Coherent Multiple Scattering and Di-hadron Correlation in Heavy Ion Collisions

1. Coherent Multiple Scattering and Di-hadron Correlation in Heavy Ion Collisions Jianwei Qiu Iowa State University (in collaboration with Dr. Ivan Vitev) 32nd International Conference on High Energy Physics August 16-22, 2004, Beijing, China Jianwei Qiu, ISU

2. K.Filimonov, nucl-ex/0403060 Nuclear dependence in d+A collisions J.Adams et al., Phys.Rev.Lett. 91 (2003) • Small broadening (and/or attenuation) is • observed in d+Au • Large attenuation is observed in Au+Au • (sensitive to the orientation relative to the • reaction plane) – clearly a final state effect J.Rak, hep-ex/0403038 Jianwei Qiu, ISU

3. If Coherent vs incoherent scattering • Consider di-hadron correlations associated with hard (approximately) back-to-back scattering • Incoherent additional scattering does not change the production probability – area under the peak • Coherentinelastic scattering does change the total production probability If Jianwei Qiu, ISU

4. Size of the hard probes • Size of a hard probe is very localized and much smaller than a typical hadron at rest • But, it might be larger than a Lorentz contracted hadron: • low x: uncertainty in locating the parton is much larger than the size of the boosted hadron (a nucleon) If the active x is small enough a hard probe can cover more than one Lorentz contracted nucleon! Jianwei Qiu, ISU

5. + + ≈ + + ≈ • For a nucleus, if , the probe cannot tell which nucleon the parton comes from Coherence for small x partons • IF x<xc, a hard probe can interact coherently with more than one low x partons at a same impact parameters Jianwei Qiu, ISU

6. Universal nuclear dependence • Scattering involves one active parton from a nucleus • Only single hard scattering and single PDF is involved! • Nuclear dependence in PDF does not interfere with the partonic hard collision – universal nuclear dependence Same factorized formula with nucleon PDF’s Replaced by effective nuclear PDF’s Jianwei Qiu, ISU

7. Leading twist contributions All power resummation Process dependent power corrections • power corrections are process dependent: • nonvanish parton transverse momentum • multiple scattering between partons • power corrections in collinear factorization: Jianwei Qiu, ISU

8. All power resummation needed Resummation of power corrections • Power corrections: Lower x  larger power corrections Jianwei Qiu, ISU

9. Dynamical power corrections in DIS • Dynamical power corrections generated by the multiple final state scattering of the struck quark The probe, virtual photon, interacts with all nucleons at a given impact parameter coherently • Coherence: High twist shadowing – process dependent Jianwei Qiu, ISU

10. After integration over Leading power corrections in DIS • Quark propagator of momentum xip+q : • Gluons are transversely polarized in light-cone gauge: • Effective scalar interaction: Jianwei Qiu, ISU

11. + • Leading power correction: • Medium length enhancement: Jianwei Qiu, ISU

12. Resummed A1/3-EnhancedPower Corrections • Results: • One parameter – scale of power corrections U-quark, CTEQ5 LO Upper limit of the saturation scale Jianwei Qiu, ISU

13. Scale for cold matter power corrections Jianwei Qiu, ISU

14. Power Corrections in p+A Collisions • Hadronic factorization fails for power corrections of the order of 1/Q4 and beyond • Medium size enhanced dynamical power corrections in p+A could be factorized to make predictions for p+A collisions • Single hadron inclusive production: Once we fix the incoming parton momentum from the beam and outgoing fragmentation parton, we uniquely fix the momentum exchange, qμ, and the probe size  coherence along the direction of qμ - pμ Ivan Vitev, ISU Jianwei Qiu, ISU

15. p A “d” Starting Point: LO pQCD Resum the multiple final state scattering of the parton “d” with the remnants of the nucleus • Isolate all the xb dependence of the integrand: • Leading power nuclear dependence with the substitution: Cd = 1for quarks, 9/4 for gluons Jianwei Qiu, ISU

16. Numerical results for the power corrections • Similar power correction modification to single and double inclusive hadron production • increases with rapidity • increases with centrality • disappears at high pTin accord with • the QCD factorization theorems • single and double inclusive • shift in ~ 2 /t Small at mid-rapidity C.M. energy 200 GeV Even smaller at mid-rapidity C.M. energy 62 GeV Qiu and Vitev, hep-ph/0405068 Jianwei Qiu, ISU

17. Acoplanarity and power corrections • Consider di-hadron correlations associated with hard (approximately) back-to-back scattering • Coherent scattering reduces: • Incoherent scattering broadens: Jianwei Qiu, ISU

18. Only small broadening • versus centrality • Looks rather similar at • forward rapidity of 2 • The reduction of the area • is rather modest • Apparently broader • distribution • Even at midrapidity a small • reduction of the area • Factor of 2-3reduction of the • area at forward rapidity of 4 Dihadron Correlation Broadening and Attenuation Mid-rapidity and moderate pT J.Adams et al., Phys.Rev.Lett. 91 (2003) Forward rapidity and small pT Trigger bias can also affect: Qiu and Vitev, Phys.Lett.B 570 (2003); hep-ph/0405068 Jianwei Qiu, ISU

19. Conclusions • Although hard partonic collisions are localized in space-time, comparing to the rest size of a nucleon, the interaction length could be larger than a size of a Lorentz contracted nucleon • Coherent multiple interactions lead to power corrections to physical cross sections: • Leading medium size enhanced power corrections are Infrared safe and can be systematically resummed into a translation operator acting on parton’s momentum fraction, which leads to a shift in parton’s momentum fraction without changing the leading twist factorized formula • Dynamical power corrections for p+A collisions lead to the centrality and rapidity dependent suppression of single inclusive spectra and the dihadron correlations • At very forward rapidity (y=4) and small pT the power corrections give a factor of 2-3 reduction of the area of the away side correlations Jianwei Qiu, ISU