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Recent results on saturation and CGC

Recent results on saturation and CGC. Kazunori Itakura Theory Group, KEK JAPAN. Stained glass by M. Chagall (1964) at United Nations in New York. Outline. Introduction/Motivation Basic questions, Important experimental results High energy limit of QCD Color Glass Condensate

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Recent results on saturation and CGC

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  1. Recent results on saturation and CGC Kazunori Itakura Theory Group, KEK JAPAN Stained glass by M. Chagall (1964) at United Nations in New York

  2. Outline • Introduction/Motivation Basic questions, Important experimental results • High energy limit of QCD Color Glass Condensate • The Balitsky-Kovchegov Equation A fresh look at the equation from the statistical physics (The Logistic equation and the FKPP equation) • Recent Progress in Phenomenology Deuteron-Au collisions at RHIC, predictions for LHC • Recent Progress in Theory Beyond the BK equation • Summary

  3. Introduction/Motivation Basic questions/problems which we want to answer/understand: What is the “high energy limit” of QCD ? If it indeed exists, … - Is it different from the ordinary picture of hadrons ? - Is it already seen in experiments ? - What is the evidence for it ? - Can we treat it in weak-coupling techniques ? as<<1, in scatt. with high Q2, or at high temperature/density What is the information of nucleons relevant for high energy scattering ? instead of static information such as mass, radius at rest, etc

  4. Important Experimental Results g* Deep inelastic scattering (DIS) at HERA  Steep rise of F2 (and gluon density) at small x 1/Q 1/xP+ Q2 = qT2: transverse resolution x =p+/P+: longitudinal mom. fraction High density gluons appear at small x =“high energy scatt.”

  5. cross section (mb) S1/2 10 102 103 104GeV Most recent PDG  consistent with ln2s. [COMPETE Collab.] -- saturatingunitarity (Froissart) bound -- The coefficient B is universal(B=0.308mb) for pp, p p, p p, etc….. Important Experimental Results Hadronic cross section at high energy (total cross sec. for pp) Including cosmic ray data of AKENO and Fly’s eye

  6. higher energy Dilute gas CGC: high density gluons High energy limit of QCD Keys: many gluons, unitarity, universality A universal form of matter at high energy ColorGlass Condensate(CGC) !! created from “frozen” random color source, that evolves slowly compared to natural time scale High density ! occupation number ~ 1/as at saturation Gluons have “color”

  7. An “evolution” equation, describing the change of the dipole scattering amplitude NY(x,y) ~ gluon number under the change of scattering energy s(Y~ ln s : rapidity) The Balitsky-Kovchegov equation A basic equation for the CGC [Balitsky, Kovchegov, Braun] √ Derived from QCD by using resummation w.r.t. (as ln s)n & strong gluonic field in the target A nonlinear differential equation, solved numerically with/without impact parameter in coordinate/momentum space [Braun,Golec-Biernat,Motyka,Stasto,Marquet,Soyez] analytically in some separate kinematical regimes [Levin,Tuchin,Iancu,KI,McLerran,Mueller,Triantafyllopoulos,Kozlov]

  8. Population dynamics Gluon dynamics N(t): (normalized) polulation density NY: gluon density When N<< 1[Malthus 1798] The BFKL eq. [’75~] Multiple gluon emission population explosion unitarity violation When N~1[Verhulst 1838] The Logistic equation The BK eq. [’99~] Gluon recombination nonlinear Time (energy) stable unstable Global energy dependence Exponential growth is tamed by the nonlinear term saturation ! Initial condition dependence disappears at late time  universal !

  9. Reaction-diffusion dynamics Munier & Peschanski(2003~) With a reasonable approximation*, the BK equation in momentum space is rewritten as theFKPP equation (Fisher, Kolmogorov, Petrovsky, Piscounov) where t ~ Y, x ~ ln k2 and u(t, x) ~ NY(k). Well-understood in non-equilibrium statistical physics including directed percolation, pattern formation, spreading of epidemics… FKPP = “logistic” + “diffusion” u=1: stable Logistic : “reaction” part, transition from unstable to stable states Diffusion : expansion of stable region  Traveling wave solution t t’ > t u=0:unstable *take the 2nd order expansion of the BFKL kernel around its saddle point

