1. QCD Processes in the Nucleus Will Brooks Jefferson Lab QCD and Hadron Physics Town Meeting, Rutgers University January 12, 2007

2. Outline Introduction to fundamental processes in QCD Transverse momentum broadening and quark energy loss in nuclei Color transparency Hadron formation lengths (time permitting)

3. Main Physics Focus QCD in the space-time domain: How long can a light quark remain deconfined? –The production time  p measures this –Deconfined quarks lose energy via gluon emission –Measure  p and dE/dx via medium-stimulated gluon emission How fast do color singlet systems expand? –Color transparency at low energies measures this –Access via nuclear transparency vs. Q 2 How long does it take to form the full color field of a hadron? –The formation time  f h measures this –Measure  f h via hadron attenuation in nuclei

4. “How long can a light quark remain deconfined?” p T Broadening, Production Time, and Quark Energy Loss

5. Nucleus “A” pTpT e e’ ** ++ Definitions p T broadening: Production time: lifetime of deconfined quark, e.g.,

6. p T Broadening and Quark Energy Loss nucleus propagating quark quarks in nuclei gluons L Quarks lose energy by gluon emission as they propagate –In vacuum –Even more within a medium Medium-stimulated loss calculation by BDMPS This  energy loss is manifested by  This  energy loss is manifested by  p T 2   p T 2 is a signature of the production time  p  E ~ L dominates in QED  E ~ L dominates in QED  E ~ L 2 dominates in QCD?  E ~ L 2 dominates in QCD?

7. Energy Loss in QCD Baier, Schiff, Zakharov, Annu. Rev. Nucl. Part. Sci. 2000. 50:37-69 Partonic energy loss in QCD is well-studied: dozens of papers over past 15 years Dominant mechanism is gluon radiation; elastic scattering is minor Coherence effects important: QCD analog of LPM effect Coherence length ~ formation time of a gluon radiated by a group of scattering centers Three regions: if mean free path is, and medium length is L, then → Incoherent gluon radiation Coherent gluon radiation ‘Single-scatter’ gluon radiation Two conditions emerge: L EE L Critical

8.  p T 2 vs. for Carbon, Iron, and Lead C Pb Fe  p T 2 (GeV 2 ) (GeV) (GeV) ~ 100 MeV/fm (perturbative formula) ~dE/dx

9. Production length from JLab/CLAS 5 GeV data (Kopeliovich, Nemchik, Schmidt, hep-ph/0608044)

10.  p T 2 vs.   for Carbon, Iron, and Lead Strongly suggests quadratic behavior of total energy loss! Data generally appear to ‘plateau’ Only statistical errors shown

11. pT Broadening - Summary What we have learned Precise, multivariable measurements of  p T 2 are feasible Quark energy loss can be estimated –Data appear to support the novel  E ~L 2 ‘LPM’ behavior –~100 MeV/fm for Pb at few GeV, perturbative formula Deconfined quark lifetime can be estimated, ~ 5 fm @ few GeV Much more theoretical work needed for quantitative results Outstanding questions Is the physical picture accurate? –Transition to  E ~L*E 1/2 behavior at higher ? –Can asymptotic behavior  E→0 be observed, →∞? –Hadronic corrections under control? Consistent with DY? Plateauing behavior due to short  p or energy loss transition? Provide quantitative basis for jet quenching at RHIC/LHC? JLAB12/EIC THEORY EIC E906 JLAB12

12. “How fast do color singlets expand?” Color Transparency (at low energy)

13. Definitions TATA Q2Q2 Complete transparency Glauber Color transparency: produce a hadron configuration of small size small hadron has small cross section Hadron must remain small over nuclear dimensions to observe effect Common signature of CT: increase of the nuclear transparency T A with increasing hardness of the reaction (Q). Coherence length l c also affects T A  (A)  o T A =

14. Color Transparency – Physics Picture Three aspects accessible experimentally: Existence and onset of color transparency Coherence in hard pQCD quark-antiquark pair production Evolution of pre-hadron to full hadron Kopeliovich, Nemchik, Schaefer, Tarasov, Phys. Rev. C 65 035201 (2002)

15. Color Transparency – Recent Experiments Three-quark systems A(e,e’p) in quasi-free kinematics (JLAB) D(e,e’p) final-state interactions (JLAB) Precise measurements, CT not observed Two-quark systems  –High-energy diffractive dissociation (FNAL) CT observed –  n→  - p (JLAB) Onset of CT??? –A(e,e’  ) (JLAB) Onset of CT??  –Exclusive electroproduction at fixed coherence length (HERMES, JLAB) Onset of CT?

