1. Direct photons and jet correlations in heavy ion collisions Andrew Adare University of Colorado For the PHENIX Collaboration WWND, February 2007

2. Andrew Adare - WWND 2007 2 Outline Motivation: how direct photon-jet correlations could improve knowledge of energy loss over R AA Expectations Analysis techniques –correlations and per-trigger yields –calculating  decay -h from  0 -h –subtraction method cross-checks and refinements results

3. Andrew Adare - WWND 2007 3 The QGP is opaque to hadrons RHIC measurements indicate that the quark- gluon plasma Is strongly interacting and flows like an ideal fluid, not a gas of hadrons. Suppresses jet yields and modifies their shapes Suppression/energy loss depends on the path length traversed. Particles produced near the surface have lower energy loss probabilities.

4. Andrew Adare - WWND 2007 4 Measuring suppressed yields  0,  from quark and gluon jets High-p T hadrons are suppressed by a factor of 5 relative to scaled- up p-p collisions. But photons are unaffected! Nuclear modification factor R AA : Yield (nuclear collisions) Yield (binary scaled pp collisions) =

5. Andrew Adare - WWND 2007 5 Shortcomings of R AA Measurement of R AA is impressive, and is an important step towards quantifying QGP properties. However, single-particle suppression does not effectively constrain detailed energy-loss pictures. T. Renk Need a tool to measure energy loss in the medium with more discriminating power than R AA.

6. Andrew Adare - WWND 2007 6 Promising solution: direct  -jets qg Calibrated probe of the QGP – at LO, E T,  = Pre-quenched E T,jet No Surface Bias – clearer picture of jet fragmentation modification Hard process – pQCD calcs agree well with data  has no E- loss in medium! Size of medium  But D(z) is effectively softened in opposing jet

7. Andrew Adare - WWND 2007 7 Assume two photon sources, (  = # photons in data sample): Measuring direct  -jet yields (I)  p T =5-7 GeV/c  p T =9-12 GeV/c Direct photons: -- LO pQCD (compton, annihilation,…) -- NLO pQCD (bremsstrahlung, fragmentation) -- Jet-thermal photons (See Takao’s talk…) Hadronic decay photons:    2    2   each  ’  decay 00  Cu+Cu:

8. Andrew Adare - WWND 2007 8 Expectations:  direct -h ± in PYTHIA High p T direct  -h: On near side, only NLO  s contribute. But at high p T, NLO contribution is small. Expectation: The near-side peak in direct  -jet correlations should be small! In p+p, away side yield ~ half that of   -h. p T  = 9-12 GeV/c, p T h =3-5 GeV/c  from  – h +/-  direct – h +/- PYTHIA 6.205, 200 GeV p+p, = 2.5 GeV/c

9. Andrew Adare - WWND 2007 9 Assume two photon sources, (  = # photons in data sample): Let Y = per-trigger conditional jet pair yield (1/N trig )dN pairs /d(  ): Write in terms of R   Measuring direct  -jet yields (II) Requires 3 components

10. Andrew Adare - WWND 2007 10 Component 1 of 3:  incl -h +/- Angular correlation technique: ID a high-p T  “trigger” particle in an event Measure distribution of  angles between trigger and h +/- associated particles in same event Measure  for mixed events. Ratio is C(  ): correlation functions:

11. Andrew Adare - WWND 2007 11 Component 1 of 3:  incl -h +/- per-trigger jet pair yields:

12. Andrew Adare - WWND 2007 12 We expect that the proportion of direct photons is enhanced as the size of the medium increases. If two different systems (e.g. Central Cu+Cu and mid-central Au+Au) suppress  0 s (and  s) by the same amount, then they should have comparable R  values. Component 2 of 3: “double ratio” R  Recall  0 R AA in Au+Au and Cu+Cu

13. Andrew Adare - WWND 2007 13 Component 2 of 3: “double ratio” R  Double ratio R  measured in AuAu, but not yet in CuCu… Use scaling to map AuAu R   CuCu. We will refer to the quantity “(  direct /  decay ) Au+Au interp. ”

14. Andrew Adare - WWND 2007 14 Component 3 of 3:  decay -h +/- correlation functions: Note: assuming    decay here

15. Andrew Adare - WWND 2007 15 Component 3 of 3:  decay -h +/- per-trigger jet pair yields:

16. Andrew Adare - WWND 2007 16 Each  0 has some probability to decay into a photon in a p T  range.  prob. to decay a  0 into a 9- 12 GeV/c  as a function of  0 p T.  decay -jet yields from  0 jets Prob(     ), 9<p T  <12 kinematically forbidden Each measured  0 – h pair is weighted by this  0   decay probability to give the  decay – h correlations.

