Hadron scattering at the LHC energies and beyond

1. Hadron scattering at the LHC energies and beyond Kazunori Itakura KEK Theory Center Dec.8th 2010 @ Nagoya

2. Plan • What happens at high energy? • Color Glass Condensate • LHC first results: pp and PbPb • CGC at LHC • Beyond LHC : ultra-high energy cosmic rays

3. What happens at high energy?

4. High energy scattering • Consider a scattering of two stable charged particles (electrons, protons, nuclei) at very high energies: Elastic scatt. + Inelastic scatt. (=diffractive +non-diffractive) s: total energy squared in the lab frame t : momentum transfer squared High energy limit = Regge limit Deep inelastic scattering :

5. “Small-x partons” are relevant x1, x2 : mom. fractions of partons (quarks+gluons) h1 Typical kinematics of hadron-hadron (hard) scattering x1 , parton a parton b outgoing particle rapidity x2 h2 pt q • Cross section • Parton distribution functionsof hadrons are necessary • High energy scattering involves very small x partons • pp @ LHC (7TeV)x1, x2 ~ 3×10-4 (h =0, pt=2GeV) , x2 ~ 7×10-7 (h =6, pt=2GeV) • pp @ cosmic ray (400TeV) x1, x2 ~ 5×10-6 (h =0, pt=2GeV) , • x2 ~ 1×10-8 (h =6, pt=2GeV) e-6~ 2.5 x 10-3

6. What do we need? To understand “high-energy” behavior of hadron scattering from first principle we need information on “parton (gluon) distribution functions”in “very small-x” region which is being exposed only recently due to high energy experiments (HERA, RHIC, Tevatron, etc)

7. Total hadronic cross sections (mb) • Taken from “Particle Data Book” including cosmic ray data • “High energy” when s >> 1 GeV(typical hadronic scale) • Cross sections GROW with increasing energies and amount to > 100 mbat cosmic ray or LHC energies (Most of the hadronic X secs. decrease with respect to energy) RHIC LHC

8. How to “read” this data? ~60mb “shadowing” ~30mb “geometric” Xsec LHC RHIC GZK energy • Proton’s “geometric” cross section prc2~ 30 mb(charge radius rc~1 fm) • maximum absorption “shadowing” ~ 2prc2~ 60 mb < 100 mb •  Proton is “expanding” !? • Particle Data Group (COMPETE Collab. Phys. Rev.D65 (2002)) Zab : constant, B independent of the species a, b ln2 s : consistent with the Froissart bound (unitarity bound)

9. Dynamic Proton Deep inelastic scattering (DIS: ep eX) can probe quarks and gluons in a proton HERA exp Two kinematical variables Q2 : transverse resolution x = Q2 /(W2 +Q2) : longitudinal mom. fraction of partons partons g* transverse 1/Q Gluons (must be multiplied by 20) 1/xP+ longitudinal Gluons are the dominant component at high energy (small x) longitudinal fraction x  higher energies

10. What can we learn? Total hadronic cross sections  At high energy, something “unusual” must be happening in hadrons. - “expansion” of a target (hadron/nucleus) - unitarity - universal picture! • Proton dynamically changes at high energy. Gluon becomes the dominant component! DIS at high energy (small x) ColorGlassCondensate

11. Color Glass Condensate

12. What is the CGC? • Dense gluonic states in hadrons which universally appear in the high-energy limit of scattering Color … gluons have “colors” Glass … gluons with small longitudinal fractions (x <<1) are created by long-lived partons that are distributed randomly on the transverse disk Condensate … gluon density is very high, and saturated • Most advanced (and still developing) theoretical picture of high energy scattering in QCD Based on QCD (weak coupling due to Qs >> LQCD , but non-perturbative ) Not the name of “model” or “approximation”, but the name of a state Unitarity effects (multiple scattering, nonlinear effects) LO description completed around 2000 High energy Color Glass Condensate (CGC)

13. R Saturation scale : Qs(x) • Gluon distribution function: xG(x,Q2) number of gluons having longitudinal fraction in the interval “x – x+dx” looked at transverse resolution scale 1/Q. • Typical pQCD cross section : s ~as/Q2 Gluons fill the transverse area of hadron(pR2) when Q satisfying this is called “saturation momentum” Qs Intuitive picture : 1/Qs is the transverse size of gluons when they fill the transverse area of a hadron. Typical transverse momentum carried by gluons in a hadron.