16. A. Larson, G. Miller and M. Strikman, nuc- th/0604022 D. Dutta et. al, JLab experiment E01-107 Direct Pion Electroproduction pion nucleus total cross-section proton nucleus total cross-section

17. Kawtar HafidiSearch for the onset of CT Chile 2006 Q 2 (GeV 2 ) T Fe Preliminary Results from CLAS EG2 data Preliminary results show a clear increase in transparency, in good agreement with CT model!  0 Electroproduction at Fixed Coherence Length JLab experiment E02-110

18. 12 GeV  0 electroproduction E12-06-107  0 Transparency E12-06-106

19. Color Transparency - Summary What we have learned –CT in 3q systems not apparent for Q 2 <10 GeV 2 –CT in 2q systems exists at high energies –Onset of CT in 2q systems at few-GeV 2 ? Several strong hints One/two clearly positive signals, more theory needed Outstanding questions –How fast does color singlet expand? Studies of medium thickness, higher energy/Q 2 Better understanding of dynamics JLAB12 THEORY

20. “How long does it take to form the full color field of a hadron?” Hadron Attenuation

21. Definitions Hadronic multiplicity ratio Airapetian, et al. (HERMES) PRL 96, 162301 (2006) Hadron formation time  f pp

22. Hadron Attenuation – Physics Picture Hadrons lost from incident flux through –Quark energy loss –Interaction of prehadron or hadron with medium z h ~0.5, larger  less attenuation z h →1, smaller  more attenuation Accardi, Grünewald, Muccifora, Pirner, Nuclear Physics A 761 (2005) 67–91

23. HERMES Data – Kr for p, K, 

24. Hermes Data – Dependence on p T and A

25. Examples of multi-variable slices of preliminary CLAS 5 GeV data for R  + z h dependence Q 2 dependence p T 2 dependence dependence Four out of ~50 similar plots for  + ! K 0,  0,  -, more, underway

26. Cronin Effect Dependence on z h Carbon Iron Lead Theoretical prediction → CLAS preliminary data z=0.5 and 0.7 Probes reaction mechanism

27. Accessible Hadrons (12 GeV)

28. 12 GeV Anticipated Data Bins in yellow accessible at 5 GeV ++

29. Hadron Attenuation - Summary What we have learned Hadronic multiplicity ratios depend strongly on hadron species, are universally suppressed at high z Main ingredients: prehadron cross sections, gluon radiation, formation lengths; possible exotic effects Verified EMC observation: Cronin-like phenomenon in lepto-nuclear scattering; new dependence on A, Q 2, x, z observed Outstanding questions Energy loss or hadron formation? How do hadrons form? Optimal method to extract formation lengths? JLAB12THEORY JLAB12THEORY

30. Conclusions Fundamental space-time processes in QCD finally becoming experimentally accessible Parton propagation, color transparency, hadron formation Plenty of exciting opportunities for the future!

31. Backup Slides

32. Kinematics for p T Broadening Choose kinematics favoring propagating quark in-medium: z (=E h / ) > 0.5 – enhance probability of struck quark z > 1 – maximize production length to ensure c  p >> nuclear size z, x such that nucleon factorization holds, to suppress target fragmentation influence x > 0.1 to avoid quark pair production

33. Hadron-Nucleus Absorption Cross Sections Hadron–nucleus absorption cross section Fit to Hadron momentum 60, 200, 280 GeV/c  < 1 interpreted as due to the strongly interacting nature of the probe A. S. Carroll et al. Phys. Lett 80B 319 (1979)    p p _ Experimentally  = 0.72 – 0.78, for p, K, 

34. FNAL E665 experiment Adams et al. PRL74 (1995) 1525 E  = 470 GeV

35. How long can a light quark remain deconfined? Physical picture, DIS Ubiquitous sketch of hadronization process: string model RG GY Microscopic mechanism not known from experiment Kopeliovich, Nemchik, Predazzi, Hayashigaki, Nuclear Physics A 740 (2004) 211–245 Alternative: gluon bremsstrahlung

36. How long can a quark remain deconfined? Characteristic time scales Two distinct dynamical stages, each with characteristic time scale: Formation time t f h Production time t p Time during which quark is deconfined Signaled by medium-stimulated energy loss via gluon emission: (p T broading) Time required to form color field of hadron Signaled by interactions with known hadron cross sections No gluon emission (Hadron attenuation) These time scales are essentially unknown experimentally S. J. Brodsky, SLAC-PUB04551, March 1988

37. Quasi-free A(e,e’p) : No evidence for CT Transparency Conventional nuclear physics calculation by Pandharipande et al. gives adequate description

38. A(e,e’p) Results -- A Dependence Fit to      = constant = 0.75 for Q 2 > 2 (GeV/c) 2  Close to proton-nucleus total cross section data!

39. Color Transparency in D Experimental ratios:  (<0.3)/  (0.1),  (0.25)/  (0.1) and  (0.5)/  (0.1) Black points: 6 GeV CLAS data already taken Magenta points: 11 GeV projections with (solid) and without (open) CT Dotted red: PWIA Dashed blue: Laget PWIA+FSI+IC

40. A(  -,di-jet) Fermilab E791 Data Coherent  - diffractive dissociation with 500 GeV/c pions on Pt and C. Fit to  A 0   >> 0.76,  -nucleus total cross-section Aitala et al., PRL 86 4773 (2001) Brodsky, Mueller, Phys. Lett. B206 685 (1988) Frankfurt, Miller, Strikman, Nucl. Phys. A555, 752 (1993)

41. Pion Electroproduction 70 degrees 90 degrees

42.  0 Electroproduction at Fixed Coherence Length HERMES Nitrogen data : T A =P 0 + P 2 Q 2 P2 = (0.097  0.048 stat  0.008 syst ) GeV -2 Airepetian et al. (HERMES Coll.) Phys. Rev. Lett. 90 (2003) 052501

43. ‘A’ Dependence of Transparency from fit of T(A) = A  at fixed Q 2  pion nucleus total cross-section proton nucleus total cross-section Usually   A  T = A 