Upload
terence-wilkinson
View
218
Download
0
Tags:
Embed Size (px)
Citation preview
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?