QCD Processes in the Nucleus
Will Brooks
Jefferson Lab
QCD and Hadron Physics Town Meeting, Rutgers University
January 12, 2007
Outline
• Introduction to fundamental processes in QCD
• Transverse momentum broadening and quark energy loss
in nuclei
• Color transparency
• Hadron formation lengths (time permitting)
Main Physics Focus
QCD in the space-time domain:
• How long can a light quark remain deconfined?
– The production time tp measures this
– Deconfined quarks lose energy via gluon emission
– Measure tp 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. Q2
• How long does it take to form the full color field of a hadron?
– The formation time tfh measures this
– Measure tfh via hadron attenuation in nuclei
“How long can a light quark remain deconfined?”
pT Broadening, Production Time, and
Quark Energy Loss
Definitions
2 DIS
T A
pT broadening: p  p
2
T
2 DIS
T D
 p
p+
e’
g*
pT
Nucleus “A”
e
Production time: lifetime of deconfined quark, e.g., t p 
 (1  z )
dE
c
dx
pT Broadening and Quark Energy Loss
• Quarks lose energy by gluon emission as they propagate
– In vacuum
– Even more within a medium
gluons
propagating quark

This energy loss is manifested by pT2

pT2 is a signature of the production time tp

E ~ L dominates in QED

E ~ L2 dominates in QCD?
quarks in nuclei
L
nucleus
Medium-stimulated loss
calculation by BDMPS
Energy Loss in QCD
• 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
c 

k 2
Coherence length ~ formation time of a gluon radiated by a group of scattering centers
c
Three regions: if mean free path is l,
and medium length is L, then →
dE
Two conditions emerge: 
L
dx
dE

 E
dx
c  l
l  c  L
c  L
L  LCritical
Incoherent gluon radiation
Coherent gluon radiation
‘Single-scatter’ gluon radiation
E
L  LCritical
Baier, Schiff, Zakharov, Annu. Rev. Nucl. Part. Sci. 2000. 50:37-69
LCritical
L
pT2 (GeV2) ~dE/dx
pT2 vs.  for Carbon, Iron, and Lead
Pb
~ 100 MeV/fm (perturbative formula)
Fe
C
 (GeV)
Production length from JLab/CLAS 5 GeV data
(Kopeliovich, Nemchik, Schmidt, hep-ph/0608044)
pT2 vs. A1/3 for Carbon, Iron, and Lead
Strongly suggests quadratic behavior of total energy loss!
Data generally appear to ‘plateau’
Only statistical errors shown
pT Broadening - Summary
What we have learned
• Precise, multivariable measurements of pT2 are feasible
• Quark energy loss can be estimated
– Data appear to support the novel E ~L2 ‘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*E1/2 behavior at higher ? JLAB12/EIC
– Can asymptotic behavior E→0 be observed, →∞? EIC
– Hadronic corrections under control? Consistent with DY? E906
• Plateauing behavior due to short tp or energy loss transition? JLAB12
• Provide quantitative basis for jet quenching at RHIC/LHC? THEORY
“How fast do color singlets expand?”
Color Transparency
(at low energy)
Definitions
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 TA
with increasing hardness of the reaction (Q).
s(A)
Coherence length lc also affects TA
TA =
TA
Aso
Complete transparency
Glauber
c 
Q2
2
( M V2  Q 2 )
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)
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
• p
– High-energy diffractive dissociation (FNAL) CT observed
– gn→p-p (JLAB) Onset of CT???
– A(e,e’p) (JLAB) Onset of CT??
• r
– Exclusive electroproduction at fixed coherence length
(HERMES, JLAB) Onset of CT?
Direct Pion Electroproduction
pion nucleus total cross-section
proton nucleus total cross-section
A. Larson, G. Miller and M. Strikman, nucth/0604022
D. Dutta et. al, JLab experiment E01-107
(Data/Simulation)A
T 
(Data/Simulation) p
Preliminary Results from CLAS EG2 data
r0 Electroproduction at Fixed Coherence Length
TFe
Preliminary results show a clear
increase in transparency, in good
agreement with CT model!
Q2 (GeV2)
Kawtar Hafidi
JLab experiment E02-110
Search for the onset of CT
Chile 2006
E12-06-106
12 GeV
E12-06-107
r0 Transparency
r0 electroproduction
Color Transparency - Summary
What we have learned
– CT in 3q systems not apparent for Q2<10 GeV2
– CT in 2q systems exists at high energies
– Onset of CT in 2q systems at few-GeV2?
• 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/Q2 JLAB12
• Better understanding of dynamics THEORY
“How long does it take to form the full color
field of a hadron?”
Hadron Attenuation
Definitions
Hadronic multiplicity ratio
tp
Hadron
formation
time tf
Airapetian, et al. (HERMES) PRL 96, 162301 (2006)
Hadron Attenuation – Physics Picture
• Hadrons lost from incident flux through
– Quark energy loss
– Interaction of prehadron or hadron
with medium
zh~0.5, larger ,
less attenuation
zh→1, smaller ,
more attenuation
Accardi, Grünewald, Muccifora, Pirner, Nuclear Physics A 761 (2005) 67–91
HERMES Data – Kr for p, K, p
Hermes Data – Dependence on pT and A
Examples of multi-variable slices of
preliminary CLAS 5 GeV data for Rp+
 dependence
Q2 dependence
Four out of ~50 similar plots for p+!
K0, p0, p-, more, underway
pT2 dependence
zh dependence
Cronin Effect
Dependence on zh
Theoretical prediction →
Carbon
Probes reaction mechanism
Iron
Lead
CLAS preliminary data
z=0.5 and 0.7
Accessible Hadrons (12 GeV)
12 GeV Anticipated Data
p+
Bins in yellow accessible at 5 GeV
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, Q2, x, z
observed
Outstanding questions
• Energy loss or hadron formation? THEORY JLAB12
• How do hadrons form? Optimal method to extract formation
lengths? THEORY JLAB12
Conclusions
• Fundamental space-time processes in QCD finally becoming
experimentally accessible
• Parton propagation, color transparency, hadron formation
• Plenty of exciting opportunities for the future!
Backup Slides
Kinematics for pT Broadening
Choose kinematics favoring propagating quark in-medium:
• z (=Eh/) > 0.5 – enhance probability of struck quark
• z << 1.0 and /mh >> 1 – maximize production length to
ensure ctp >> nuclear size
• z, x such that nucleon factorization holds, to suppress target
fragmentation influence
• x > 0.1 to avoid quark pair production
Hadron-Nucleus Absorption Cross Sections
K

