Post on 11-Jan-2016
description
Particule production and saturation
Cyrille MarquetSPhT, Saclay
ISMD 2005, Kromeriz, Czech Republic
• IntroductionBjorken limit and Regge limit of perturbative QCD
• High-energy QCD (the Regge limit) and saturationscattering matrix for high-energy partonsqq dipoles, gg dipoles, multipoles, … observables at small-x
• HERA Phenomenologyforward jetsvector mesons, DVCSdiffractive jets
• Conclusion and outlook
Contents
Introduction
The Bjorken limit of pQCDConsider a collision of hadronic particules with a center-
of-mass energy W and a hard scale Q >> QCD
• The Bjorken limit: Q² , W² with Q²/W² fixed ( xBj in DIS)
• Operator product expansion• At leading twist:
collinear factorizationgluon distributionDGLAP evolution
• Higher twists suppressed by powers of Q²
• Scattering amplitudes decrease with increasing Q²
Transverse view of
the proton in DIS
The Regge limit of pQCD
• The Regge limit:W² with Q² fixed (xBj 0 in DIS)
• One has to introduce a new scale:the saturation scale Qsat(W²)
Consider a collision of hadronic particules with a center-of-mass energy W and a hard scale Q >> QCD
• If W is such that Qsat(W²) < Q,no higher-twist effectskT-factorization, unintegrated gluon distribution, BFKL evolutionscattering amplitudes increase with increasing W
• If W is such that Qsat(W²) > Q, density effects are important (higher-twist)need to go beyond the OPE,strong gluon fields, CGC, saturation …scattering amplitudes approach unitarity limit
Qsat(W²)
High-energy QCD(the Regge limit)
• For an incoming quark of color i, at transverse position x:
The action of the S matrix is
Scattering matrix for high-energy partons
target...,, iin x
)/1(target...,,)( 2WOjWS ijF
jinout xx
• For a gluon: the same with the adjoint Wilson line WA
• Wilson lines WF and WA: the degrees of freedom of high-energy QCD
),(exp)( xATdxigPW aaSF xx Y = log(W²) : total rapidity
Tqq(x, x’,Y): the scattering amplitude of a qq dipole off the target:
Tqq(x, x’; y, y’,Y): the scattering amplitude of two qq dipoles:
Tgg(x, x’,Y): the scattering amplitude of a gg dipole:
and more generally any multipole
Dipoles and multipoles
t
abA
bF
aF zWTWTWTr )....(....))()'(( xx
tFF
cqq WWTr
NYT ))()'((11),',( xxxx
tAA
cgg WWTr
NYT ))()'((
111),',( 2 xxxx
tAFFF
cqq WWTrWWTr
NYT ))()'(())()'((11),',;',( 2
)2( yyxxyyxx
(2)
• Instead of directly the Wilson lines, colorless combinations arise as the degrees of freedom:
• We have denoted target.target. t
Simplest illustration : DIS
r: transverse size of the dipole
b: impact parameter
z: longitudinal momentum fraction of the quark
qqzrrdzbdd )Q,,( 222*
2* pSfd f
does not depend on z in the high-energy limit
the qq dipole amplitude Tqq(r, b, Y) appears
2
22 )Q,,()Q,( zrdzr
Y: total rapidity
);,()Q,( 222 YbrTbdrrd qqDIS
Observables at small-x
• Particule production phenomenology: jet cross-sections, heavy-quark production, diffractive vector mesons production, di-lepton production, multiplicities …have been studied in this high-energy QCD framework
The same dipole amplitudes enter in the formulation of
inclusive, diffractive, exclusive cross-sections
Y[A], and therefore Tqq, Tgg, Tqqg … are mainly non-perturbative, however the Y evolution is computable (in the leading logarithmic approximation)
for more on these equations, see Larry McLerran’s talk tomorrow
