Quarkonium Production in Nucleus-Nucleus Collisions

1. Quarkonium working group – 2nd Workshop on Quarkonium September 20-22, 2003 at FNAL Quarkonium Production in Nucleus-Nucleus Collisions Jianwei Qiu Iowa State University Based on work done with G. Sterman; X.F. Zhang and J.P. Vary; and others. Jianwei Qiu

2. Hadronic Production of J/ψ Mesons • Process: • Parton model picture: • Energy exchange: • J/Ψ is unlikely to be formed at: Jianwei Qiu

3. Production of cc pairs • Energy exchange is much larger than 1/fm • Spectators are “frozen” during the hard collision • Their interactions are suppressed • Cross section is factorized: Plus power corrections in 1/(QR) • The debate is on the transition from the cc state to a J/Ψ meson state Jianwei Qiu

4. Transition from cc to J/Ψ Q2 • Large phase space available for gluon radiation: • Large possible velocity in production: • Very different from decay: Jianwei Qiu

5. Production models • Total cross section: Plus states with more than two gluons • Differential cross section at high qT: Plus states with more than two gluons • Models  Different transition distributions: (Qiu and Sterman) Jianwei Qiu

6. Color Evaporation Model (CEM) • Transition distribution • vanishes above the open charm threshold • independent of pair’s mass and color, and • is a constant • Cross section and its energy dependence are very sensitive to the mass of charm quark Q2 Jianwei Qiu

7. Non-relativistic QCD (NRQCD) model • Transition distribution • is a narrowly peaked distribution • velocity expansion is valid • both singlet and octet states can become J/y • proportional to local matrix elements Q2 • The velocity expansion may not be a good approximation (vprod~0.88 for Mc=1.4GeV) Jianwei Qiu

8. J/y Production at low momentum • NRQCD factorization is not valid at low momentum Spectator interactions are equally important as the terms in velocity expansion (Qiu – Sterman) Jianwei Qiu

9. Role of semihard gluon radiation • Over 6 GeV2 phase space for gluon radiation • Pair with large Q2 has a vanishing chance to become J/y in NRQCD Model Q2 Q2 Q2 • Radiation pays a penalty in coupling But, gains a lot on wave function as(Q2) ln(Q2/4Mc2) F(4Mc2) Q2 • Threshold behavior in transition distri. Jianwei Qiu

10. Production in nuclear medium • If J/y were produced at the collision point: • Nuclear effect in PDFs • Medium dependence from J/y-nucleon absorption • Glauber model: sAB • Expect a straight line on a semi-log plot • Need a much too larger sabs LAB Jianwei Qiu

11. Multiple scattering at a parton level • Final-state: Increases the relative momentum of the pair Q2 > Q2 leads to suppression of J/y • Initial-state: Broadening in kT kT’ > kT leads to xF-dependence of the suppression in pA Jianwei Qiu

12. Final-state multiple scattering Threshold behavior  Nonlinear in LAB Jianwei Qiu

13. Suppression at fixed target energies Qiu, Vary, Zhang, PRL 2002 Jianwei Qiu

14. Initial-state multiple scattering • Broadening in parton’s transverse momentum • Larger effective kT smaller longitudinal momentum fraction x is needed for producing the cc pairs PDFs x • Increases cross section as much as5 % Jianwei Qiu

15. Summary and Outlook • Both initial-state and final-state multiple scattering are relevant for nuclear dependence of Quarkonium production • Final-state multiple scattering is a main and effective source of J/ysuppression because of the shape threshold behavior • Initial-state multiple scattering re-distributes J/y’s xF – dependence, and tends to produce more J/y’s at higher energies (smaller x) • More data from RHIC can help us understand QCD production mechanism of quarkonia better Jianwei Qiu