1. Thomas D. Gutierrez UC Davis 1 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Bose-Einstein Correlations from pp Collisions at RHIC Thomas D. Gutierrez University of California, Davis Introduction Analysis Results Outlook UCD Nuclear Physics Seminar

2. Thomas D. Gutierrez UC Davis 2 Wednesday April 30, 2003 UCD Nuclear Physics Seminar What are Bose-Einstein Correlations? Bose-Einstein correlations (BEC) are a joint measurement of more than one boson in some variable of interest. P2 P1 L >> (d & R) d R r A1 r B1 r A2 r B2 In its simplest form, BEC often predicts an enhancement of boson coincident counts (relative to the experiment performed with non-bosons). This is usually associated with Bose-Einstein statistics. But things are rarely this simple. For example, if the variable of interest is momentum then information about the geometry of boson emission source can be obtained (more on this later) BEC often goes under the name HBT or GGLP. I’ll use HBT.

3. Thomas D. Gutierrez UC Davis 3 Wednesday April 30, 2003 UCD Nuclear Physics Seminar What is HBT? The technique was originally developed by two English astronomers Robert Hanbury-Brown and Richard Twiss (circa 1952) It’s a form of “Intensity Interferometry” -- as opposed to “regular” amplitude-level (Young or Michelson) interferometry -- and was used to measure the angular sizes of stars A quantum treatment of HBT generated much controversy and led to a revolution in quantum optics Later it was used by high energy physicists to measure source sizes of elementary particle or heavy ion collisions (the GGLP effect) But how does HBT work? And why use it instead of “regular” interferometry ?

4. Thomas D. Gutierrez UC Davis 4 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Two slit interference (between coherent sources at A and B) P1 L >> d Monochroma tic Source Plane wave d A B r A1 r B1 “source geometry”(d) is related to interference pattern (brackets indicate time average -- which is what is usually measured)

5. Thomas D. Gutierrez UC Davis 5 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Two monochromatic but incoherent sources (i.e.with random, time dependent phase) produce no interference pattern at the screen -- assuming we time-average our measurement over many fluctuations L >> d A B r A1 r B1 P1 (brackets again indicate time average) “Two slit interference” (between incoherent sources at A and B) d

6. Thomas D. Gutierrez UC Davis 6 Wednesday April 30, 2003 UCD Nuclear Physics Seminar As before... HBT Example (incoherent sources) But if we take the product before time averaging... where A B P2 P1 L >> (d & R) d R r A1 r B1 r A2 r B2 Important: The random phase terms completely dropped out. We can extract information about the source geometry!

7. Thomas D. Gutierrez UC Davis 7 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Increasing angular sizeIncreasing source size d Particle physics Astronomy Notice that the “widths” of these correlation functions are inversely related to the source geometry For fixed k A source can also be a continuous distribution rather than just points Width w source Width ~1/w Correlation function The width of the correlation function will have a similar inverse relation to the source size I’ll drop

8. Thomas D. Gutierrez UC Davis 8 Wednesday April 30, 2003 UCD Nuclear Physics Seminar More About HBT As we’ve seen, when treated with classical waves, HBT is basically just a kind of beat phenomenon When treated quantum mechanically (i.e. actually counting particles) the situation is more complex Lets define the two particle correlation function as: The density matrix in the second expression tells us two very important things: C2 is sensitive not only to the quantum statistics (determined by the commutation relations of the a and a’) but also the quantum field configuration; C2 is sensitive to the source distribution, the dynamics of the problem, as well as any space-momentum correlations

9. Thomas D. Gutierrez UC Davis 9 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Sill more about HBT C2 Q=|p 1 -p 2 |  1/R Thermal Bosons 1 2 Partly coherent bosons+thermal+contamination 0 Non-interacting fermions Two quantum field configurations of interest: coherent state (like a “laser”) and thermal state (following a Bose-Einstein distribution) Momentum difference Totally coherent Joint probability of measuring a particle at both detectors 1 and 2 Probability of measurement at 1 times probability of a measurement at 2 Measuring the correlation function is really just a counting game Note: if the two measurements are statistically independent then C2=1 Chaoticity parameter C2 is often measured as a function of the momentum difference and can often be parameterized like a Gaussian:

