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Multiple parton interactions
in heavy-ion collisions
Cyrille Marquet
Columbia University
High-energy heavy-ion collisions
relativistic heavy ion collisions
 multiple partonic interactions (MPI)
what can be described with QCD at
weak coupling (1st principle calculation)?
maybe the early stages of the collision
space-time picture of heavy-ion collisions
5. Individual hadrons
freeze out
4. Hadron gas
cooling with expansion
3. Quark Gluon Plasma
thermalization,
expansion
2. Pre-equilibrium state  Glasma
MPI at weak coupling
 the saturation scale
collision
1. Nuclei (initial condition)  CGC
Outline
• The saturation scale in the Color Glass Condensate
the nuclear wave function at small-x
the saturation phenomenon
• The saturation scale in the Glasma
multiple partonic interactions
particle production in AA collisions
• The saturation scale in the quark-gluon plasma
medium-induced energy loss and pT broadening
weakly-coupled vs strongly-coupled plasma
The saturation scale in the
nuclear wave function
Color Glass
Condensate
The hadron wave function in QCD
hadron  qqq  qqqg  ...  qqq......ggggg
• one can distinguish three regimes
hadron  kT ~ QCD  kT  QCD , x  1  kT  QCD , x  1
S (kT ) << 1
non-perturbative
regime: soft QCD
relevant for instance for
the total cross-section in
hadron-hadron collisions
perturbative regime,
dilute system of partons:
hard QCD (leading-twist
approximation)
relevant for instance for
top quark production
weakly-coupled regime,
dense system of partons (gluons)
non linear QCD
the saturation regime
not relevant to experiments
until the mid 90’s
with HERA and RHIC: recent gain of interest for saturation physics
The dilute regime
hadron  kT ~ QCD  kT  QCD , x  1  kT  QCD , x  1
transverse view of the hadron
hadron = a dilute system of partons
1/kT ~ parton transverse size
leading-twist regime
evolution: as kT increases,
the hadron gets more dilute
Dokshitzer Gribov
Lipatov Altarelli Parisi
the partons interact incoherently
for instance, the total cross-section in DIS
 DIS ( xBj , Q2 ) 
1
  dx 
a/ p

( x, Q 2 )ˆ a ( xBj / x, Q 2 )  O Q02 Q 2

partons a x
Bj
parton density
partonic cross-section
higher twist
not valid if x is too small when the hadron becomes a dense system of partons
(A/x) 1/3
Q2
The saturation regime
hadron  kT ~ QCD  kT  QCD , x  1  kT  QCD , x  1
the separation between the dilute and dense
regimes is caracterized by a momentum scale:
the saturation scale Qs(x)
in the saturation regime, QCD
Qs (x)
,
~1

1
higher-twists are important: kT
kT
Balitsky Fadin Kuraev Lipatov
hadron = a dense system of partons
evolution: as x decreases,
the hadron gets more dense
in the saturation regime,
the evolution becomes non linear
the partons interact coherently
the saturation regime of QCD:
- non-linear yet weakly-coupled
- describes the collective behavior of
partons in the nuclear wave function
The saturation scale and MPI
• gluon recombination in the hadronic wave function
gluon density per unit area
it grows with decreasing x
recombination cross-section
recombinations important when
gluon kinematics
the saturation regime: for
with
occupation numbers are large
• multiple scattering
so far I only discussed the nuclear
wave function, multiple scatterings
occur during the collision, when
parton saturation is as important as MPI, to be consistent, both should be included
The Color Glass Condensate
the idea in the CGC is to take into account saturation via strong classical fields
• the CGC: an effective theory to describe the saturation regime
McLerran and Venugopalan (1994)
lifetime of the fluctuations
in the wave function ~
high-x partons ≡ static sources
low-x partons ≡ dynamical fields

hadron  qqq  qqqg  ...  qqq......ggggg

CGC wave function
valence partons
as static random
color source
separation between
the long-lived high-x partons
and the short-lived low-x gluons
small x gluons
as radiation field
2
classical Yang-Mills equations
D F 

 a

hadron   D  x [  ]   CGC
   ( x )  ( x )

