Nuclear effect on charm production
in pA in the CGC framework
H. Fujii (U of Tokyo, Komaba)
w/ F.Gelis, R. Venugopalan

Outline●Introduction●

CGC framework: MV model+BK evolution●Open Charm●Charmonium●Summary and discussion

Introduction: CGC in A●

Initial condition for AA collisions–Small-x partons:–

Color Glass Condensate in high E limit●

 s x A=k1 e− y1k2 e− y2

Boost = seeing short time fluctuations⇒ dense patonic system⇒ parton saturation–In nuclei, larger partons/trans area by A1/3
●Earlier saturation than proton●Multiple scatterings in A

ATHIC2008, Oct.13 H.Fujii

AyIntroduction: CGC in A
●Evidence of CGC–HERA (DIS) :  ~ Q2/Qs2(x)–BRAHMS : RdA(y)●Large xp and small xA

A

ATHIC2008, Oct.13 H.FujiiyIntroduction: Charm●●Heavy flavors: mQ>>QCD–initial hard productions only ⇒ pQCD predictions–

Calibrated impurity probing medium property–

Caveats: nuclear pdf, intrinsic kT, multiple scattering

Quarkonia:–Rare formation–Caveats: longer formation time O(1/sm2)
formation mechanism not fully understoodestimate for cold nuclear effects

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Introduction: Why charm in CGC?
●Heavy flavors: mQ>>QCD but– Produced from gluon fusion– Multiple interactions possible at RHIC●

1/(2m) ~ 0.07 fm/c vs RA/ ~ 0.13 fm●

1/(1/sm2) ~ 0.3 fm/c

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CGC framework

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CGC framework: MV Gauss model●“Valence” partons : random charge on x+ axis

●Small-x partons:

classical fieldpure gauge●

Compute observables O ()●Average over W the distribution of ●

McLerran-Venugopalan (MV) model222–Gaussian : W[] =exp[− d x  xa /2  ]–2 ~ Qs2 : mean charge density–valid for small x, but s ln(1/x) < 1 e.g., x~0.01∫ATHIC2008, Oct.13 H.Fujii

FCGC framework: pA collision●pA coll = two sourcesApure gauge●

dilute+dense system: g2A=O(1)●Classical EoM sums tree graphs O(–pure gauge)

Multiple scatterings

pAATHIC2008, Oct.13 H.Fujii

Blaizot-Gelis-Venugopalan (2004)

CGC framework: gluon production●x-section:Apure gauge●“Unintegrated gluon dist.fn.” (uGDF)
includes multiple interactions

pure gauge

Blaizot-Gelis-Venugopalan (2004)

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CGC Framework: uGDF●

MV model assumed at x~0.01●

scale 2 ~ Qs2 ~ A1/3 in the model characterizes targets–0.22 GeV2 ...”proton”–

2.0 GeV2 ... “nucleus”●

intrinsic kT distribution●

1/k2 – perturbative tailATHIC2008, Oct.13 H.Fujii

gg

CGC Framework: x-evolution●

BK equation (large N & A)
–Evolve from x0=0.01●MV model for x>x0

–Linear: BFKL sums up (s y)–Nonlinear: gluon fusion effectφgg(kT, x) =ATHIC2008, Oct.13 H.Fujii~ Qs

CGC Framework: x-evolution●

BK equation (large N & A)–

Evolve from x0=0.01–

Nonlinear: gluon fusion effect–Peak moves to higher pT–

RpA suppressed due to fastersaturation for A

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CGC Framework: x-evolution●

BK equation (large N & A)
–Evolve from x0=0.01–

Nonlinear: gluon fusion effect–Peak moves to higher pT–RpA suppressed due to fastersaturation for A–Forward suppression for gluons
similar to BRAHMS

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preliminary
y=0,1,2,3

Open charm production

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Open charm production●Analytic formula to O(ρp1 ρAinfty)

2+

hardnucleus proton●kT factorization is broken, but small●

Collinear approx for proton may be OK= hybrid ; cheaper numerical task
HF,Gelis,Venugopalan

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Open charm production●

CGC= uGDF for p & A ; Hybrid = uGDF for A and xG for p–Hard spectrum in medium- x region–Small-x contrib is small–Look forward

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Open charm production●

Ratio of pA/pp●

Hybrid: R = “xG . uGDF(2.0)” / “xG . uGDF(0.22)”–Cronin enhancement @ RHIC

–moves to higher pT w/ y–Large suppression @ LHC

RHIC
LHC

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CharmoniumATHIC2008, Oct.13 H.Fujii

Other approach, Kharzeev et al.

Charmonium in CEM●Color evaporation model:
Assume separation of pair production and b.s. formations●Effects of dense gluons––}

M

Initial gluon saturation
Multiple scatterings of cc pair

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M-dist vs Qs2 (MV model)

Charmonium in CEM●Momentum distribution– Hardened too much
– Difficulty of model?
hybrid=kT kick only from A or need improve medium-x?

PHENIX PRC77
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Charmonium in CEM●Rapidity dependence of RdA

Ratio of dN/dycharm
J/psi

PHENIX PRC77ATHIC2008, Oct.13 H.Fujii

YSummary and Discussion●

CGC model for cc production in pA is presented–LO(s), but O(–Mid-rapidity at RHIC rather insensitive to small-x●)

Medium-x part is important–Saturation is reflected in forward rapidity–

LHC will be best place to see the saturation–

CGC model is still in primitive stage

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Discussion●

More post-dictions and predictions–

Improve the CGC model●

medium-x pdf, onium formation, ..., etc–

Centrality dep thru Qs(x,b)–AA at very forward y–

Test the model; azimuthal correlation of cc●intrinsic kT & multiple scattering

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Just preliminary