Alexey Svyatkovskiy scientific advisor: M.A.Braun

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 20th Nordic Particle Physics Meeting, Spåtind, Norway, 3-7 January 2008

2. Outline • QCD: collinear factorization formulain 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 Before the collision. Initial state PDF in proton is a probability density to find a parton of sort j (or i) carrying a fraction x2 (or x1) of proton at a scale Q. PDFs are non-perturbative (soft, long distances physics) objects. Defined at the starting scale Q0, they can be obtained at any scale using (perturbative) DGLAP evolution equations. (We used GRV98 LO parameterization for our calculations.) Nuclear case: PA(x,Q2) ≠ APp(x,Q2) – EMC effects.

4. Hard scattering elements: partonic two-body subprocesses Hard scattering: high-energy limit – massless structureless particles (partons). 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=(1-4pT2/s)1/2 . In our case s>>pT2 which implies small scattering angles, cosθ→1 . and therefore t→0. QCD partonic two-body subprocesses (perturbative, LO). Computed using Feynman diagram techniques.

5. Final state: FFs After (hard) collision. Final state: Fragmentation functions: (non-perturbative, LO) probability density for a parton k produced at a scale mF to form a jet, which will finally fragments into hadron h, carrying the fraction z of the momentum of pT – 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 LQCD<< pT<<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. Starting from the expression: [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] 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 In the expressions below we have accounted for the difference in parton species and scale dependence of the partons from the projectile nucleus: Here: j = g,u,d,s; Ijk is the elementary inclusive cross-sections referring to collisions of partons j and k.

9. Double scattering term h A PA/i Dk/h k ui i xk sji sjm wj j X wm B PB/j PB/m m

10. Diagrams. (double scattering term) j Sj sji sjm = i m 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 RAA(x) = dsAA/dsoptAA Except for central region, RAA(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).

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. parton splitting parton recombination We assumed here that transition from partons into hadrons takes place at the scale mF = qT/2. Where qT – 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: <qT(x)>= <pT(x)><z>. Where <pT(x)> and <z> depend on the flavour of the fragmenting parton and on the energy of the collision. [K.J.Eskola, H.Honkanen, NPA 713(2003),167] p+p- K+ K- p pbar time Q2 ~ pT2 pT ~2-20GeV mF2 ~ q2T mF~ 1 – 2 GeV Scale:

15. Hadronic spectrum x=pparton/pnucleon– scaling variable of observed partons (here: partons coming from the projectile), z=phadron/pparton - scaling variable of hadrons, b – 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 RAA(z) was found to be substantially smaller than unity. Contrary to RAA(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)]