a
the evolution of  x [ ] with x is a
renormalization group equation
Jalilian-Marian, Iancu, McLerran,
Weigert, Leonidov, Kovner (1997-2002)
the solution gives Qs ( x, A) ~ A1/ 3 x 0.3
2
The saturation scale
in the Glasma
Glasma
Collision of two CGCs
• the initial condition for the time evolution in heavy-ion collisions
before the collision:
J      ( x  ) 1 ( x )     ( x  )  2 ( x )
1
2
the distributions of ρ contain the small-x
evolution of the nuclear wave function
• after the collision
compute the gluon field in the forward light-cone
the fields decay, once they are not strong (classical)
anymore, a particle description is again appropriate
express cross-sections in terms of the field
this is where multiple partonic
interactions should be included
Particle production in the Glasma
• single scattering
factorization theorems in
pQCD answer this question
• multiple scatterings
this is what happens in heavy-ion collisions
one needs to reformulate quantum
field theories to address the problem
Gelis, Lappi and Venugopalan (2006-now)
one needs to understand how strong
color fields decay into particles
the time scale is
possible application to pp collisions:
a first principle calculation of the underlying event
Total multiplicity in AA
• predictions including NLO evolution
Albacete (2007)
the extrapolation from RHIC to LHC
is driven by the small-x evolution
yellow band: uncertainties due to the
starting point of the small-x evolution
and the initial saturation scale
caveat: kT factorization is assumed,
meaning MPI are not treated properly
the focus was the correct NLO evolution,
however numbers are similar with an exact
numerical treatment of MPI (but an
approximate treatment of the evolution)
Lappi (2008)
• day-1 measurement
~ 1400 charged particles is a robust prediction,
if one gets <1000 or >2500, this rules out the CGC
The saturation scale
in the QCD plasma
Quark-Gluon
Plasma
The heavy quark wave function
• consider a heavy quark of mass M and energy E
the heavy quark wave function at lowest order
the energy of the gluon is denoted
its transverse momentum is denoted
the virtuality of the fluctuations is measured by their lifetime or coherence time
short-lived fluctuations are highly virtual
the probability of this fluctuation is
Lorentz factor of the heavy quark
• the dead cone effect
compared to massless quarks, the fluctuation with
 absence of radiation in a forward cone
are suppressed
Dokshitzer and Kharzeev (2001)
Medium induced gluon radiation
• multiple scattering of the radiated gluon
Baier, Dokshitzer, Mueller,
Peigne, Schiff (1997)
this is how the virtual gluon in the heavy quark wave function is put on shell
it becomes emitted radiation if it picks up enough transverse momentum
the accumulated transverse momentum picked up by a gluon of coherence time
average pT picked up
in each scattering
mean free path
only property of the medium needed
• the saturation scale of the pQCD plasma
only the fluctuations which pick up enough transverse momentum are freed

this discussion is also valid for light quarks
Heavy quark energy loss
• the case of infinite extend matter
for heavy quarks, the radiated gluons which dominate the energy loss have
and
this allows to express Qs in terms of T and E/M only

and
and the heavy quark energy loss is
• the case of finite extend matter of length
the relevant fluctuations in the wave function have a smaller energy
the maximum transverse momentum that gluons can pick-up is
the radiated gluons which dominate the energy loss have
Indications from RHIC data
• light-quark energy loss
comparisons between models and data indicate the need for
however, for a weakly-coupled pQCD plasma we expect
• heavy-quark energy loss
STAR, PRL 192301 (2007)
PHENIX, PRL 172301 (2007)
suppression similar to light
hadron suppression at high pT
Energy-loss at strong coupling?
• it is unclear if the perturbative QCD approach can describe the
suppression of high-pT particles in Au+Au collisions at RHIC, in
particular for heavy-quark energy loss:
high-pT electrons from c and b decays indicate similar suppression
for light and heavy quarks, while the dead-cone effect in pQCD
implies a weaker suppression for heavier quarks
 this motivates to think about a strongly-coupled plasma
• for the N=4 SYM theory, the AdS/CFT correspondence allows to
investigate the strong coupling regime
limited tools to address the QCD dynamics at strong coupling
 the results for SYM may provide insight on strongly-coupled
gauge theories, some aspects may be universal
main result: one can also identify a momentum scale which
controls what fluctuations become emitted radiation
Energy loss and Qs
Dominguez, C.M., Mueller, Wu and Xiao (2008)
results for energy loss
QCD at weak coupling SYM at strong coupling
heavy-quark energy loss
coherence time
infinite matter or
finite matter with
- same parametric form for the energy loss in pQCD and SYM at strong coupling !
- first estimate of the plasma length dependence of heavy quark energy loss
Conclusions
• MPI in heavy-ion collisions
- are not only important but crucial (HIC probe non-linear QCD)
- are at the origin of the interesting phenomena
• MPI at weak coupling
- are characterized by the saturation scale Qs
- at RHIC, Qs may be hard enough to justify using weak coupling
- CGC & Glasma : first-principle description of the early stages
- parton saturation & MPI equally important
• MPI in the quark-gluon plasma
- are responsible for the energy loss and pT-broadening of hard probes
- the corresponding saturation scale is related to
- at strong coupling, MPI can be also described in terms of a saturation
scale