Hadron–nucleus
absorption cross section
p
p
_
p
Fit to
Hadron momentum
60, 200, 280 GeV/c
 < 1 interpreted as due to the strongly interacting nature of
the probe
Experimentally  = 0.72 – 0.78, for p, K, p
A. S. Carroll et al. Phys. Lett 80B 319 (1979)
FNAL E665 experiment
E = 470 GeV
Adams et al. PRL74 (1995) 1525
deconfined?
• Ubiquitous sketch
of hadronization
Physical
picture,process:
DIS string model
• Alternative: gluon bremsstrahlung
GY
RG
Microscopic mechanism not known from experiment
Kopeliovich, Nemchik, Predazzi, Hayashigaki, Nuclear Physics A 740 (2004) 211–245
deconfined?
• Two distinct dynamical
stages, each with
characteristic
Characteristic
time
scales
time scale:
Formation time tfh
Production time tp
Time during which quark is deconfined
Signaled by medium-stimulated
energy loss via gluon emission:
(pT 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
Transparency
Quasi-free A(e,e’p) : No evidence for CT
Conventional nuclear
physics calculation by
Pandharipande et al.
gives adequate description
A(e,e’p) Results -- A Dependence
Fit to s  s0 A

for Q2 > 2 (GeV/c)2
 = constant = 0.75
Close to proton-nucleus total cross section data!
Color Transparency in D
• Experimental ratios:
s(<0.3)/s(0.1),
s(0.25)/s(0.1) and
s(0.5)/s(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
A(p-,di-jet) Fermilab E791 Data
Coherent p- diffractive dissociation
with 500 GeV/c pions on Pt and C.

Fit to s  s 0 A
 >> 0.76, p-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)
Pion Electroproduction
70 degrees
90 degrees
r0 Electroproduction at Fixed Coherence Length
HERMES Nitrogen data : TA=P0 + P2Q2
P2 = (0.097  0.048stat  0.008syst) GeV-2
Airepetian et al. (HERMES Coll.) Phys. Rev. Lett. 90 (2003) 052501
‘A’ Dependence of
Transparency
(Data/Simulation)A
T 
(Data/Simulation)p
Usually s (A)  s0 A
 T = A1
pion nucleus total cross-section
proton nucleus total cross-section
from fit of
T(A) = A1 at fixed Q2