10. Thomas D. Gutierrez UC Davis 10 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Practicalities of HBT Interferomertry using particles in HEP Compare relative 4-momenta (Qinv) of identical particles (e.g. pions) to determine information about space-time geometry of source. Experimentally, 1D C2 correlation functions are created by comparing relative 4- momenta of pairs from a “real” event signal to pairs from “mixed” events. The mixed background presumably has no HBT signal! STAR Preliminary

11. Thomas D. Gutierrez UC Davis 11 Wednesday April 30, 2003 UCD Nuclear Physics Seminar More HBT practicalities in HEP The correlation function, C2, is created by dividing the “real” pairs by “mixed” pairs. The histogram is then normalized to the baseline. The data are fit to a Gaussian or an exponential to extract fit parameters R inv and λ. ~1/R ~λ e The Coulomb repulsion experienced by identical charged pairs tends to deplete the correlation function at low Q -- this can be corrected Both fits are to the Coulomb corrected data (dark blue) STAR Preliminary =0.397 +/- 0.013; R g =1.16 fm +/- 0.032; =0.749 +/- 0.030; R e =1.94 fm +/- 0.071 C 2g = 1 + λexp(-Q inv 2 R inv 2 ) C 2e = 1 + λexp(-Q inv R inv )

12. Thomas D. Gutierrez UC Davis 12 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Why study HBT in pp Collisions? There is a long history of doing Bose-Einstein pion correlations in elementary particle collisions In the context of RHIC, it provides a baseline for the heavy ion results Dowell., Proc. Of the VII Topical Workshop on Proton-AntiProton Collider Physics, p115, Word Scientific 1989. Lindsey. “Results from E735 at the Tevetron Proton-AntiProton Collider with root s= 1.8TeV”, Presented at the Quarkmatter 1991, Gatlinberg, Tennessee, Nov 11-15, 1991. OPAL Collaboration. Physics Letters B. Vol 267 #1, 5 September, 1991. NA22 Collaboration “Estimation of Hydrodynamical model parameters from the invariant spectrum and the Bose- Einstein Corrilations…”, Nijmegen preprint, HEN-405, Dec. 97. NA22 AMY OPAL UA1 E735 π+/p e+/e- p/pbar Just a sampling fm

13. Thomas D. Gutierrez UC Davis 13 Wednesday April 30, 2003 UCD Nuclear Physics Seminar What is HBT Actually Measuring? Quark scattering and creation PT z t   NK  Hadronization “freeze out” surface (mean) For non-static sources, HBT becomes sensitive to regions of homogeneity; this gives rise to a phase space dependence of the radii HBT radii will often be much smaller than actual hadronization surface y1 y2 In this 1D inside-out fragmentation picture, rapidity and z are correlated. Particles near each other in rapidity, will also be near each other in space. Particles close in space and momentum contribute most strongly to the HBT signal Regions of Homogeneity

14. Thomas D. Gutierrez UC Davis 14 Wednesday April 30, 2003 UCD Nuclear Physics Seminar HBT Study of the pp System HBT studies in pp interactions provide a peek into the fascinating soft- physics regime of hadronic collisions Some HBT-related questions: What do the regions of homogeneity look like? What is the pair source distribution function? How do the HBT parameters depend on event multiplicity? Do the HBT parameters depend on the polarization of the initial state (a fun idea but won’t have time to talk about it today)? This analysis is a first step in answering some of these questions

15. Thomas D. Gutierrez UC Davis 15 Wednesday April 30, 2003 UCD Nuclear Physics Seminar The STAR Experiment STAR main detector: Time Projection Chamber (a large-acceptance cylindrical detector) E field and B field along the beam direction. 12 million reversed full field and full field, minimum bias pp events at 200GeV from RHIC using the STAR detector; some data presented include only the 7 million RFF Particle identification done by measureing dE/dx (specific energy loss)

16. Thomas D. Gutierrez UC Davis 16 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Track and Event Selection (I) For negative and positive pions at two mid-rapidity ranges (-0.5<y<0.5; - 1<y<1), four kt ranges were analyzed (0.15<kt<0.25, 0.25<kt<0.35, 0.35<kt<0.45, 0.45<kt<0.65 GeV/c) Particle identification was done by taking a one sigma cut around the pion bethe- bloch curve while excluding other particles at the two sigma level. dEdx vs. P (GeV/c) similar STAR Preliminary Kt is the average PAIR transverse moment Y is the TRACK rapidity

