Space-time picture of hadronic and nuclear collisions

1. From low to high energies Space-time picture of hadronic and nuclear collisions

2. collision @ alice

3. collision @ alice It is essential to understand hadronic interactions at LHC! • the structure of the underlying event • behaviour of σtot, σel and σdiff with energy... • 99,9999% of event!! • pp interactions at LHC are small AA systems? ...or else, no discovery! junk? Higgs?

4. What is a hadron/nucleus? What are the relevant degrees of freedom? How does a hadron interact with another hadron? What about nuclei? What is the difference of these interactions going from low to high energies? overview

5. hadrons, nuclei complex building blocks

6. strongly interacting composite subatomic particle • consists of quarks • baryons: 3 quarks, fermion • mesons: quark – anti-quark pair, boson • excited states - resonances • at high enough temperatures they dissolve! what is a hadron? d u u d u d u

7. strange and strong interaction q q q q q q q q • Quantum ChromoDynamics (QCD) – fundamental • calculable for short distance processes • calculable on lattice for static situations • useless for large distance physics, dynamics... • need approximations, models, ideas!

8. ”macroscopic” volumes • conditions ~early Universe • free quarks and gluons? • Quark-Gluon Plasma (QGP) nuclear physics at high energies u d u

9. need to assume • infinitesimally small cells are locally thermalized • large rate of interaction • can define temperature, energy density and pressure hydrodynamical picture Lev Landau

10. usually: particles start with an arbitrary velocity distribution • ”equilibrate” over time, maximization of entropy • take the continuum limit – loosing the concept of ”particles” thermalization

11. boost invariant initial condition, adiabatical expansion the longitudinal motion is uniform: vz=z/t gives rise to a central plateau – height independent of energy! initial energy density Bjorken initial condition

12. pictUre of a fast hadron

13. in a frame where the hadron is moving infinitely fast, it consists of infinitely many partons • the partons carry a fraction of the total momentum of the hadron each • the partons are free! feynmans (naive) parton model u d u

14. uncertainty principle! • the constituent quarks can • interact via gluon exchange • fluctuate into a quark-antiquark pair • when boosting the proton, the timescales related to these fluctuations are Lorentz dilated • interactions of quarks now take place over much larger timescales.. how can this be?

15. distribution of quarks and gluons • the probatility of finding a parton (quark, gluon, heavy quark...) with momentum fraction x of the total proton • non-perturbative quantity • but dependence on ”resolution” given by QCD • universal quantity • measured in ep collisions • can predict νp, pp etc... heavy-ion collisions at RHIC!

16. picture of a fast hadron fast partons Strong ordering from fast to slow partons: V.N. Gribov slow partons Only correlation between ”nearest neighbours”... target < < The lifetime of the fluctuation can be quite large!

17. transverse space picture • random walk in the transverse plane • each step ~1/μ • # of steps ~ln(E) • interaction range initial parton target “octopus” picture

18. picture of a fast hadron soft part of the fast hadron is not Lorentz contracted! fast partons - localized in a contracted disc slow partons - spread out on long itudinal distances at high energy the proton can become larger than a nucleus! mostly gluons at low-x:

19. from a nucleus’ point of view... • overlap of nucleons in the nucleus • huge density of gluons

20. hadron-hadron, hadron-nucleus, nucleus-nucleus collisions

21. in principle an infinite series • need to find the most important terms • single-Pomeron diagram describes existing data quite OK! • problems with the theory at high energies, eg. LHC! • need multi-Pomeron exchanges complicated problem + + + ... ... Donnachie, Landshof

22. the reggeon can be seen as an exchanged ladder of particles in the t-channel the partons take a fraction ε of the initial energy #of particles in the fluctuation: n~ln(E) Reggeon is a highly non-local object multiperipheral model Amati, Fubini, Stanghellini Gribov

23. in the center of mass frame • single-ladder exchange • a large amount of additional particles are created! • Feynman-plateau y y projectile FINAL STATE ”central plateu” target

24. 1st correction to the single-ladder exchange ”classical” rescattering picture low and intermediate energies – potential scattering multiple scattering

25. the glauber model • heavy-ion collisions • in each rescattering there is a certain probability for particle production

26. the glauber model 2RA • entropy density related to number of interactions • ”initial condition” # of collisions 2RA/γ

27. but is this picture valid at high energies?

28. at high energies, multiple ladders can start to evolve simultaneously gives rise to novel physical phenomena multiple ladder structure

29. planar diagram vanishes at high energies • ladders require a long time to develop • critical energy E0=mNμRA • the projectile goes into a fluctuation long before the collision takes place • ladders develop at the same time non-planar graphs Mandelstam Gribov

30. coherent interaction • the projectile becomes large compared to the target • interacts simultaneously with the whole system • effectively less interaction - shadowing • dramatic change of space-time picture

31. change of space-time picture + + . . . • the diagrams corresponding to ”classical” rescatterings are suppressed at high energies! • Gribov trick: Glauber is OK after all! Almost... • have to take into account diffractive intermediate states!

32. the observables don’t feel the change of space-time picture at high energy: nuclear shadowing are there any observables that are sensitive to this transition? smooth behaviour of observables |Δσ2| total σdiffractive planar diagrams non-planar E

33. cascading – enhanced diagrams Enhanced in AA collisions k A1/3 All particles with can interact. Triple-Pomeron coupling: = • quite small or quite large? • important at high energies • parton saturation!

34. interesting physics! • probing the strongest force in new domain! • evolution of partons resembles growth of bacteria colony • reaction-diffusion process • striking experimental features! what happens at lhc?

35. OUTLOOK • will large interaction of partons early on prepare a thermalized system • in AA? in pp?

37. σtot=σ(hp)+σ(hn)=2(σinel+σel)=2Sξ+Sξ2/2 impulse approximation result coherence corrections Bartels, Ryskin Z. Phys. C 76, 241 AGK ratios • Corrections: • loss of flux in the second interaction -Sξ2 • contrib to double multiplicity event -Sξ2 • contrib to double multiplicity event Sξ2 • enhancement of elastic cross section Sξ2/2 -4 2 1

39. nucleus target hadron target #particles y

40. correction factor absorption shadowing E

41. Stages of a heavy-ion collision Nuclear Geometry Parton distributionsNuclear shadowing 0 fm/c Parton production& reinteraction Chemical Freeze out &Quark Recombination 2 fm/c Jet FragmentationFunctions 7 fm/c Hadron Rescattering Thermal Freeze out &Hadron decays >7 fm/c