An Introduction to the Thesis Topic of Janus Schmidt-Sørensen at the

1. An Introduction to the Thesis Topic of Janus Schmidt-Sørensen at the Department of PhysicsLund University W.A. Zajc

2. Central Truths of Nuclear Physics • We are nothing • We are dust • We don’t matter W.A. Zajc

3. We are nothing (c. 1900) Atom Nucleus (“ion” when alone) Key Proton Neutron Quarks Held together by gluons (not shown) Most of “us” is (nearly) empty space • 99.9% of the mass of atoms is contained in the nucleus • The nucleus is about one-trillionth ( 1/1,000,000,000,000 ) the size of the atom W.A. Zajc

4. We are dust (c. 1950) • Only the lightest elements (Hydrogen and Helium) were created in the Big Bang • The rest of “us” is stardust • All heavy elements (like the Carbon and Nitrogen we’re made of) were “cooked” together inside stars • Explosions of those (early) stars spread the heavier elements throughout the universe. W.A. Zajc

5. We don’t matter (c. 2000) • More accurately: We’re not matter • Recall nearly all the mass of each atom is concentrated in the nucleus: • Each nucleus consists of neutrons and protons • Each neutron and proton consists of 3 quarks • Each quark has the mass of about 1% of a proton or neutron(!) • The rest of the mass of protons and neutrons (and hence our mass) is “frozen energy” from the Big Bang W.A. Zajc

6. Phase Transitions • The “great freeze” took place about 10 millionths of a second after the Big Bang • General name for such phenomena:Phase transition Examples: • Steam to water to ice • (Free quarks and gluons) to (protons and neutrons) to (??) W.A. Zajc

7. Phase Diagrams Water Nuclear Matter W.A. Zajc

8. Boiling Neutrons and Protons • Fundamental Method: Collide heavy nuclei at the highest possible energies: • Fundamental Goals: • Create (new) dense forms of matter • Re-create the quark-gluon phase transition W.A. Zajc

9. Measuring Phase Space • Recall the phase diagram axes were Temperature and Density: • Temperature: “How hot is the system ?” about the same as “What energy are the particles?” • Density: “How dense is the system?”is (inversely) equivalent to “How spread out is the system?” • The “spread” of the system may be measured bytwo-particle correlations W.A. Zajc

10. Particle Correlations Imagine the break-up of a large crowd (nuclear collision) • Most people (particles) leave singly • Some leave as correlated pairs • The correlation depends on • The strength of the attraction between people (particles) • The density of attractive partners • The size of the crowd (collision) W.A. Zajc

11. Bose Correlations • Some correlations depend on (complicated) interactions between particles: Example: Coalescence of protons and neutrons to deuterons • Other correlations depend on fundamental properties of the particles: • Fermions: Can’t be in identical states (Fermi-Dirac statistics) • Bosons : Prefer to be in identical states (Bose-Einstein statistics) Caveat: Indeed, any problem which calls for the relevantapplication of Bose-Einstein or Fermi-Dirac statistics in principle excludes pictorial illustration. (Niels Bohr) W.A. Zajc

12. An Invocation • There is a connection (not even an analogy) between stellar HBT measurements and “HBT” in heavy ion collisions: • In particular, the geometry of a collision is not a scale model of imaging a star W.A. Zajc

13. An Inspiration • The usual “derivation” is really more inspiration: • Neglects • Momentum dependence of source • Quantum mechanicsup to x and y • Final State Interactionsafter x and y • Nonetheless • C2(q) contains shape information • True component-by-component in q W.A. Zajc

14. Extension to Three Pions The formalism extends readily to three particles: • Let • Then • Notes: • Limiting value for 3 pions at q=0 is 3! • Last term is the “true” three-particle effect: • Other terms are just parts of the respective two-particle correlation functions • It is in principle sensitive to a global phase present when W.A. Zajc

15. This Thesis • A study of three-pion correlations in • S+Pb • Pb+Pb collisions at the CERN SPS • Investigations of: • Reductions of intercept • Coulomb • Resonances • Coherence • Search for true 3-bodyeffect W.A. Zajc

16. Coulomb Effects • As q  0, Coulomb repulsion becomes important: • “Easy” to parameterize for 2 particles from a point source: • “Less easy” when source has a non-zero spatial extent • No simple results for the 3-body case • This thesis: an investigation of extensions to 3, 4, 5 bodies W.A. Zajc

17. Other Effects S-Pb • Resonances: • Reduce q=0 intercept due to decays of o, h , etc. “far” from “true” source • Larger effective source • (Unresolved) structure at very small q • Lowered intercept • Parameterize in terms of “core fraction” fC • Coherence: • (Implicit) assumption of random phasesin standard derivation • Coherent emission would lead to no enhancement • Parameterize in terms of “coherent fraction” p This thesis: Study of interplay between these two effects. Pb-Pb W.A. Zajc

18. True Three-Particle Effect • (Assuming other effects understood) • Can look for “global phase” from • This thesis: • Study of W.A. Zajc