17. Thomas D. Gutierrez UC Davis 17 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Track and Event Selection (II) Some additional cuts used for this analysis Verices accepted 3m across the STAR TPC Analysis done separately for 20cm wide regions (results then added) For the non-multiplicity dependent analyses: event Multiplicity < 30 Analysis performed separately for like-multiplicity events (results then added) Only accept events with at least 2 tracks Track level -0.5 < y < 0.5 and -1<y<1 PID cuts as discussed Primary tracks only Pair level Four kt bins between: 0.15 < kt <0.65 GeV/c anti-merging and anti-splitting cuts applied fail pass zvertex The effects of pileup in pp have not yet been studied in the context of HBT The first order effect would be to reduce the lambda factor (a pileup would act like a mixed event thus “watering down” the signal) STAR Preliminary

18. Thomas D. Gutierrez UC Davis 18 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Pair Cuts (I): Track Merging looks similar The above correlation functions are a measure of track merging (2 tracks mistaken as one) relative to a mixed background which presumably has no track merging Accept >9cm -0.5<y<0.5 -1<y<1 0.15 < kt <0.65 GeV/c for Qinv<0.2 GeV/c STAR Preliminary

19. Thomas D. Gutierrez UC Davis 19 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Pair Cuts (II): Track Splitting Accept -0.5<Quality<0.6 -0.5<y<0.5 0.15 < kt <0.65 GeV/c Qual~0 no splitting (really DO have 2 tracks) Qual=1 totally split (one track mistaken as 2) Pads with two hits are circled The above correlation function is a measure of the quality relative to a mixed background. The mixed background presumably has no splitting (high quality means more splitting) Splitting is when one track is mistaken as 2 and +/- 1 y looks similar STAR Preliminary

20. Thomas D. Gutierrez UC Davis 20 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 1D Qinv Correlation Functions (I) All fits are to the Coulomb corrected data: All plots here 0.15<kt<0.25 GeV The pi+ pi- combined over -1<y<1 will serve as the standard All STAR Preliminary

21. Thomas D. Gutierrez UC Davis 21 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 1d Qinv Correlation Functions (II) All plots here 0.15<kt<0.25 GeV; -1<y<1; pi+ and pi- The strength of this high Qinv tail depends on the kinematic cuts; The effect is currently under study The traditional Gaussian fit (black) isn’t very good; The exponential fits do much better; various parameterizations are under study All STAR Preliminary

22. Thomas D. Gutierrez UC Davis 22 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 1D Qinv Correlation Functions (III) All plots here 0.15<kt<0.25 GeV; Baseline curvature depends only very weakly on particle species and zvertex choices; depends more strongly on rapidity and kt cuts; Still a rather small effect overall The current hypothesis is that the effect is due to energy-momentum conservation Pythia pi- (no afterburner); 0.15<pt<1.1; -0.5<y<0.5; 1M events; ignore normalization; evidence of some sloping; will perform a more systematic study Qinv C2 All STAR Preliminary

23. Thomas D. Gutierrez UC Davis 23 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 1D Qinv HBT Parameters R (fm) All are from 0.15<kt<0.25 GeV; -1<y<1; pi+ and pi- Highly parameterization dependent values = bad

24. Thomas D. Gutierrez UC Davis 24 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Source Image Another interesting way to approach HBT is one can transform the correlation function to obtain the actual source numerically S is the source distribution and represents the probability of emitting a pair of particles with relative 4-momentum=Qinv separated by a distance r; S is the quantity we want to extract Thermal limit: Koonin-Pratt equation K0 is the angle averaged integration kernel and is given by is the pair wavefunction and includes all the appropriate quantum statistics and relevant interactions between the pair

25. Thomas D. Gutierrez UC Davis 25 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Source Image Qinvr (fm) Reconstructed correlation function; red is the non- Coulomb corrected input Qinv Correlation function Pair source emission function S(r); log scale Generated using Brown and Danielewicz's HBTprogs v.1.0 0.15<kt<0.25; -0.5<y<0.5; pi- Qinv ` The different colors represent different parameters in the HBTprogs program Is there a double Gaussian structure in the source function? More work needs to be done to really determine this. log(S)C2 STAR Preliminary A promising method: still a work in progress

26. Thomas D. Gutierrez UC Davis 26 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 3D Correlation Functions y x y x By looking at a 3D correlation function we can extract a more complete picture of the source.

