STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate
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Transcript of STAR azimuthal correlations of forward di-pions in d+Au collisions in the Color Glass Condensate
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STAR azimuthal correlations of forward di-pions ind+Au collisions in the
Color Glass Condensate
Cyrille Marquet
Institut de Physique Théorique, CEA/Saclay
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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
- I will focus on di-hadron azimuthal correlations
a measurement sensitive to possible modificationsof the back-to-back emission pattern in a hard process d Au → h1 h2 X
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Outline
• Introduction to parton saturation
- the hadronic/nuclear wave function at small-x- non-linear parton evolution in QCD- the saturation scale and the unintegrated gluon distribution
• Di-hadron correlation measurements
- at high-pT/central rapidities in p+p collisions : high-x physics- at low-pT/forward rapidities in p+p collisions : small-x physics- at low-pT/forward rapidities in d+Au collisions : saturation physics
• Comparing d+Au data with CGC predictions
- parameters fixed with single particle spectra (Javier’s talk, last meeting)- forward di-pion correlations : monojets are produced in central d+Au
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Parton 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
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Di-hadron correlation measurements
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Di-hadron final-state kinematics11 , yk 22 , yk
s
ekekx
yy
p
21 21
s
ekekx
yy
A
21 21
final state :
forward rapidities probe small x
xp ~ 1, xA << 1
• azimuthal correlations
• scanning the wave-function
high pT’s probe large x
xp ~ xA < 1
- but are very sensitive to possible non-linear effects (modification of the back-to-back
emission pattern in a hard process)
- are only a small part of the information contained in
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Dijets in standard (linear) pQCD
this is supported by Tevatron data
in pQCD calculations based on collinear factorization, dijets are back-to-back
transverse view
peak narrower with higher pT
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Azimuthal correlations in p+ptypical measurement in p+p collisions at RHIC:
coincidenceprobability
this is probing small-x, but not quite the saturation regime
rather one is sensitive to the growth of the gluon distribution
(near side)
(away side)
(rad)
at RHIC this is done
with low-pT pions
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Azimuthal correlations in d+Authe evidence for parton saturation:
d+Au central
(near side)
(away side)
(rad)
p+p
transverse view
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Comparison with CGC predictions
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Forward particle production
kT , y
yT eksx 1
transverse momentum kT, rapidity y > 0
yT eksx 2
forward rapidities probe small values of x
values of x probed in the process:
),(),( 22
212
2TT
TT kxfkxg
dykd
dk
the large-x hadron should be described by
standard leading-twist parton distributions
the small-x hadron/nucleus should be
described by a Color Glass Condensate
the cross-section:single gluon production
probes only the (unintegrated)
gluon distribution
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NLO-BK description of d+Au data
this fixes the two parameters of the theory:- the value of x at which one starts to trust (and therefore use) the CGC description- and the saturation scale at that value of x
in very forward particle production in p+p collisions at RHIC (where NLO DGLAP fails), using this formalism to describe the (small-x) proton also works
Albacete and C.M. (2010)
Betemps, Goncalves, de Santana Amaral (2009)
the shapes and normalizations are wellreproduced, except the 0 normalization
the speed of the x evolution and of
the pT decrease are predicted
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Forward di-hadron production
the CGC cannot be describedby a single gluon distribution
involves 2-, 4- and 6- point functions
no kT factorization
is sensitive to multi-parton distributions, and not only to the gluon distribution
the saturation regime is better probedcompared to single particle production
a good test for the theory
C. M. (2007)
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The two-particle spectrum
collinear factorization of quark density in deuteron Fourier transform k┴ and q┴
into transverse coordinates
pQCD q → qg wavefunction
b: quark in the amplitudex: gluon in the amplitudeb’: quark in the conj. amplitudex’: gluon in the conj. amplitude
interaction with hadron 2 / CGC
n-point functions that resums the powers of gS A and the powers of αS ln(1/xA)
computed with JIMWLK evolution at NLO (in the large-Nc limit),and MV initial conditions no parameters
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Monojets in central d+Au• in central collisions where Qs is the biggest
there is a very good agreement of thesaturation predictions with STAR data
suppressed away-side peak
an offset is needed toaccount for the background
• the focus is on the away-side peak
where non-linearities have the biggest effect
to calculate the near-side peak, oneneeds di-pion fragmentation functions
standard (DGLAP-like) QCD calculations cannot reproduce this
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The centrality dependenceit can be estimated by modifying the initial condition for NLO-BK evolution
for a given impact parameter,the initial saturation scale used is
no data yet,
but hopefully soon
peripheral collisions are like p+p collisions
the away-side peak is reappearing
when decreasing the centrality
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with higher pT, one goes away from the saturation regime
the away-side peak is restored at higher pT
The pT dependence
so far, only p+p data have been shown
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Conclusions
• New d+Au RHIC data show evidence for parton saturation
• Single particle production at forward rapidities- the suppressed production at forward rapidities was predicted- there is a good agreement with NLO-BK calculations
• Two-particle correlations at forward rapidities- probe the theory deeper than single particle measurements- mono-jets were predicted and are now seen in central d+Au collisions- first theory(CGC)/data comparison successful, more coming
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Back-up slides
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The non-linear QCD evolution
)()( )( )( )()()(
)(
2 )( 22
22 yzzxyxyzzx
yzzxyx
yx
YYYYYY NNNNNzdNdYd
this is a leading-order equation in which the coupling doesn’t run
• BK equation in coordinate space
• the unintegrated gluon distribution
Balitsky-Kovchegov x evolution
BK evolution at NLO has been calculated
one should obtain from the evolution equation
• 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, saturation models are used for (with a few parameters adjusted to reproduce the data)
before
nowBalitsky-Chirilli (2008)
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BK evolution at NLO• running coupling (RC) corrections to the BK equation
taken into account by the substitution
Kovchegov
Weigert
Balitsky
RC corrections represent most of the NLO contribution
(2007)
• the begining of saturation phenomenology at NLO
first numerical solution
first phenomenological implementation
Albacete and Kovchegov (2007)
to successfully describe the proton structure function F2 at small x
Albacete, Armesto, Milhano and Salgado (2009)
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2- 4- and 6-point functionsthe scattering off the CGC is expressed through the following correlators of Wilson lines:
if the gluon is emitted before the interaction, four partons scatter off the CGC
if the gluon is emitted after the interaction, only the quarks interact with the CGC
interference terms, the gluon interacts in the amplitude only (or c.c. amplitude only)
Blaizot, Gélis and Venugopalan (2004)
need more than the 2-point function: no kT factorization same conclusions in sea quark
production
and two-gluon productionusing Fierz identities that relate WA and WF, we recover the z → 0 (soft gluon) limit
Jalilian-Marian and Kovchegov (2004)
Baier, Kovner, Nardi and Wiedemann (2005)
we will now include the xA evolution
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Performing the CGC average
characterizes the density of color charges along the projectile’s path
with this model for the CGC wavefunction squared, it is possible to compute n-point functions
• a Gaussian distribution of color sources
is the two-dimensional massless propagator
• applying Wick’s theorem
when expanding in powers of α and averaging,
all the field correlators can be expressed in terms of ),'(),( yx zz dc
the difficulty is to deal with the color structure
Fujii, Gelis and Venugopalan (2006)
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MV model and BK evolution
in the large-Nc limitis related to in the following way
With this model for the CGC wavefunction squared, it is possible to compute then-point functions:
Blaizot, Gélis and Venugopalan (2004)
and obeys the BK equation:
we will use the MV initial condition: McLerran and Venugopalan (1994)
with the initial saturation scale
→