1. 1 Measuring the Size of Subatomic Collisions Thomas D. Gutierrez University of California, Davis November 25, 2002 What Physicists Do Department of Physics and Astronomy Sonoma State University

2. 2 http://particleadventure.org Hadrons = Made of quarks Meson = qq  + = ud K + = us “A neutron is a dud…” Baryon = qqq p = uud n = dud Particle Physics at a Glance Free quarks have never been observed! This is interesting and strange… Quarks knocked loose during a collision quickly form bound states through a process called “ hadronization ”...

3. 3 “Hadronization of the universe” occurred here Particle Accelerators allow us to study aspects of the early universe in the lab

4. 4 Perspectives on Temperature ~10 -6 K ~3 K ~300 K ~6000 K ~10 6 K ~10 12 K ~ 120 MeV Trapped Ions Cosmic Microwave Background Room Temperature ~ 1/40 eV Solar Surface Solar Interior ~10 9 K Neutron Star Thermonuclear Explosion ~10 -10 K Rhodium metal spin cooling (2000) (Low-T World Record!) (Terrestrial Nuclear explosions) ~10 7 K Graphic courtesy JLK Nucleus-Nucleus collisions

5. 5 Nuclear Collisions in Action “Projectile” “Target” Baryons (p,n, , ,…) Mesons ( ,K, , ,…) Particle Key Note the length contraction of the nuclei along the direction of motion! This is because v~c

6. 6 Proton-proton (pp) collisions are the simplest case of nucleus-nucleus (AA) collisions... This is akin to colliding blocks of ice to study the phase diagram of water! pp collisions form the “baseline” for AA collisions “AA” is used to evoke the image of “Atomic Number” …and by colliding nuclei, the bulk properties of nuclear matter can be studied under extreme conditions... Collisions fling normal nuclear matter into exotic states “material science” Density of the system compared to normal nuclear density (0.13/fm 3 ) High energy pp collisions tend to be somewhere in here Why study proton-proton and nucleus-nucleus collisions at all?

7. 7 Why collide protons at all? While AA collisions probe the material science of nuclear matter (phase diagrams, etc.) pp collisions more directly probe hadronization The Relativistic Heavy Ion Collider (RHIC) on Long Island, NY slams gold nuclei head-on at 0.99995c, creating “little Big Bangs”! But why is that? Let’s look at two situations

8. 8 1. Space-Time Evolution of High Energy Nucleus-Nucleus Collision Quark Formation & creation ~ 1fm/c QGP PT Mixed Phase Hadron Gas NK    Thermal Freeze-out z t Projectile Fragmentation Region Lots of stuff happens between when the hadrons are formed and when they fly off to be detected Hadronization

9. 9 2. Space-Time Evolution of proton-proton Collision Quark scattering and creation PT z t   NK  Because the system size is so small, there are very few interactions from the moment of impact to when particles are free-streaming towards the detector That’s why pp collisions are a cleaner probe of what is going on during hadronization Measuring the extent of this “space-time surface of hadronization” is what is meant by the “size of the collision” Hadronization

10. 10 Why measure the size of pp collisions? Measuring the size of pp collisions gives information about what the collision looked like when the hadrons were created -- this gives us insight into the mysterious process of “hadronization” Source sizes are measured using a technique called Hanbury-Brown Twiss Intensity Interferometry (or just HBT for short) HOW do you measure the size?

11. 11 What is HBT? The technique was originally developed by two English astronomers Robert Hanbury-Brown and Richard Twiss (circa 1952) (Sadly, RHB passed away in January of this year) It’s 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 (photons can act strangely!) Later it was used by high energy physicists to measure source sizes of elementary particle or heavy ion collisions But how does HBT work? And why use it instead of “regular” interferometry ?

