forward particle production in d+au collisions in the cgc framework
DESCRIPTION
Forward particle production in d+Au collisions in the CGC framework. Cyrille Marquet. Institut de Physique Théorique, CEA/Saclay. - but single particle production probes limited information about the CGC. (only the 2-point function). - PowerPoint PPT PresentationTRANSCRIPT
Forward particle productionin d+Au collisions
in the CGC framework
Cyrille Marquet
Institut de Physique Théorique, CEA/Saclay
the spectrum and
Motivation- after the first d+Au run at RHIC, there was a lot of new results on
single inclusive particle production at forward rapidities
kdyddN
kdyddN
NR
hXpphXdA
colldA 22
1
the suppressed production (RdA < 1) was predicted in the Color Glass Condensate picture of the high-energy nucleus
d Au → h X
y increases
the modification factor were studied
- but single particle production probes limited information about the CGC(only the 2-point function)to strengthen the evidence, we need to study
more complex observables to be measured with the new d+Au run
- the experimental focus has been on IdA
a correlation measurement sensitive to possible modificationsof the back-to-back emission pattern in a hard process d Au → h1 h2 X
Outline
• Saturation and the Color Glass Condensatethe unintegrated gluon distribution and the BK equationmulti-parton distributions in the nuclear wave function
• Single particle production at forward rapiditiesdifferent parametrizations of the unintegrated gluon distributionRdA and the success of the CGCrunning coupling corrections to the BK equation
• Probing small x with two-particle correlationsthe ideal final-state kinematicscorrelations in azimuthal angle and IdA
some results of CGC calculations
Saturation and theColor Glass Condensate
Gluon saturationx : parton longitudinal momentum fraction
kT : parton transverse momentum
the distribution of partons
as a function of x and kT :
dilute/dense separation characterized by the saturation scale Qs(x)
QCD linear evolutions:
DGLAP evolution to larger kT (and a more dilute hadron)BFKL evolution to smaller x (and denser hadron)
QCD non-linear evolution: meaning
recombination cross-section
gluon density per unit areait grows with decreasing x
recombinations important when
the saturation regime: for with
this regime is non-linearyet weakly coupled
The Color Glass Condensatethe idea of the CGC is to describe the saturation regime with strong classical fields
McLerran and Venugopalan (1994)
lifetime of the fluctuations
in the wave function ~
high-x partons ≡ static sources
low-x partons ≡ dynamical fields
small x gluons as radiation field
),(,
z zFD cc
valence partonsas static random
color source separation between
the long-lived high-x partons
and the short-lived low-x gluons
CGC wave function
classical Yang-Mills equations
• an effective theory to describe the saturation regime
gggggqqqqqqgqqq .........hadron CGC][hadron xD
from , one can obtainthe unintegrated gluon distribution,
as well as any n-parton distributions
2][x
in the A+=0 gauge
The small-x evolution
the solution gives 3.03/12 ~),(Q xAAxs
the evolution of with x is a renormalization-group equation2
][x
for a given value of k², the saturation regime in a nuclear wave functionextends to a higher value of x compared to a hadronic wave function
22][][
)/1ln( x
JIMWLKx H
xd
d
• the JIMWLK equation
is mainly non-perturbative, but its evolution is known
Jalilian-Marian, Iancu, McLerran, Weigert, Leonidov, Kovner
2][x
the energy evolution of cross-sections is encoded in the evolution of2
][x
in the CGC framework, any cross-section is determined by colorless combinations ofWilson lines , averaged over the CGC wave function
][][2
SDS xx ][S
• Observables
Scattering off the CGC
scattering of a quark:
• this is described by Wilson lines
dependence kept implicit in the following
))()((1
1][ xyxy FFc
WWTrN
T
x : quark space transverse coordinatey : antiquark space transverse coordinate
the dipole scattering amplitude:qq
this is the most common averagefor instance it determines deep inelastic scattering
• the 2-point function or dipole amplitude
xTxy
it is used in many CGC calculations without precaution
when only the two-point function enters in the formulation of
a cross-section, the so-called kT-factorization is applicable
• more complicated correlators for less inclusive observables
The Balitsky-Kovchegov equation
YYYTTTT zyxzzyxz the BK equation is a closed equation for obtained by assuming
YTxy
YYYYYY
TTTTTzd
TdYd
zyxzxyzyxzxy yzzxyx
22
22
)()()(
2
robust only for impact-parameter independent solutions
• the BK equation
r = dipole size• the unintegrated gluon distribution
• modeling the unintegrated gluon distribution
the numerical solution of the BK equation is not useful for
phenomenology, because this is a leading-order calculation
