Color Glass Condensate and UHECR physics

Kazunori ItakuraKEK, Japan

SOCoR @ Trondheim

Background photo: “deformation of a polyethylene folio” by Zdenka Jenikova 2002

ContentsContents

• What is the CGC, and why?

• Facts about the CGC

• Comparison with the existing EAS models

• Possible application of the CGC to CR physics

What is the CGC?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 >> QCD , but non-perturbative )

Unitarity effects (multiple scattering, nonlinear effects) LO description completed around 2000

Color Glass Condensate (CGC)

High energy

Why CGC?Why CGC?Indispensable for correct understanding of CR physics Primary collision proton-Air collision at extremely large energy

(LHC) TeV 14 TeV 433 eV,1020lab pppp ssE

e1s

px t

e2s

px t

A1A1

A2A2

102 102~e

s

px t

1.0 and GeV 2 take

TeV, 433

1

xp

s

t

pp

Forward scattering > 0 x1 is large ~ 1 (valence) but x2 is extremely small

projectile(proton/nucleus)

target (light nucleus)

x1, x2 : longitudinal momentum fractions

pt : transverse momentum of produced hadrons

: rapidity > 0 forward direction

Cf: the smallest value in colliders x ~10-6 (HERA)

Do we really need hard physics?Do we really need hard physics?Example: typical “mini-jet” models increase of cross section is explained by increasing hard (mini-jet) contributions

pp, ppbar charged particle multiplicity pp, ppbar total cross sectionsX.N.Wang, Phys. Rep. 280 (1997) 287 A.Achilli, et al. PLB659 (2008) 137

Unitary, but no effects of “true” saturation/CGC (coherent scattering) eikonalization = sum of multiple independent scattering we expect hard (and semi-hard) components are important

),(),(),( , 1 ),(22 sbsbsbebd hardsoftsb

inel

hardcontr.

Proton composition changes with energyProton composition changes with energy

Q2 : transverse resolution x : longitudinal fraction

1/Q

1/xP+

*

transverse

longitudinal

partons

longitudinal fraction x

higher energies

Gluons (must be multiplied by 20)

Deep inelastic scattering (ep eX) can probe quarks and gluons in a proton

Gluons are the dominantcomponent at high energy (small x)

Phase diagram of a proton as seen in DISPhase diagram of a proton as seen in DIS

No

np

ertu

rba

tiv

e re

gio

n

1/x in log scale

Q2 in log scale

Parton gas

Color glass condensate

Hig

her

Hig

her

ener

gies

ener

gies

Transverse resolution

DGLAP

QCD2

BFKL

BK

Gluon density

high

low

Multiple

gluon

emissionsx

g eN 1/ln ~

Recombination

of gluons

1gN unitarity

Parton number increases, but density decreases

Saturation scale Qs(x)

Qs-1 is typical transverse size.QS

2(x) ~ 1/x increases (x 0)

s(QS2) << 1 weak coupling

Facts about the CGCFacts about the CGC2009 2009

Nonlinear evolution equations (govern energy dependence of Xsecs)

LO (s ln 1/x)n : Balitsky-Kovchegov equation (1996)

NLO s (s ln 1/x)n : completed by Balitsky and Chirilli (2008) running coupling effects (necessary for “long” evolution from low to high energies)

Dipole scatt. amp

)/(log2 , )(2exp),(

, )(exp),(

220

20000

22

3/1200

20

2

QCDQCDS

S

QcybyycbAyQ

AQyyQAyQ

Facts about the CGCFacts about the CGC20092009

Saturation scale depends on rapidity (y=ln 1/x) and atomic mass number A

Can be determined by LINEAR evolution equations (LO, resummed NLO BFKL ) Fixed coupling Qs grows exponentially and works at HERA and RHIC energies Exponent is consistent with resummed NLO BFKL (2003)

but should be taken over by running coupling Qs showing milder growth

Evidences in collider experiments (HERA, RHIC) Geometric scaling (ep & eA DIS, diffractive DIS) existence of Qs 2001 ~ 2006

extends outside of the saturation regime kt < Qs2/QCD

new wide window “extended scaling regime” (Iancu-KI-McLerran,2003)

Suppression of particle production at forward rapidity in dAu collision (RHIC 2004) Enhancement (Cronin effect) at mid-rapidity can also be understood.

Geometric ScalingGeometric ScalingDIS (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

*p total

Q2/Qs2(x) Q2/Qs

2(x,A)

Q2/Qs2(xP)

• Existence of saturation scale Qs• Can determine x and A dependences of Qs• Extends outside of the saturation regime kt < Qs

2/QCD

ep eA Diffractive ep

Correct recognition for the importance of saturation

How about existing EAS models?How about 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.

But, in Sibyll, particles below the cutoff (p < pmin) are absorbed into soft partand in QGSJETII, only soft Pomeron interactions were included. “semi-hard” contributions (QCD<pt< Qs) are missing!! main part of the CGC physics

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) kt

2

dN/dkt2

1/kt2

So, what should be done?So, what should be done?

kt2

dN/dkt2

No

n-p

ert

urb

ativ

e

(Re

gge

)

Q2

Parton gas

Extended scaling regime

CGCH

igh

er

en

erg

ies

Transverse resolution

QCD2

QS4(x)/QCD

2

1/x

QS2(x)

QS2(x) QS

4(x)/QCD2QCD

2

CGC

scaling regime

pQCD(minijet)

Most of gluons have momenta around Qs !! Need to include “CGC+scaling regime” in between soft (Regge) and hard (minijet)

Some attemptsSome attemptsModification of the minijet modelF.Carvalho, et al. arXiv:0705.1842v1

Use IIM (Iancu-Itakura-Munier) parametrization Problems matching procedure (dijet vs monojet) impact parameter dependence (black disk expansion) running coupling effects (included in v2) M.F.Cheung, C.Chiu, and K.Itakura, work in progress

BBL modelH.Drescher, A.Dumitru, and M.Strikman, PRL 94 (2005) 231801. use a simple model to calculate cross section - McLerran-Venugopalan model for quark scattering - kt factorized cross section for gluon production too naïve application of CGC (no impact parameter dep. etc) need improvement

Problems still to be clarifiedProblems still to be clarifiedImpact parameter dependence Not precisely known (non-perturbative) high energy behavior of cross section # A simple “assumption” eg: exp{ –b/2m}

leads to (Ferreiro,Iancu,KI,McLerran,2002)

(dipole-CGC

scattering)

consistent with the Froissart bound# Still need to put IR regulator for the gluon propagators# Can be (somewhat) determined from d/dt , scaling with Qs(y,A,b)?

Energy conservation # BFKL pomeron is not energy conserved. problem for realistic simulation Need to include the effects of energy conservation (Avsar et al. 2005)

black disk expansion

SummarySummary• High energy hadron scattering is described by the “Color Glass

Condensate (CGC)” which is a dense gluonic state.

• Its theoretical framework is established up to “leading-order” except for the impact parameter dependence which includes non-perturbative physics. “Next-leading-order” analysis has just started.

• The kinematical region for the CGC expands with increasing energy, and thus we naively expect the CGC will be important at CR energies.

• Why don’t you consider the CGC in CR physics?