1. Parton energy loss in cold nuclei and
Hard Probes 2012
Cagliari, May 27 – June 1, 2012
Parton energy loss in cold nuclei
and
implications on jet quenching in AA collisions
Hongxi Xing & Xin-Nian Wang
CCNU & LBNL

2. Multiple Interaction in QCD
Multiple Interaction in QCD: A way of life
Everywhere, all the time, indispensable
Hard probes employ multiple scattering as a tool

3. Deeply Inelastic Scattering
k=xp p
Quark distribution in collinear factorized pQCD parton model:
quarks carrying momentum fraction x of the nucleon (nucleus)

4. Leading-twist parton distribution in DIS
Belitsky, Ji and Yuan (2002) k p
....
f_A^q(x,\vec k_\perp)=\int\frac{d y^-}{4\pi}\frac{d^2y_\perp}{(2\pi)^2}
e^{ixp^+y^- -i \vec k_\perp\cdot \vec y_\perp} \langle A |\bar \psi(0) \gamma^+ {\cal L}(0,y)\psi(y) | A\rangle
{\cal L}(0,y)={\cal L}^\dagger_\parallel(\infty,0;\vec 0_\perp)
{\cal L}_\perp^\dagger(\infty;\vec y_\perp,\vec 0_\perp) {\cal L}_\parallel(\infty,y^-;\vec y_\perp)
{\cal L}_\parallel(-\infty,y^-,\vec y_\perp)={\cal P} \exp\left[-ig\int_{y^-}^{-\infty} d\xi^- A_+(\xi^-,\vec y_\perp)
\right]
{\cal L}_\perp(-\infty;\vec y_\perp,\vec 0)={\cal P} \exp\left[-ig\int_{y^-}^{-\infty} d\vec\xi_\perp\cdot \vec A_\perp (\xi^-,\vec y_\perp)\right]
{\cal L}_\perp(-\infty;\vec y_\perp,\vec 0)={\cal P} \exp\left[-ig\int_{\vec 0_\perp}^{\vec y_\perp} d\vec\xi_\perp\cdot \vec A_\perp (-\infty,\vec \xi_\perp)\right]

5. Higher Twist Contributions in Multiple Scatteringk p
....
H(x_i, \vec k_{Ti}) =H(x_i,\vec k_{Ti}=0)+\vec k_{Ti}\cdot \vec\partial_{k_T}H(x_i,\vec k_{Ti}=0)+\cdots
Jet Transport
Liang, XNW & Zhou （2008）

6. Parton energy loss in cold nuclear matter
DIS of large nuclei
DY production in pA

7. Leading Twist Drell-Yan
Factorization: Separation of short- from long-distance
NLO partonic diagram to PDF, LO + NLO collinear part
Scaling violation – DGLAP evolution

8. Annihilation-like processes (q+gq)
Double scattering: …
Single-triple interference: …

9. Compton-like processes (g+gq)
Double scattering: …
Single-triple interference: …

10. LPM interference in DY Final result for particular example Hard-Hard
Soft-Hard 10

11. Medium modified projectile PDF
Modified quark distribution - Vacuum + Medium
Modified splitting function
Modified DGLAP evolution

12. “factorized” gluon-quark correlation function
Jet transport parameter 12

13. Modified fragmentation function in DIS
Guo, XNW 2000

14. DIS of large nuclei
Deng & XNW (2010)

15. Nuclear effects in Drell-Yan
Energy loss VS. Shadowing (FNAL-E866 ELab = 800 GeV) 15

16. Parton energy loss in Drell-Yan
Energy loss VS. Shadowing (FNAL-E906 ELab = 120 GeV)
FNAL-E906 provide unambiguous measurement of initial state energy loss 16

17. Jet quenching in hadronic phase of QGP
Chen, Greiner, Wang, XNW, Xu （2010）
30% quenching from
hadronic phase

18. Multiple scattering in eA and Drell-Yan in pA important
Summary
Multiple scattering in eA and Drell-Yan in pA important
eA modified fragmentation function
DY in pA modified beam PDF
qhat in cold nuclear matter 0.02 GeV^2/fm
Parton energy loss during hadronic phase in AA collisions is non-negligible
W. Deng, CNM effect in pA at LHC, Thursday Parallel VC (T1C)

21. Modified DGLAP Equations
\frac{\partial \tilde{D}_q^h(z_h,\mu^2)}{\partial \ln \mu^2}&=&\frac{\alpha_s(\mu^2)}{2\pi}\int_{z_h}^1
\frac{dz}{z}\left [\tilde{\gamma}_{q\rightarrow qg}(z,\mu^2)\tilde{D}_q^h(\frac{z_h}{z},\mu^2)\right.
\left. +\tilde{\gamma}_{q\rightarrow gq}(z,\mu^2)\tilde{D}_g^h(\frac{z_h}{z},\mu^2)\right ]
\frac{\partial \tilde{D}_g^h(z_h,\mu^2)}{\partial\ln \mu^2}&=&\frac{\alpha_s(\mu^2)}{2\pi}\int_{z_h}^1
\frac{dz}{z}\left [ \sum_{q=1}^{2n_f}\tilde{\gamma}_{g\rightarrow q\bar q}(z,\mu^2)\tilde{D}_q^h(\frac{z_h}{z},\mu^2) \right.
+\left. \tilde{\gamma}_{g\rightarrow gg}(z,\mu^2)\tilde{D}_g^h(\frac{z_h}{z},\mu^2)\right ]
\tilde \gamma _{a\rightarrow bc}(z,l_{T}^{2})=\gamma_{a\rightarrow bc}(z)
+ \Delta \gamma_{a\rightarrow bc}(z,l_{T}^{2})
Modified splitting functions