and Robi Peschanski’s talk sunday
)()( YTKYTdYdH
dYd
qqqqYY
• More generally, any cross-section is a function of Tqq, Tgg, Tqqg …
• The more exclusive the final state is, the more complicated the corresponding multipoles are
• How does one compute Tqq, Tgg, Tqqg …? With ][][][ AfADAAf Yt
HERA phenomenologyfor particule production
* -proton collisions
Forward-jet production• proton + * forward-jet + X
photon virtuality: Qjet transverse momentum: kwith Q k » QCD and xBj <<1, small-x effets expected
• photon qq dipole and jet emission gg dipole
C.M., R. Peschanski and C. Royon, Phys. Lett. B 599 (2004) 236
C.M. and C. Royon, in preparation
• the different observables are well described by BFKL and saturation models
• NLOQCD is a factor 2 below the data at small-x
data: see Leif Joensson’s talk later today
Diffractive vector-meson productionS. Munier, A. Stasto and A. Mueller, Nucl. Phys. B 603 (2001) 427
),()Q,,()Q,( 22 zrzrdzr V
22.22 )Q,();,(
161 reYbrTbdrd
dtd biq
)Q,,( 2zr ),( zrV
t = -q²
• the S-matrix is extracted from the data for • S(1/r 1Gev, b 0, x 5.10-4) 0.6
HERA is entering the saturation regime
biqqq eYbrTbd .2 );,();,( YbrT qq or
need a parametrization for
Diffractive J-Psi production (1)H. Kowalski and D. Teaney, Phys. Rev. D 68 (2003) 114005
dipole amplitude: ansatz for the b dependence
),()Q,,()Q,( /22 zrzrdzr PsiJ
22.22 )Q,();,(
161 reYbrTbdrd
dtd biq
))()/1,(exp(1);,( 22 bTrxxgarYbrT qq 2
)( bebT Y = log(1/x)
Diffractive J-Psi production (2)E. Gotsman, E. Levin, M. Lublinsky, U. Maor and E. Naftali, Acta Phys. Polon. B34 (2003) 3255
• dipole amplitude obtained from a numerical solution of the BK equation
• ansatz for the b dependence in the initial condition
2222 );,()Q,( YbrTrrdbd qq
),()Q,,()Q,( /22 zrzrdzr PsiJ
Deeply Virtual Compton Scattering
• they compute
• they assume
L. Favart and M. Machado, Eur. Phys. J C29 (2003) 365Eur. Phys. J C34 (2004) 429
Bt
te
dtd
dtd
0
2222
0)Q,();,(
161 rYbrTbdrd
dtd
qqt
0
1
t
dtd
B
Bartels Golec-biernatKowalski model
• to do better and compute , one needs a model for
• need an analysis of the BK equation at non zero momentum transfer:
biqqq eYbrTbd .2 );,(
dtd
with t = -q²
C.M. and G. Soyez, Nucl. Phys. A, in pressC.M., R. Peschanski and G. Soyez, Nucl. Phys. A 756 (2005) 399
))/1,(exp(1 22 rxxgar
Y = log(1/x)
• Diffractive photon dissociation is the dominant contribution to the diffractive cross-section diff at large MX in DIS:
elas: involves the qq dipole fluctuation, dominant for small-mass final states dissoc: involves higher Fock state fluctuations: qqg, …dominant for large-mass final states
Diffractive jet production (1)
= Q²/MX² <<1
dissocelasdiff
rapidity gap
= log(1/xpom)xpom<<1target
proton
k: transverse momentum of the final-state gluon
C. M., Nucl. Phys. B 705 (2005) 319
K. Golec-Biernat and C. M., Phys. Rev. D 71 (2005) 114005
• 1/k0: typical size at which the S-matrices are cut off
observable strongly sensitive to unitarity effects
• measuring could select between saturation and Regge-based models
kddMd
X 2
0 k
modeldependent
kddMdk
X
dissoc2
2
k²1/k²
modelindependent
modelindependent
k0
Tqq and Tqq
(2)
Diffractive jet production (2)kmax/QS = independent of Q², QS
1.5
saturation predictions for HERA:
RHIC phenomenologysee Larry McLerran’s talk tomorrow
quark-antiquark pair productionsee Hiro Fujii’s talk sunday