12. 12 L >> d Monochromatic Source Plane wave d Two slit interference (between coherent sources at A and B) A B r A1 r B1 P1 “source geometry” is related to interference pattern (brackets indicate time average -- which is what is usually measured)

13. 13 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

14. 14 Average of I over a very short time What does mean? Average of I over a medium timeAverage of I over a fairly long time Long/Short compared to what? The time scale of the random fluctuations Position on the screen in radians (for small angles) For very long time averages we get

15. 15 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 and left us with a non-constant expression! (will be related to source and detector geometry) Difference of the path length differences

16. 16 This quantity is known as a correlation function It is important to note that for coherent sources (remembering in that case =I) Time average of the product Product of the time averages so C=1

17. 17 What does C mean? It’s not exactly the usual “statistical correlation function”… but it is related I1I1 I2I2 If I 1 and I 2 tend to increase together beyond their averages over the fluctuation times... This gives a big correlation A plot of I 1 *I 2 with the I’s treated as variables If we independently monitor the intensity as a function of time at two points on the screen... If either I 1 or I 2 (or both) tend to be below their averages or are near zero over the fluctuation times… the correlation tends towards zero If I 1 and I 2 both tend to stick around their individual averages over the fluctuation times… the correlation tends towards one

18. 18 For two incoherent point sources…. If R>>d (like an elementary particle experiment): 2121 ˆˆ ~)(kkkdrrk  If d>>R (like an astronomy experiment): Two interesting limits (with a “little” algebra)... The momentum difference is called: Recall

19. 19 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

20. 20 What I just described was HBT for classical waves In this sense, you can do HBT with sound waves, water waves, and radio waves But how to interpret the HBT result for particles where the waves involved are quantum mechanical probability amplitudes?

21. 21 Bosons and Fermions Bosons are integer spin particles. Identical Bosons have a symmetric two particle wave function -- any number may occupy a given quantum state... Fermions are half-integer spin particles. Identical Fermions have an antisymmetric wave function -- only one particle may occupy a quantum state Photons and pions are examples of Bosons Protons and electrons are examples of Fermions The HBT effect at the quantum level is deeply related to what kind of particle we are working with

22. 22 More about Correlation functions At the quantum level a non-constant C(Q) arises because of I) the symmetry of the two- particle wave function for identical bosons or fermions and II) the kind of “statistics” particles of a particular type obey The correlation function for Gaussian source distributions can be parameterized like: Chaoticity parameter Joint probability of measuring a particle at both detectors 1 and 2 Probability of measurement at 1 times probability of a measurement at 2 At the quantum level: A series of independent events should give C=1 (same as a coherent source) Momentum difference C Q=|p 1 -p 2 |  1/R Thermal Bosons 1 2 Partly coherent bosons+contamination 0 Fermions Coherent sources (like lasers) are flat for all Q Fermions exhibit anticorrelation

23. 23 HBT Summary and Observations The correlation function contains information about the source geometry The width of the correlation function goes like 1/(source width) The HBT correlation function is insensitive to random phases that would normally destroy “regular” interference patterns

24. 24 Back to pp Collisions Pions (also bosons) are used in the HBT rather than photons Basic idea is the same: Correlation function contains information about pion emission source size in the collision and may give clues about the nature of hadronization

25. 25 Practicalities of HBT Interferomertry using particles Compares relative momenta of identical particles to determine information about space-time geometry of source. Experimentally, 1D Qinv 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

26. 26 More HBT practicalities The correlation function, “C 2 ”, 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 C 2g = 1 + λexp(-q inv 2 R inv 2 ) or an exponential C 2e = 1 + λexp(-q inv R inv ) to extract fit parameters R inv and λ. lambda_g=0.397 +/- 0.013; R_g=1.16 fm +/- 0.032; lambda_e=0.749 +/- 0.030; R_e=1.94 fm +/- 0.071 ~1/R ~λ The Coulomb repulsion experienced by 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

27. 27 C(Q) Q (MeV/c) NA44 at CERN NPA610 240 (96) From Craig Ogilvie(2 Dec 1998) Typical AA Data This isn’t my analysis C is narrower so R is bigger Just for comparison... R really increases with system size!

28. 28 What have we learned? Boffin: A Personal Story of the Early Days of Radar, Radio Astronomy, and Quantum Optics R. Hanbury Brown Intensity Interferometry R. Hanbury-Brown Quantum Optics Scully and Zubairy Quantum Theory of Light Loudon Two-Particle Correlations in Relativistic Heavy Ion Collisions Heinz and Jacak, nucl-th/9902020 More reading for the interested viewer... Lots more interesting work to be done! pp collisions are smaller than AA collisions! Measuring the size of subatomic and nuclear collisions using HBT can be subtle and fun and interesting Quark hadronization is complicated but studying the size of proton-proton collisions using HBT may be able to tell us something about it; Still a lot to learn == perhaps the subject of another talk I guess we expected this :)