17. Andrew Adare - WWND 2007 17 Weighted  0 vs.  from  in PYTHIA Black: PYTHIA “true” decay   -h PTY Red: PYTHIA pair-weighted   -h PTY Trigger p T : 5-7 7-9 9-12 h p T : 1-2 3-5 The weighting method closely reproduces the true   -h +/- correlations:

18. Andrew Adare - WWND 2007 18 We can test principles of the analysis method with Monte Carlo: Does the subtraction formula work? Calculating  decay -h jet correlations from  0 -h: what effects must be accounted for? Cross-checking with simulations energy smearing perfect detector EMCal energy resolution  and other decays decay angle smearing  from  – h +/-  decay – h +/- 9-12 x 2-5

19. Andrew Adare - WWND 2007 19 Full test of method in PYTHIA Black: correlations with “true” direct photon triggers (ID’ed in event record) Blue: direct photon correlations produced by subtraction method The bias toward a low jet yield is worse for lower p T photon triggers, where R is smaller. If one increases R by ~10%, the “true” correlation is roughly recovered. We use this 10% to gauge the systematic error from the subtraction method. Magenta: direct  -jet per-trigger yield, subtraction method as above, but with R  scaled up by 10% R  = 1.90 R  = 1.1*1.90 *Please note: This bias is due to the method, not uncertainty in R  ! We are currently working hard to reduce this systematic error. Direct  -h pairs/trigger

20. Andrew Adare - WWND 2007 20 Preliminary Cu+Cu Results: direct  -h +/- per-trigger jet pair yields: systematic from R  systematic from subtraction method

21. Andrew Adare - WWND 2007 21 Cu+Cu  direct -h +/- vs.   -h +/- jet yields per-trigger jet pair yields: systematic from R  systematic from subtraction method

22. Andrew Adare - WWND 2007 22 200 GeV p+p direct  -jet results Near side consistent with expectations Away side peak visible, but systematics are probably underestimated.

23. Andrew Adare - WWND 2007 23 200 GeV Au+Au direct  -jet results Both near and away side yields appear consistent with 0 But again, systematic errors need improvement….

24. Andrew Adare - WWND 2007 24 Summary Correlations involving direct photons are an important probe of energy loss and fragmentation function modification in the QGP. Subtraction method shows promise, but current measurements don’t yet deliver good resolution. Expectations seem to be matched on the near side, where we see ~no signal compared to  0 -h for example. These are early results: reduction in systematic errors still needed to make strong statements about away-side jet yields. Stay tuned!

25. Andrew Adare - WWND 2007 25 Backups

26. Andrew Adare - WWND 2007 26  0  2  phase space is flat Consider sample of many  0 s, all with the same p T  : pTpT decay  prob. density (proportional to dN  /dp T  ) pTpT 2/p T  Normalization requirement of prob. density fn. means prob. to get a photon at p T  drops like 2/p T  as p T  increases. Therefore, dN  /dp T  = 2/p T  In reality, dN/dE  is what is truly flat, but we assume dN/dp T  is also flat at midrapidity. *A more mathematical way to get dN  /dp T  = 2/p T   is to boost isotropic decay into lab frame.

27. Andrew Adare - WWND 2007 27 Photons from  0 s Number of photons in bin p1<p T  <p2 from the  0 bin: Two cases: 1.  0 s are in same p T bin as photons 2.  0 s are in higher p T bin than photons

28. Andrew Adare - WWND 2007 28 Weighting curves for pi0 decay probability Using analytic form: Decay probabilities above are combined with falling pi0 spectrum to give the decay photon “spectra”. The decay gamma-h PTY is independent of the normalization, since both the pairs and triggers are applied the same weight. Each pi0-h pair gets weighted by these 3 curves to produce the decay gamma-h correlation for the appropriate photon pT bin. 5<p T  <7 7<p T  <9 9<p T  <12 measured pi0 spectrum, centrality 0-20%   “spectra”. Integral = #   triggers