14. Saturation scale : Qs(x) • Small-x limit of DGLAP equation (Double Log App.) • BFKL equation(resummation : LO (asln1/x)n, NLO: as (asln1/x)n ) • gluon number (LO) ~ewy LO NLO [Iancu,Itakura,McLerran’02] Qs grows with increasing energy (decreasing x)  weak-coupling at high energies [Triantafyllopoulos, ’03]

15. Recombination of gluons Unitarity Nonlinear effect Multiple gluon emissions Parton number increases, but density decreases Phase diagram of a proton as seen in DIS Qs-1 is typical transverse size. QS2(x) ~ 1/xlincreases (x  0)as(QS2) << 1 weak coupling Color glass condensate Higher energies high Saturation scale Qs(x) Gluon density BK Nonperturbative region low Parton gas BFKL 1/xin log scale DGLAP LQCD2 Transverse resolution Q2 in log scale

16. Evidence : Geometric Scaling DIS (ep, eA) cross sections scale with Q2/Qs2 Stasto, Golec-Biernat, Kwiecinski Freund, Rummukainen, Weigert, Schafer Marquet, Schoeffel PRL 86 (2001) 596 PRL 90 (2003) 222002 Phys. Lett. B639 (2006) 471 ep eA Diffractive ep g*p total Q2/Qs2(x) Q2/Qs2(x,A) • Existence of saturation scale Qs • Can determine x and A dependences of Qs • Extends outside of the saturation regime kt < Qs2/LQCD(Iancu,Itakura,McLerran) Q2/Qs2(xP)

17. Red line: the CGC fit Blue line: BFKL w/o saturation DIS at HERA: How it works [Iancu,Itakura,Munier‘04] “IIM model” • Fit to the data with small x • and moderate Q2 • x < 0.01 & 0.045 < Q2<45 GeV2 • Analytic solutions to Balitsky-Kovchegov equation built in: geometric scaling & its violation, saturation. • Only 3 parameters: • proton radius R, x0(nonpert.) • and lfor QS2(x)=(x0/x)lGeV2 • - Good agreement with the data • x0 = 0.26 x 10-4, l = 0.25 • Also works well for vector • meson (r, f ) production, • diffractive F2, FL • [Forshaw et al, Goncalves, Machado ’04]

18. Qualitative picture Higher energy “Black disk” Dilute parton gas Color glass condensate • Once saturated, • no evolution at local impact parameter • Transverse • expansion Independent of initial conditions (universal) Gluon saturation (Unitarity effects) One can compute how the black disk expands with appropriate information of nonperturbative physics. (ex: Ferreiro,Iancu,Itakura,McLerran2002)

19. Early physics results from LHC

20. LHC as the “QCD machine” Most of produced particles are “standard-model” particles including hadrons. # of hadrons = 1010 # of Higgs Early time measurement  global event properties May ~8nb-1 2009 ~10mb-1 July/2010 ~350nb-1 Figure : Tokushuku2010 July 26 @ KEK

21. Key Measurements #Events 104-105 • Global event properties • dN/d, dN/dnch, <pT>(nch), dN/dpT • Particle ratios • Anti-Baryon/Baryon (Baryon Number Transfer, Asymmetry vs rapidity) • Particle correlations • Quantum correlations (Bose-Einstein) • Angular correlations • Identified particle spectra up to the perturbative regime • Underlying event studies (trigger on rare processes) • Particle density, energy density, <pT>(nch) • High-Multiplicity pp (needs trigger) • All of the above 109 Andreas Morsch, LHCC Open Session

22. pp collisions at LHC • Multiplicity (rapidity and pt dep) • Most of particles have pt < 1GeV • Global event properties incl. soft + semi-hard physics (underlying event) (pseudo)rapidity pt q fragmentation proton proton hard collision Two particle (angular) correlation  Jet structure, ridge • Total number of produced particles • A few tens to more than 100 • high multiplicity event

23. pp @ 900GeV (ATLAS) Charged particle multiplicity • Discrepancy btw MC simulations and datais visible already at 900GeV. • (MC were tuned with data of TevatronRun I (CDF, D0)at 1.8TeV) • Unnatural behaviors of MC simulations

24. pp @ 7TeV (ATLAS) Discrepancy becomes more evident. MC simulations: PYTHIA and PHOJET

25. Only apparently similar…. PYTHIA MC09 vs PHOJET Large difference in treating diffractive scatterings, reflecting our poor knowledge about soft physics.

27. Ridge appeared in high-multiplicity event Tiny, but important observation consistent with CGC picture (see later)

28. Pb-Pb collisions at LHC • To create “quark-gluon plasma” • Multiplicity  rich information on the dynamics • Elliptic flow  viscosity of QGP • Jet quenching

29. Pb-Pb collisions at LHC (2.76ATeV)

30. 17 Nov: arXiv:1011.3914, acc. PRL STAR at RHIC Pb-Pb collisions at LHC (2.76ATeV) • Just finished – already plenty of new results Most of them are surprising and challenging! • Charged particle multiplicity at mid-rapidity (h=0) 30% larger than CGC predictions  CGC fails at LHC energy? • Elliptic flow similar to RHIC  again sQGP??? Strong if QGP is created Strongest if viscosity is small (RHIC-QGP~ ideal fluid)

