1. Glauber shadowing at particle production in nucleus-nucleus collisions within the framework of pQCD. Alexey Svyatkovskiy scientific advisor: M.A.Braun Saint-Petersburg State University, Department of High-Energy Physics and Elementary Particle Physics. The 20 th Nordic Particle Physics Meeting, Spåtind, Norway, 3-7 January 2008

2. Outline QCD: collinear factorization formula in hard processes (nonperturbative x perturbative physics) Multiple scattering theory. (based on Glauber approach + parton model) Jet spectra: review of results (inclusive cross-sections, shadowing factors) Hadronic spectra: jet fragmentation

3. Initial state elements: PDFs PDF in proton is a probability density to find a parton of sort j (or i) carrying a fraction x 2 (or x 1 ) of proton at a scale Q. PDFs are non-perturbative (soft, long distances physics) objects. Defined at the starting scale Q 0, they can be obtained at any scale using (perturbative) DGLAP evolution equations. (We used GRV98 LO parameterization for our calculations.) Nuclear case: P A (x,Q 2 ) ≠ AP p (x,Q 2 ) – EMC effects. Before the collision. Initial state

4. Hard scattering elements: partonic two-body subprocesses Hard scattering: high-energy limit – massless structureless particles (partons). QCD partonic two-body subprocesses (perturbative, LO). Computed using Feynman diagram techniques. All possible QCD subprocesses (2 → 2) : gg → gg, gq → gq, qq → qq, qq’ → qq’, gg → qqbar, qqbar → gg, qqbar → qqbar, qqbar → q’qbar’, are taken into account. Subprocesses with no rotation in flavour space are dominant – they have singularity in t-channel. Indeed, t = -s/2(1-cosθ), where scattering angle θ is given by: cosθ=(1-4p T 2 /s) 1/2. In our case s>>p T 2 which implies small scattering angles, cosθ→1. and therefore t→0.

5. Final state: FFs After (hard) collision. Final state: Fragmentation functions: (non-perturbative, LO) probability density for a parton k produced at a scale  F to form a jet, which will finally fragments into hadron h, carrying the fraction z of the momentum of p T – parent parton. (We used KKP LO parameterization for calculations)

6. Multiple Scattering. Main assumptions. Partonic longitudinal momenta before and after collision coincide (good approximation for the region where  QCD << p T <<p || ) Factorization of nuclear S matrix into the product of elementary partonic S matrices (Glauber model; elastic, binary collisions only) QCD (collinear) factorization Medium-induced parton energy loss, initial partonic correlations, hard partons in the initial state – are phenomena not accounted for, while deriving the multiple scattering formulae

7. Multiple Scattering. Hard spectrum. [M.A.Braun, E.G.Ferreiro, C.Pajares, D.Treleani; Nucl. Phys. A 723 (2003) 249, E.Cattaruzza, D.Treleani; Phys Rev D 64 (2004) 094006] Starting from the expression: After integration over transverse momentum p and distance between interacting partons r we get: Where Is the Furier transform of the parton transverse momentum distribution in the parton – parton interaction averaged over parton scaling variable distribution of the nucleus B.

8. Multiple Scattering. Parton species Here: j = g,u,d,s; I jk is the elementary inclusive cross- sections referring to collisions of partons j and k. In the expressions below we have accounted for the difference in parton species and scale dependence of the partons from the projectile nucleus:

9. Double scattering term P A/i P B/j P B/m D k/h A h X i j k uiui wmwm B wjwj xkxk m  ji  jm

10. Diagrams. (double scattering term)  ji  jm = jj j im Diagrams for amplitudes (Glauber-like) contributing to double scattering term: +

11. Results: inclusive partonic cross- sections at a given x and centrality

12. Results: shadowing factors Except for central region, R AA (x) is considerably lower than unity for all x. The value of shadowing factors considerably grows with mass number, which is due to the change in corresponding dependence of the cross-section, which becomes proportional to A, i.e. to the number of participants (generally, such a behavior is related to the soft collisions). R AA (x) = d  AA /d  opt AA

13. Hadronic spectra: fragmentation Collinear factorization No dense medium. (no jet quenching=in medium energy loss) Fragmentation of partons coming from the projectile (recoil parton fragmentation not assumed)

14. Jet fragmentation. Q 2 ~ p T 2 p T ~2-20GeV  F 2 ~ q 2 T  F ~ 1 – 2 GeV time + -+ - K+K+ K - p pbar parton splitting parton recombination Scale: We assumed here that transition from partons into hadrons takes place at the scale  F = q T /2. Where q T – is the transverse momentum of observed hadron, which approximately depends on its scaling variable z and on the transverse momentum of the initial parton in the following way: =. Where and depend on the flavour of the fragmenting parton and on the energy of the collision. [K.J.Eskola, H.Honkanen, NPA 713(2003),167]

15. Hadronic spectrum x=p parton /p nucleon – scaling variable of observed partons (here: partons coming from the projectile), z=p hadron /p parton - scaling variable of hadrons,  – overall (nuclear) impact parameter, sum goes over all projectile parton flavours.

16. Results: shadowing factors At 200GeV hadronic shadowing appeared to be very small (of the order of magnitude of partonic shadowing). At 5500GeV factor R AA (z) was found to be substantially smaller than unity. Contrary to R AA (x) for jets it showed nontrivial scaling variable dependence. It can be explained by the change in the relative contributions to the fragmentation of quark and gluon jets as x changes.

17. Conclusions The influence of multiple hard parton rescatterings on jet and particle production is investigated. Calculations showed, that the effect of Glauber shadowing which suppresses particle production via multiple parton rescatterings within the nucleus is an important phenomenon at the LHC energy. [For more details see: M.A.Braun, A.V.Svyatkovskiy, Phys. At. Nucl. (to be published)]