27. Thomas D. Gutierrez UC Davis 27 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 3D Correlation Functions C 2 = N[1 + λexp(-q out 2 R out 2 -q side 2 R side 2 -q long 2 R long 2 )] Fits and correlations projected 80MeV in the “other” directions kt cut with ~0.15 GeV/c pid pt cut causes Qout “hole” out side long C2 All plots here 0.15<kt<0.25 GeV; -1<y<1; pi+ and pi- y cuts cause Qlong “cutoff” All STAR Preliminary

28. Thomas D. Gutierrez UC Davis 28 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 3D Correlation Parameters C 2 = N[1 + λexp(-q out 2 R out 2 -q side 2 R side 2 -q long 2 R long 2 )] Rout Rside Rlong 0.15<kt<0.25 GeV; -1<y<1; pi+ and pi-

29. Thomas D. Gutierrez UC Davis 29 Wednesday April 30, 2003 UCD Nuclear Physics Seminar 3D Correlation Functions: kt dependence kt R(fm) Rlong Rside Rout What causes kt dependence? STAR Preliminary Central Midcentral Peripheral AuAu 200GeV M. Lopez-Noriega QM2002

30. Thomas D. Gutierrez UC Davis 30 Wednesday April 30, 2003 UCD Nuclear Physics Seminar What Causes Kt Dependence? Rside Rout Kt = pair Pt Space momentum correlations If the source is not static or collective effects are present then space-momentum correlations can develop and cause the radii to change as you look in different locations in phase space. Some examples Inside-out fragmentation/ hadronization jets (the ultimate space-momentum correlation) fireball-like expansion collective flow Not all of these will give the same kt dependence. The trick is in distinguishing between them. This is currently under study We are looking at a region of homogeneity caused by:

31. Thomas D. Gutierrez UC Davis 31 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Multiplicity Dependence of HBT parameters It has been reported by some experiments (e.g. UA1 ppbar at 630 GeV) that lambda tends to drop with event multiplicity while the radius increases slowly Other experiments (e.g. NA27 pp at 27 GeV) report that lambda is flat as a function of event multiplicity This puzzle has numerous explanations from the mundane to the exotic. Some current speculations: All of the above would have the tendency to reduce lambda Pion emission becomes more coherent in high multiplicity events involving particle-antiparticle collisions but not particle-particle High multiplicity events from ppbar may involve multistring fragmentation -- pions from different strings will not correlate strongly Resonance contributions and other contaminates may contribute to different degrees at different multiplicities at different experiments

32. Thomas D. Gutierrez UC Davis 32 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Multiplicity dependence of 1D HBT UA1 ppbar 630 GeV (Gaussian) NA27 pp 27 GeV (Gaussian) STAR Gaussian STAR Exponential charged This preliminary STAR pp result indicates lambda is flat as a function of event multiplicity This is clearly not the case at UA1 NA27, NA23, and NA22 all reported similar results Using full RFF+FF NA27 ZPC 54,21 1992 UA1 PLB 226, 410, 1989 Low multiplicity bins (<4) have large systematic error bars -- still being studied Very Important: Not corrected for resonances or efficiency STAR Preliminary

33. Thomas D. Gutierrez UC Davis 33 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Multiplicity Dependence of 1D Radius NA27 ZPC 54,21 1992 UA1 PLB 226, 410, 1989 This preliminary STAR pp result indicates rinv is flat as a function of event multiplicity Low multiplicity bins (<4) have large systematic error bars -- still being studied Very Important: Not corrected for resonances or efficiency STAR Exponential STAR Gaussian STAR Preliminary

34. Thomas D. Gutierrez UC Davis 34 Wednesday April 30, 2003 UCD Nuclear Physics Seminar Summary Bose-Einstein correlations provide a means of probing the space-time geometry of the pion emission source in high energy collisions; The pion emission source size is ~1 fm A kt dependence is seen in the 3D HBT parameters of pp collisions indicating a pion source with space-momentum correlations; The nature of ths source is still under study Lambda and rinv are constant as a function of event multiplicity; This is consistent with other pp experiments but differ from ppbar results; The effect is still under study