31. 0-10% central 102 GeV Including CDF data 47 GeV 0.9 TeV * NLO (2.76 TeV)/NLO(0.9 TeV) Df Dh Jet quenching RAA = 1 for (very) hard QCD processes in absence of nuclear modifications This will be a pure final state effect (not the initial state effect like CGC)

32. CGC at LHC pp collision

33. Global properties from CGC McLerran-Praszalowicz,Acta Phys.Polon.B41 (2010)1917, arXiv:1006.4293 [hep-ph] Energy dependence of various physical quantities are determined by Qs . ~ Qsat (Al Mueller ’99) l=0.23  Consistent with Qs(x) Qs2(x) ~Q02 (1/x)l, l ~ 0.25--0.3  Consistent with exp data

34. Improved IIM model Levin-Rezaeian, PRD 82 (2010) 014022 [arXiv:1005.0631] • Semi-analytic approach based on kt factorization unintegrated gluon density from CGC similarly parametrized as IIM model • Works well for global properties Also consistent with data at 7 TeV(CERN theory institute, August 2010)

35. CGC at LHC Pb-Pb collision(and ridge in pp)

36. 1/Qs CGC and Glasma in HIC • CGC provides “initial condition” • How does CGC change into QGP? • Glasma (glass + plasma) non-equilibrium state btw CGC & QGP: rapidly expanding gluonic state key: Nielsen-Olesen instability (Fujii-Itakura-Iwazaki, 2008) Unstable wrt fluctuations Flux tube structure

37. Long range correlation space-time rapidity C hA, hB : rapidity of particles A,B Space-time coordinates at the freeze-out time The last point of correlation Long-range rapidity correlation must be embedded at very early time after the collision

38. “Ridge” from glasma flux tubes Glasma provides strong Yang-Mills fields coherently directed to the z axis  Flux tube structure constant in the rapidity direction, random on the transverse plane Decay of rapidity-independent fields  ridge like long-range correlation Radial flow gives nontrivial correlation in the azimuthal dependence Dumitru, et al, “The ridge in proton-proton collisions at the LHC” arXiv:1009.5295 [hep-ph] “Ridge” from glasma flux tubes is applicable even in pp collisions  strongly suggests the importance of CGC in pp @ LHC

39. CGC fails in HIC at LHC?? • “CGC predictions [7][8]” based on the most-advanced calculation underestimated dN/deta (eta=0). CGC survived 200AGeV@RHIC. Need to understand the origin of discrepancy - CGC is not applicable at LHC ?? - New effects started to appear? - Present CGC calculation is not enough… Not plausible Perhaps, and interesting We are now working hard

40. Beyond LHC

41. CGC in astrophysics? • Most violent high-energy phenomena exist in space • Where are energetic particles? Ultra-High Energy Cosmic Rays Cosmic jets (AGN, g-ray burst, etc) AGN Microquasar Pulsar GRB

42. A1 A2 Application to EAS (Extensive Air Shower) CGC is indispensable for correct understanding of CR physics Primary collision  proton-Air collision at extremely large energy Forward scatt. h > 0 x1 is large ~ 1 (valence) but x2 is extremely small Precise understanding of EAS is crucial for the determination of primary energy, mass composition, acceleration mechanism.

43. Comments on existing EAS models T. Stanev, “High Energy Cosmic Rays” (2004), p208 When the parton density (at low x values and high energy) reaches a very high value, the individual partons cannot see each other and thus interact; they are obscured by intervening particles. This is obvious in the simple geometrical definition of a cross-section, but certainly also happens in the real world. Correct recognition for the importance of saturation Existing models are supposed to include “effects of saturation” Sibyll 2.x : hard part is given by mini-jet model with an “energy dependent” cutoff similar to Qs(x) with running coupling (x~1/s) QGSJET II: Pomeron-pomeron interaction (nonlinear effects) dN/dkt2 1/kt2 kt2 But, in Sibyll, particles below the cutoff (p < pmin) are absorbed into soft part and in QGSJETII, only softPomeron interactions were included.  main part of the CGC physics (“semi-hard” part LQCD<pt< Qs) is missing! Currently, a project (Kiban B) is going on to create a new EAS simulation code including the effects of CGC.

44. Summary • Hadronic scattering in the high-energy limit requires a new formulation so as to have “unitarity (multiple scattering)”, “multiple production/saturation of gluons”, and so on. • They are realized in the framework of “Color Glass Condensate”. • CGC is consistent with many of the LHC results at pp collisions, but still needs improvements at PbPb collisions. • Cosmic ray air shower is the ideal place for the small-x physics, and CGC must be included in the simulation code. Also interesting to apply to high-energy phenomena in astrophysical jets.