Ali Hanks Journal Club November 21, 2005. Outline. Why is centrality important? The ZDC detector The BBC detector Glauber Model Negative Binomial Distrbution (NBD) Putting it all together. A few familiar examples.

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Determining Centrality at PHENIX

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  1. Determining Centrality at PHENIX Ali Hanks Journal Club November 21, 2005 Ali Hanks - Journal Club

  2. Outline • Why is centrality important? • The ZDC detector • The BBC detector • Glauber Model • Negative Binomial Distrbution (NBD) • Putting it all together Ali Hanks - Journal Club

  3. A few familiar examples • Many things we measure depend on centrality • RAA (Jaimin) • ET and Nch => energy density P.R. C71, 034908 Ali Hanks - Journal Club

  4. The ZDC detector Ali Hanks - Journal Club

  5. RING ID BBC • inner ring • middlering • outer ring BBC R-direction Collision point beam pipe Z-direction The BBC detector Ali Hanks - Journal Club

  6. p+p (Run3) d+Au (Run3) Au+Au (Run4) BBC Charge Sum • BBC charge sum is related to number of participant • It has also anti-correlation with ZDC energy sum. participants go into BBC spectator go into ZDC Ali Hanks - Journal Club

  7. The Glauber Model • Nucleons are distributed according to a density function (e.g. Woods-Saxon) • Nucleons travel in straight lines and are not deflected as they pass through the other nucleus • Nucleons interact according to the inelastic cross sectionsNN measured in pp collisions, even after interacting • Participants – counts nucleons which interact • Binary collisions – counts collisions nucl-th/0112039; (Lectures in the theoretical physics, ed. W. E. Brittin, L. G. Dunham, Interscience, N. Y., 1959, v. 1, p. 315.) Ali Hanks - Journal Club

  8. The Woods-Saxon density function Electron Scattering Measurements H. DeVries, C.W. De Jager, C. DeVries, 1987 Ali Hanks - Journal Club

  9. Some details Probability of a nucleon-nucleon collision occuring at impact parameter b Probability of finding a nucleon at a certain b and z in the nucleus Probability for a nucleon-nucleon collision occurring when nuclei A and B are at a relative impact parameter b Probability of n collisions occuring where Ali Hanks - Journal Club

  10. Npart & Ncoll from Glauber So the probability of having  participants in nucleus A is: the probability no nucleons collide = So the total averages for a nucleus-nucleus collision at an impact parameter b are: and the average is: Ali Hanks - Journal Club

  11. What do we do? • Monte-Carlo Glauber model (MCG) • Generate events with range of impact perameters using Glauber • Divide these events into centrality classes and get a table like this • How do we get back to real data? • Remember the BBC count can be related to Npart … but how? Ali Hanks - Journal Club

  12. NBD NBD distributions scaled with Glauber probabilities Measured BBC count for fixed number of PC1 hits • The Negative Binomial Distribution (NBD) is given by: • P(n,,k) = (n+k)/((k)n!)·(/k)n/(1+/k)n+k where (/)2 = 1/k + 1/ give the width of the distribution • Assuming Nhits~ Npart =>  ~ Npart • Assuming all hits are uncorrelated => k ~ Npart Ali Hanks - Journal Club

  13. Fitting the BBC distribution • for Nhit  50 the trigger efficiency can assumed equal to 1 • P(Nhit) = (Nhit)NpartNBD(Npart,,k)xMCG(Npart) • Use fit to extract NBD parameters:  and k • Now we have a relationship between Npart and the actual Nnit in the BBC Ali Hanks - Journal Club

  14. Trigger Efficiency • The last thing is to see how efficiently the BBC is tagging collisions • Integrating this efficiency function gives the total trigger efficiency ~ 94% in Au-Au collisions Ali Hanks - Journal Club

  15. Centrality Bins • Each color corresponds to a centrality bin • The bins are just percentage of total area under the curve • This gives Nhit in the given bin • Use the NBD/MCG fit to relate this to <Npart> from the Glauber model • Can we do better? • Recall that the efficiency get low for very periferal events (low Nhit) • The ZDC can help us Ali Hanks - Journal Club

  16. 15-20% 10-15% 5-10% 0-5% 0-5% BBC vs ZDC • Centrality bins are again determined as a function of the total geometric cross section • Relating these bins to Npart is a little tricky now • Use detector response simulations to match data and determine Npart • Similar to NBD but complicated by ZDC Ali Hanks - Journal Club

  17. Bibliography • S.S. Adler et al, PRC 71, 034908 (2005) • Analysis Note 210 • Analysis Note 461 • P. Shukla, nucl-th/0112039 Ali Hanks - Journal Club

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