Addition of a potential to the Klein-Gordon equation to determine ‘fireball’ size

1. Addition of a potential to the Klein-Gordon equation to determine ‘fireball’ size HBT Pion Correlations Laniece Miller – Clarkson University Dr. Ralf Rapp – Texas A&M University, Cyclotron Institute

2. The Project My project is to look at the optical potential in the Klein-Gordon equation and attempt to determine a more exact form. Included is: • A physical overview • A look at HBT interferometry • A few details of the project • A look at where the project currently stands

3. The RHIC Experiment Au Au

4. Quark Gluon Plasma • Result from some Au-Au collisions • Restores chiral symmetry • Quarks and gluons become unbound and do not ‘know’ which nucleon they belong to • Allows other particles to form which posses a shorter lifetime

5. Current Ideas

6. What is HBT Interferometry? • Often called two particle correlation • Initially discovered by Robert Hanbury-Brown and Richard Twiss in the 1950’s • They used HBT to determine the size of stars using photons • Photons (and pion) tend to arrive in pairs, so the source size can be determined

7. HBT 1 a 2 b

8. What is HBT interferometry? • Goldhaber, Goldhaber, Lee, and Pais applied the same idea (independently) to pions • In 1960, they discovered angular correlation between identical pions

9. Determining the Radii • The ‘fireball’ is assumed to be cylindrically symmetric • Allows the number of integrals to be greatly reduced (8 to 2) • From the correlation function, the individual radii can be determined

10. Current Ideas • The standard idea has been not to include an optical potential (plane-wave) • This gives smaller radii than is experimentally observed • Recently the idea of adding an optical potential to match theoretical and experimental data better • The current optical potential possesses some other problems with parameters being inconsistent

11. Our Idea • Write code to calculate the radii and graph it • Determine parameters to get correct radii • Determine is parameters are consistent • Temperature and chemical potential were most inconsistent on the Miller model

12. Current State • At the moment we’re in the process of writing the computer code to calculate the correlation function and the resulting radii. • We ran across several issues with the code and the math slowing progress. • We are beginning to find some of the solutions to the problems we have come across so the code is beginning to make a little headway

13. Where to Now? • Get the code completely working and completely program the necessary equations • Determine a new form for the optical potential • Determine what the parameters need to be • Determine the reasonableness of the parameters • Try a new potential if the parameters are not realistic

14. References J.G. Cramer, G.A. Miller, J.M.S. Wu, J.H.Yoon, Quantum Opacity, the RHIC Hanbury Brown-Twiss Puzzle, and the Chiral Phase Transition, Phys. Rev. Left. 94, 102302 (2005)

15. Special Thanks Dr. Ralf Rapp, my mentor this summer Dr. Hendrik van Hees, Dr. Rapp’s post-doc who has spent a lot of time helping me sort out the computer code Cyclotron Institute at Texas A&M University The Department of Energy The National Science Foundation