  10. x(t) ~ ln Qs2(Y) Saturation scale ! saturated 1/QS(Y) : transverse size of gluons when the transverse plane of a target is filled by gluons. “Boundary” btw dilute and saturated regimes Precise form of QS(Y) determined dilute R NLO BFKL : x - v(t)t~ ln k2/Qs2(Y) Geometric scaling !! Observed in HERA DIS at small x QS(Y) from the data consistent with theoretical results. Geometric scaling approximately holds even outside of CGC!!  “Scaling window” [Iancu,KI,McLerran] [Stasto,Golec-Biernat,Kwiecinski] Saturation scale & Geometric scaling Fact 1: For a “traveling wave” solution, one can define the position of a “wave front” x(t) = v(t)t . Fact 2: At late time, the shape of a traveling wave is preserved, and the solution is only a function of x – vt.

  11. “Phase diagram”of a proton as seen in DIS QS2(x) ~ 1/xl: grows as x  0 as(QS2) << 1 weak coupling CGC Extended scaling regime QS4(x)/LQCD2 Higher energies  BFKL, BK Non-perturbative (Regge) 1/x in log scale Parton gas DGLAP LQCD2 Q2 in log scale Fine transverse resolution 

  12. Recent progress in phenomenology

  13. *[Golec-Biernat,Wusthoff, Bartels, Kowalski,Teaney] @[Iancu,KI,Munier] • A cornerstone providing the most precise information about CGC • Golec-Biernat & Wusthoff model and its improvements* work relatively well. • The CGC fit@ (based on the BK eq) works very wellfor F2 at small x. •  QS2(x) = (1 GeV)2 (x0/x)l , x0=0.26 x 10-4, l=0.25 • CGC initial condition for heavy ion collision; “seeds” of QGP • Most of produced particles have pt < 1 GeV ~ QS(RHIC)  bulk quantities • Multiplicities (centrality and rapidity dependences) [Kharzeev,Levin] • Hydro-dynamical calculation with CGC initial condition [Hirano,Nara] Numerical studies [Krasnitz,Nara,Venugopalan,Lappi] • next slides • [Jalilian-Marian,Dumitru,Drescher,Strikman] • Ideal situation for CGC with x ~ 10-9 or smaller • Effects of saturation examined for pA and n-p scattering Phenomenological applications DIS at HERA Au-Au at RHIC Deuteron-Au at RHIC p-Pb and Pb-Pb at LHC (predictions) High Energy Cosmic Rays

  14. h- (h-+h+)/2 Deuteron-Au at RHIC d q, g g Going forward in p(d)-A collision corresponds to probing nuclear wavefunction at smaller x Nuclear modification factor(Brahms) If RdAu=1, d-Au is just a summation of pp (up to iso-spin effect) Au Cronin enhancement at h=0, suppression at h=3.2 Lots of studies in the CGC framework (see a review by Kovchegov & Jalilian-Marian) • Qualitative behaviors consistent with predictions of CGC. • Cronin peak multiple Glauber-Mueller scattering (McL.-V. model) • High pt suppression due to mismatch between “evolution speeds” • of proton & nucleus. Nucleus grows only slowly due to saturation. • Quantitative results also available [Albacete,Armesto,Kovner,Salgado,Wiedemann,Gelis,Jalilian-Marian,Kharzeev,Kovchegov,Tuchin, Accardi,Gyulassy,Levin,McLerran,Iancu,KI,Triantafyllopoulos,Venugopalan]

  15. Deuteron-Au at RHIC • Running coupling effects evaluated [Iancu,KI,Triantafyllopoulos] • DGLAP improvements on the projectile side (deuteron) necessary • Averaged x2 in 21 kinematics is ~ 10-3 for RHIC y~3 (private communication) • [Dumitru,Hayashigaki,Jalilian-Marian] see talk by Jalilian-Marian • Various observables show “suppression” due to saturation. • EM probes:dileptons, photons[Jalilian-Marian,Baier,Mueller,Shiff,Gay-Ducati,Betemps] • qqbar (meson) production [Blaizot,Fujii,Gelis,Venugopalan,Kharzeev,Tuchin] •  see talks by Fujii & Lappi • Jet azimuthal correlations disappear due to “mono-jet” production. • [Kharzeev,Levin,McLerran,Baier,Kovner,Nardi,Wiedemann] • Other approaches…. • Standard nuclear shadowing (NLO Leading Twist) with 22 process • [Vogt,Guzey,Strikman,Vogelsang] • Parton recombination  identified particle dependence [Hwa,Yang,Fries] • Re-scattering effects with factorization formalism of pQCD [Qiu,Vitev]  Need more detailed investigation to be convinced …