instead, CGC-inspired parameterizations are used for ,
with a few parameters adjusted to reproduce the data
Single particle productionat forward rapidities
Forward particle production
),(),( 22
212
2TT
TT kxfkxg
dykd
dk
kT , y
yT eksx 1
transverse momentum kT, rapidity y > 0
yT eksx 2
• forward rapidities probe small values of x
the large-x hadron should be described by
standard leading-twist parton distributions
the small-x hadron/nucleus should be
described by CGC-averaged correlators
values of x probed in the process:
the cross-section:single gluon production
probes only the unintegrated
gluon distribution (2-point function)
The KKT parametrization• build to be used as an unintegrated gluon distribution
the idea is to play with the saturation exponentKovchegov, Kharzeev and Tuchin (2004)
• the DHJ version
• the BUW version
KKT modified to feature exact geometric scaling
Dumitru, Hayashigaki and Jalilian-Marian (2006)
Boer, Utermann and Wessels (2008)
in practice is always replaced by before the Fourier transformation
KKT modified to better account for geometric scaling violations
RdA and forward pion spectrum
Kharzeev, Kovchegov and Tuchin (2004)
RdA
• first comparison to data
qualitative agreement
with KKT parametrization
kdyddN
kdyddN
NR hXpp
hXdA
colldA
2
21
xA decreases(y increases)
• the suppression of RdA was predicted
in the absence of nucleareffects, meaning if the gluons in the
nucleus interact incoherently like in A protons
What about the large-x hadron?
Dumitru, Hayashigaki and Jalilian-Marian (2006)
shows the importance of both
evolutions: xA (CGC) and xd (DGLAP)
shows the dominance
of the valence quarks
for the pT – spectrum
with the DHJ model
• getting a quantitative agreement requires correct treatment
it has been proposed as an alternative explanation
pA collisions at the LHC would answer that
• suppression of RdA due to large-x effects?
both initial particles should not be described by a CGC, only the small-x hadron
Running coupling corrections• running coupling corrections to the BK equation
taken into account by the substitution
Kovchegov
Weigert
Balitsky
• consequences
similar to those first obtained by the simpler substitution
running coupling corrections slow down the increase of Qs with energy
also confirmed by numerical simulations, howeverthis asymptotic regime is reached for larger rapidities
Probing small x withtwo-particle correlations
Final-state kinematics
• the best situation
11 , yk 22 , yks
ekekx
yy
p
21 21
s
ekekx
yy
A
21 21
probes 2-, 4- and 6- point functions
final state :
one can test more information about the CGC compared to single particle production
at forward rapidities in order to probe small x
two hadrons close in rapidityboth in the same forward direction
xp ~ 1, xA << 1
xp ~ 1, xA ~ 1BFKL evolution ?
this increases xA a lot (~ a factor 20)probes initial condition, not evolution
• a large rapidity separation between the two particles ?
this does not probe the nuclear wavefunction at small-x
- doesn’t probe large parton densities- as much effect in pp as in d+Au- we know from Tevatron that for y < 5 there is no effect
C. Marquet, NPA 796 (2007) 41
RHIC d+Au measurements
PHENIX STAR
• central/forward correlation
trigger at central rapidity : high-x
correlation function coincidence probability
conditional yield
signal
STAR, PRL 97 (2006) 152302PHENIX, PRL 96 (2006) 222301
trigger at forward rapidity : low-x
transverse momentum range includes the region
• need to do forward/forward correlation
first measurments for x > 0.01problems to calculate the pp baseline
Status of CGC calculation• the d+Au part
results at parton level ready
but problems with pdf’s and fragmentation functions at low pT
(meaning pT < 1.5 GeV, which includes most experimental bins)
• the p+p part needed for IdA
to be computed in NLOQCD framework
potential problems for low pT bins
results at hadron level ready at high-pT
not yet ready to put numberson this plot, but hopefully soon
Conclusions• Forward particle production in d+Au collisions
- the suppressed production at forward rapidities was predicted- there is a good agreement with CGC calculations
• What we learned from single particle production- both d and Au should not be described by a CGC, the deuteron pdf is important- this only tests limited information about the CGC: 2-point function ~ gluon density- now that NLO-BK is known, one should stop using models for- if the suppression is due to (small)large-x effects, there will be (more)less suppression at the LHC
• Two-particle correlations- probe more than the 2-point function- no large rapidity interval is needed between the two particles, in fact this wouldn’t probe large parton densities- only forward/forward correlations will probe x as small as in the RdA measurement- CGC predictions almost ready