recent review on particule production and saturation at RHIC: J. Jalilian-Marian and Y. Kovchegov, hep-ph/0505052
• Particule-production cross-sections are sensitive to the small-x regime of QCD they contain important complementary information w.r.t. DIS for Tqq but also for Tgg, Tqqg, … on impact parameter/momentum transfer dependence
• Diffractive vector meson production at HERA: saturation models with ansatz for the impact parameter profile work quite well but that is not evidence for saturation need to start working with the momentum transfer
• Jet production in diffraction at HERA: great place to look for saturation effect can distinghuish between soft models and saturation
Conclusions
• Universality of Tqq:there are several parametrizations for Tqq
but could we describe everything that Tqq should describe with only one? new global analysis
• Has RHIC really provided evidence for saturation? waiting for the LHCor listen to Larry McLerran tomorrow
Outlook
RHIC phenomenologysee also Larry McLerran’s talk tomorrow
see recent review: J. Jalilian-Marian and Y. Kovchegov, hep-ph/0505052
R. Baier, A. Kovner and U. Wiedemann, Phys. Rev. D 68 (2003) 054009D. Kharzeev, Y. Kovchegov and K. Tuchin, Phys. Rev. D 68 (2003) 094013E. Iancu, K. Itakura and D. Triantafyllopoulos, Nucl. Phys. A 742 (2004) 182J.P. Blaizot, F. Gélis and R. Venugopalan, Nucl. Phys. A 743 (2004) 13J.Albacete, N. Armesto, A. Kovner, C. Salgado and U. Wiedemann, Phys. Rev. Lett 92 (2004) 082001
Nuclear modification factor in deuteron-gold collisions (1)
);,()/1log()(1 20
/1
022
beamgg
gXdA
brTbdr
rr
rkrJdrkkdd
dN
kdddN
kdddN
NR hXpp
hXdA
colldA
2
21
with the parton-level cross-section
predictions with a toy-model for Tgg and with a numerical solution of the BK equation
Nuclear modification factor in deuteron-gold collisions (2)
first comparisons to the data:
D. Kharzeev, Y. Kovchegov and K. Tuchin,Phys. Lett. B 599 (2004) 23D. Kharzeev, E. Levin and M. Nardi, Nucl.Phys. A 747 (2005) 609
A. Dumitru, A. Hayashigaki and J. Jalilian-Marian, hep-ph/0506308
recent work:
shows the importance
of both x and DGLAP
evolutions
shows the importance
of the quark component
Azimutal correlationsD. Kharzeev, E. Levin and L. McLerran, Nucl. Phys. A 748 (2005) 627
J. Jalilian-Marian and Y. Kovchegov, Phys. Rev. D 70 (2004) 114017N. Nikolaev, W. Schäfer, B. Zakharov and V. Zoller, hep-ph/0504057R. Baier, A. Kovner, M. Nardi and U. Wiedemann, hep-ph/0506126
but: correlators with product of up to four Wilson lines enter in the formulation
of the cross-section
preliminary data:predictions using kT-factorization assumption
Other Observables• Dilepton production
electromagnetic probe very clear signal, no fragmentation functionbut need data
• Heavy quark productionsee Hiro Fujii’s talk sunday
N. Armesto and M. Braun, Eur. Phys. J C22 (2001) 351B. Kopeliovich and A. Tarasov, Nucl. Phys. A 710 (2002) 180K. Tuchin, Phys. Lett. B 593 (2004) 66N. Nikolaev and W. Schäfer, Phys. Rev. D 71 (2005) 014023J.P. Blaizot, F. Gélis and R. Venugopalan, Nucl. Phys. A 743 (2004) 57
B. Kopeliovich, J. Raufeisen and A. Tarasov, Phys. Lett. B 503 (2001) 91F. Gélis and J. Jalilian-Marian, Phys. Rev. D 66 (2002) 094014M. Betemps, M. Gay Ducati, M. Machado and J. Raufeisen, Phys. Rev. D 67 (2003) 114008R. Baier, A. Mueller and D. Schiff, Nucl. Phys. A 741 (2004) 358