  16. nucleus (A~200) x A1/3 ~ 6 x2 in log y=4 10-4 LHC y=0 10-2 y=2 RHIC y=0 103 A1/3x100 k2 in log Phase diagram with numbers From the CGC fit Qs2(x)~(10-4/x)0.25 proton x in log Extended Scaling ~BFKL CGC 10-4 Parton gas HERA 10-2 100 103 Q2 in log

  17. Predictions Multiplicities in PbPb and p-Pb RpA(red dashed line) [Kharzeev,Levin,Nardi] [Kharzeev,Kovchegov,Tuchin] CGC at LHC LHC √sNN = 14 TeV for pp, 5.5 TeV for PbPb For the same pt, Qs2(LHC) is increased by a factor of 3 than Qs2 (RHIC). Qs2(LHC) ~ 3 -- 10 GeV2 Number of gluons in the saturation regime increases.  Effects of saturation will be more visible!! mid forward

  18. Recent progress in theoryBeyond the BK equation

  19. Beyond BK BK projectile C-odd C-even Pomeron appears as a “collective” state of the “JIMWLK” Hamiltonian which governs the small-x evolution. The same is true for the other exchanges. JIMWLK Hamiltonian correctly describes Odderon PPP Fan diagram Ploop P PPP O target Beyond the BK equation The complete picture of high energy scattering in QCD will contain Pomeron : 2 gluon exchange, C-even state Odderon : 3 gluon exchange, C-odd state Reggeon : quark-antiquark exchange,….. and interaction among them The BK equation-- multiple exchange of P, and P-merging PPP  Need to go beyond the BK equation !! In order to correctly describe the interaction among them, one needs to modify JIMWLK Hamiltonian so that it contains “P-splitting” PPP . This allows one to have Pomeron loops.

  20. Beyond the BK equation Small-x physics beyond the Kovchegov equation, Mueller and Shoshi, Nucl.Phys. B692 (2004) 175-208 Universal behavior of QCD amplitudes at high energy from general tools of statistical physics, Iancu, Mueller, and Munier, Phys. Lett. B606 (2005) 342-350 A Langevin equation for high energy evolution with pomeron loops, Iancu and Triantafyllopoulos, Nucl.Phys. A756 (2005) 419-467 Extension of the JIMWLK Equation in the Low Gluon Density Region Mueller, Shoshi and Wong, Nucl.Phys. B715 (2005) 440-460 Non-linear QCD evolution with improved triple-pomeron vertices Iancu and Triantafyllopoulos, Phys.Lett. B610 (2005) 253-261 In pursuit of Pomeron loops: the JIMWLK equation and the Wess-Zumino term Kovner and Lublinsky, Phys.Rev. D71 (2005) 085004 From target to projectile and back again: selfduality of high energy evolution Kovner and Lublinsky, Phys.Rev.Lett. 94 (2005) 181603 Duality and Pomeron effective theory for QCD at high energy and large Nc Blaizot, Iancu, Itakura, Triantafyllopoulos, Phys.Lett. B615 (2005) 221-230 High energy amplitude in the dipole approach with Pomeron loops: asymptotic solution Levin, hep-ph/0502243 Effective Hamiltonian for QCD evolution at high energy Hatta, Iancu, McLerran, Stasto, Triantafyllopoulos, hep-ph/0504182, see also hep-ph/0505235 The high energy asymptotics of scattering processes in QCD Enberg, Golec-Biernat, Munier, hep-ph/0505101 On the Projectile-Target Duality of the Color Glass Condensate in the Dipole Picture Marquet, Mueller, Shoshi, Wong, hep-ph/0505229 Fluctuations effects in high-energy evolution of QCD, Soyez, hep-ph/0504129. Perturbative Odderon in the Dipole Model, Kovchegov, Szymanowski, Wallon, Phys. Lett. B586 (2004) 267 Odderon in the Color Glass Condensate, Hatta, Iancu, Itakura, McLerran, hep-ph/0501171 A classical Odderon in QCD at high energies, Jeon and Venugopalan, Phys. Rev. D71 (2005) 125003 Keep an eye on this subject !!

