Measuring k T from 2-Particle Correlations

1. Measuring kT from 2-Particle Correlations Patrick Scott August 2009

2. Introduction • Jets at ALICE • Jet analysis – event by event and correlations • Initial partonic transverse momentum: the kT effect • Results: jT and kT • Conclusions: will correlations be a useful technique at ALICE?

3. Jets Classic dijet event: hard parton scattering -> coloured particle production -> fragmentation -> jets Fragmentation Dijet event from ALEPH at LEP Hard parton scattering

4. Jets at ALICE • Heavy ion • Jet quenching – one of the key signatures of quark-gluon plasma formation • p-p • Baseline measurements for heavy ion studies • QCD tests (e.g. studying fragmentation): complementary to other LHC detectors: low pT cutoff and excellent PID

5. Jet analysis Event-by-event • Conceptually simplest • Threshold energy in cone in h-f • Problems with large multiplicity: not much used at previous HI colliders (though will be at ALICE, and has been recently at RHIC) Angular correlations • Historically first method • Angular correlations between hadron pairs • Main method used at previous HI colliders • All particles included: doesn’t discriminate • Tannenbaum: “Almost everything you want to know about jets can be found from 2-particle correlations.” Here, I looked for the intrinsic parton transverse momentum kT (explained later)

6. Uncorrected Normalised Mixed Sample plots produced from MC truth jet data, 5<pTt<10 GeV and 5<pTa<10 GeV. Angular Correlations • Correlation function: • Ratio of uncorrected (real) and mixed distributions • Uncorrected: directly measured Df between “trigger” and “associated” • Mixed: Df between triggers of one event and associated of previous event – corrects for pair detection efficiency (though less important for truth data: mixed distribution ~constant)

7. Angular Correlations • Characteristic shape: near and away side peaks on ~flat background • Fit to Gaussian + Gaussian + constant • Sensitive to most jet physics apart from fragmentation function • Different pT cuts on trigger and associated • Will angular correlations be a useful technique at ALICE? Uncorrected Normalised Mixed Sample plots produced from MC truth jet data, 5<pTt<10 GeV and 5<pTa<10 GeV.

8. Initial partonic pT: kT effect ? • If parton collisions collinear with p-p axis, scattered partons would have equal pT and opposite f • Actually: initial partonic transverse momentum kT • Naively expect kT~100 MeV: size of proton • This is not observed! CCOR measured ~ GeV at ISR and even higher observed at RHIC: suggests radiative origin • Can’t explain with only NLO + intrinsic (E706 at Fermilab) kT measurements from various experiments (Apanasevich et al. 1999) dependence

9. Some more about kT • Comprised of kTy (perpendicular to scattered parton pT) and kTx (parallel): different experimental effects • kTy -> acoplanarity • kTx -> unequal partonic pT • , but : radius vector - this is what we are trying to find • Assume same distribution of kTx and kTy pTt pTa

10. Some terminology (looks complicated, but just definitions and geometry) Two partons scatter back to back in CM (seen here in plane perpendicular to beam axis) ...and at an angle in the lab frame, due to kT... ...they fragment into hadrons (here assuming zero jet width)... ...we define kTy (perpendicular to parton pT) and pout (perpendicular to hadron pT)... ...and we introduce jT (jets have width), making everything more complicated! Remember hat => parton, no hat => hadron

11. Getting kT (from PHENIX: Adler et al. 2006) From theory From correlation function Solve for kT

12. Solving for kT • RHS can be extracted directly from data and correlation function • In limit that , solving for kT is easier • This corresponds to low CM energy: CCOR method • Attempted this method here, but limit does not apply (plots below): must solve another way! Plots of zt and xh for 100 GeV jets, 5<pTt,a<10 GeV from quick MC

13. Solving for kT • As LHS is a (complicated) function of kT, analytical solution of this is difficult: solve numerically • Produced simple, quick Monte-Carlo: generates pairs of “partons,” applies pre-defined kT, produces pairs of final state particles (following appropriate pT and zt distributions, shown below)

14. Iterative solving for kT Generate large number of events, outputting mean and Insert RHS into quick MC as kT Calculate RHS Insert kT into quick MC Calculate Once kT(n) and kT(n-1) are sufficiently close, we have found kT!

15. Previous work on kT • Correlations used successfully for this purpose at PHENIX • jT independent of pTjet and √s (though probably not for arbitarily low pTjet: phase space limitation) • kT=kT(√s) Plots of jT and kT from PHENIX (Adler et al. 2006)

16. The data sample • 1700 events • LHC08q sample: • Pythia 6.214 • p-p • √s = 14 TeV • pThard > 100 GeV (pThard = minimum pTjet) • MC truth data: want to understand method as well as possible before further confusing things with reconstructed data • “Perfect detector”: included final-state charged particles over all h,f

17. Results • Preliminary! Some things left to be resolved: • Fitting correlation functions: different approaches? • Understanding systematics: at present only statistical errors included • Possible systematics: width of bins in pT, assumption of fragmentation function shape and pt distribution in simple MC • Trying with lower pThard: the one used was quite high – distorted results?

18. Correlation functions 1 5 GeV < pTa < 10 GeV Distribution 1: 5 GeV < pTt < 10 GeV Distribution 2: 10 GeV < pTt < 15 GeV Distribution 3: 15 GeV < pTt < 20 GeV

19. Correlation functions 2 10 GeV < pTa < 15 GeV Distribution 1: 5 GeV < pTt < 10 GeV Distribution 2: 10 GeV < pTt < 15 GeV Distribution 3: 15 GeV < pTt < 20 GeV Poorly fitted peak: problem with Minuit. Under investigation

20. jT results • Plotted jT against mean pTt in bin • Results fit expectations of independence of pTt and , and show agreement with PHENIX data (and in fact better agreement with CCOR, not shown here) • Fitted to constant: (PHENIX data: Adler et al. 2006)

21. kT results • Plotted kT against mean ptt in bin • Results ~constant in pTt/a (of order 34 GeV, but not fitted yet), and show clear increase over PHENIX data • Fitted to constant: • Expected ~15 GeV from min bias Pythia: communication with ALICE members and Torbjorn Sjostrand

22. So our plot from earlier… • Is this reasonable? Probably not! Expected ~15 GeV • Excluding bugs in code etc, most likely explanation is the high pThard (> 100 GeV) • This could have had the effect of increasing the kT values: higher jet pT effectively corresponds to higher √s 22

23. Conclusions • As stated previously, results are still preliminary • Results fit expectation that jT is independent of √s and show agreement with PHENIX results • Results show clear increase of kT with √s, and give a result of kT(√s = 14 TeV) = 32.0 ± GeV • Possibly influenced by high pTjet: could push kT higher. Need to repeat with lower pT jets • Errors, especially systematics, need better understanding • Once the method is polished with truth data, move on to reconstructed • Correlations are a useful method to use at ALICE!

24. Any questions? 24