  21. Summary High enegy limit of QCD is theColorGlassCondensate - high density gluonic matter which shows  saturation of gluon distribution (non-linearity),  unitarization of scattering amplitude,  universal(insensitive to initial conditions)  provides natural interpretation of geometric scaling All of these are confirmed by the close analogy with the FKPP equation for “reaction-diffusion dynamics”. CGC can be compared with experiments  small x data in DIS at HERA  suppression of RpA in deuteron-Au at forward rapidity Theoretical framework under re-construction: new direction: BEYOND the BK equation We are now approaching the complete description of high energy scattering in QCD.

  22. Thanks to My collaborators(chronological) Larry McLerran, Edmond Iancu, Elena Ferreiro, Yuri Kovchegov, Derek Teaney, Stephen Munier, Dionysis Triantafyllopoulos, Yoshitaka Hatta, Jean-Paul Blaizot My colleagues(possible future collaborators, alphabetical) Adrian Dumitru, Rikard Enberg, Hiro Fujii, Francois Gelis, Arata Hayashigaki, Tetsu Hirano, Jamal Jalilian-Marian, Dmitri Kharzeev, Cyrille Marquet, Al Mueller, Yasushi Nara, Robi Peschanski, Gregory Soyez, Kirill Tuchin, Raju Venugopalan, and all the people who are interested in CGG !!

  23. Backup slides

  24. projectile target Pomeron Loops Necessary ingredient for the complete description of the high energy limit of QCD The BK equation describes multiple exchange of BFKL Pomerons and “fan” diagrams (merging) BUT, not the opposite “Pomeron splitting” diagrams  asymmetric under the exchange btw projectile and target Need to supply “Pomeron splitting” to obtain a Lorentz inv. description ! • a new concept : duality btw proj. & target  related to “fluctuation” (BK is the mean field approximation) Modification to BK (and JIMWLK) done:  stochastic FKPP equation

  25. C-even C-odd Odderon Perturbative QCD  “hard” Odderon 3 reggeized gluon exchange in C-odd state, obeys the BKP equation [Bartels, Kwiecinski-Praszalowicz] Recent progress The BK eq. is for the hard Pomeron = two reggeized gluon exchange even under the charge conjugation. New description of Odderon in CGC [Kovchegov,Szymanovsky,Wallon,Hatta,Iancu,KI,McLerran,Jeon,Venugopalan] • Can define relevant C-odd operators for dipole-CGC & 3quark-CGC scatt. • Reproduce the BKP equation in the linear regime • In the dipole-CGC scattering, nonlinear effects kills the Odderon. A big step towards the description of n-reggeized gluon exchange !!

  26. g*p total cross section Geometric scaling Observed in HERA DIS at small x and moderate Q2 [Stasto,Kwiecinski,Golec-Biernat] The saturation scale from the data is consistent with the theoretical results Extended Scaling regime CGC Geometric scaling approximately exists even outside of CGC!!  “Scaling window”

  27. Geometric scaling with fluctuation Inclusion of Pomeron loops Stochastic FKPP equation [Iancu, Mueller, Munier] Geometric scaling is strongly violated by the “fluctuation” • Numerical analysis • by R.Enberg et al. • Geometric scaling is still valid for not so smallx

  28. ptspectrum in the CGC More about deuteron-Au @ RHIC Kharzeev-Kovchegov-Tuchin quark+gluon production Valence quark distribution + KKT param. + FF(LO,KKP) +nonpert.Cronin Jalilian-Marian quark production LO GRV98 for deuteron +IIM param. (the CGC fit) +FF(LOKKP) +K factor Dumitru-Hayashigaki- Jalilian-Marian Quark + gluon production DGLAP for deuteron + FF(LO KPP) + LO CTEQ5 with K factor + KKT param. x- and DGLAP evolution

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