F.S.N., V.P. Gonçalves and E. Cazaroto

IFUSP / BRAZIL

Charm production in the dipole approach Introduction

Summary

Charm structure function

Charm pt distribution in eA

Charm production in pp and pA

(focus on saturation effects)

Introduction

Collinear factorization + DGLAP evolution

KT factorization + unintegrated gluon densitiesColor dipole + dipole cross section

Dipoles: easy inclusion of saturation effects

Why charm ?

Heavy enough for perturbative QCD

Light enough to be abundant

How to calculate ?

Nikolaev, Zakharov (1991), A. Müller (1994)

sc Qm ~ saturation effects ?

22 25.0 FF c more important at low x

Zotov´s talk

ep: boson-gluon fusion

pp: gluon-gluon fusion

color (singlet) dipole

color (octet) dipole

A Ap

Charm structure function in eA

)(4

),(2

22

2 LTem

A QQxF

),(|),,(| 22,

2, rxQrdrd dALTLT

),,(2),( 2 brxNbdrx AdA

])(),(2

1[exp1),,( bTrxbrxN AdpA Armesto (2002)

QCD input: in the dipole – proton cross section !

Albacete´s talk

Stasto´s talk

AA

Dipole – proton cross section

Kowalski - Motyka - Watt bCGC (2006)

Iancu – Itakura - Munier IIM (2004)Kharzeev - Kovchegov -Tuchin KKT (2004)

Dumitru - Hayashigaki – Jalilian-Marian DHJ (2006)

Boer - Utermann - Wessels BUW (2008)

Gonçalves – Kugeratski – Machado – Navarra GKMN (2006)

Marquet - Peshanski - Soyez MPS (2007)

Albacete – Armesto – Milhano - Salgado rcBK (2009)

Kowalski - Teaney IPsat (2003)

(and others...sorry for omissions)

Golec-Biernat - Wüsthoff GBW (1998)

Bartels – Golec-Biernat - Kowalski BGK (2002)

Linear limit with dipoles

})(4

1{exp1),( 22

sQrrxN

)(4

1{exp1),( 22

sQrrxN }

)](lnexp[1 2sQrba

),( rxN

20

sQrN

eff22sQr

2sQr

linear

saturationfull

GBW )(4

1),( 22

sQrrxN

)(4

1),( 22

sQrrxN

KKT

IIM

dp

0r

rcBK

(all numerical)

Color transparency (CT)

Color transparency + Shadowing (CT + Shad)gR from EKS98

Ng from GRV98

Mixed description: ),(3

),( 222

2 Qxgxrrx AsdA

),(),( 22 QxgxAQxgx NA

),(),(),( 222 QxgxQxRAQxgx NgA

dA

])(),(2

1[exp1),,( bTrxbrxN AdpA dp linear

Linear - p:

Saturation: reduction by a factor 3 to 4 at

Charm structure function in eA

510x

Pb

Gonçalves, Kugerastski, Navarra (2010)

Pb

Linear - p

Gonçalves, Kugerastski, Navarra (2005)

Almost no reduction

Stasto´s talk Saturation: reduction by a factor ~ 2

Linear limit without dipoles

pc

Ac

c FA

FR

2

2Collinear factorization approach:

),(),(2

)(),,(

1 212

222

xgy

xC

y

dyemQxF

x xa

scc

c ),( zC Coefficient function from pQCD

),( 2Qxgx A

DS: de Florian, Sassot (2004)

EPS: Eskola, Paukkunen, Salgado (2008) Cazaroto, Gonçalves, Carvalho, Navarra (2009)

Linear limit without dipoles

Difficult tosee saturation

Heavy quark pt distribution

Flöter, Kopeliovich, Pirner, Raufeisen (2007)

eA

AA

charm

bottom

Gonçalves,Kugerastski, Navarra (2010)

5 - 83 - 4

1.5 - 2

~1.5

~2 ~3

22 2 GeVQ

eA

charm

bottom

Gonçalves,Kugerastski, Navarra (2010)

22 4 GeVpT

~1.5

~3 ~4

5 3 - 42

eA

D meson pt distribution

Gonçalves,Kugerastski, Navarra (2010)

eA

Petersonfragment.

Charm production in pA collisions

Kopeliovich, Tarasov (2002)

),(|),(|}{ 21

0

21

0

qgqQQgddXQQNg

)(8

1)]()([

8

9),( dpdpdpqgq

})()()({)2(

)(|),(| 2

12222

02

2

22

QQQQ

sQQg mKmmKm

}{),(}{ 2

11 XQQpgxGxyd

XQQppd

}{),(2}{ 211

)2/ln(

0

XQQpgxGxydXQQppQms

)( 1xG

s

emx

yQ2

1

s

emx

yQ

2

2

)(ln2

1

2

1

x

xyGRV 98 22

cm

pp

Cazaroto, Gonçalves, Navarra in progress

PHENIX

UA2

C-Rays Merino et al. (2009)

Merino,Pajares,Ryzhinskiy, Shabelski,Shuvaev, arXiv:0910.2364

NLO QCD

KT factorization

KT fac

C-Rays nucl-ex/0607015

])])(2

1[exp1(2[2

0

bTbbd Adp

R

dA

A

pA

Saturation: reduction by 10 % with x going down to

62 10x

Total cross section

linear p

220

4 sdp Q

Rapidity distribution

Saturation: reduction by 1.7 at y = 6

yd

XQQppd }{

Summary

Dipole models reproduce well the data on

Well established dipole model for charm production in ep, eA, pp and pA

eA @ 1TeV: large suppression factors (1.5 – 8) in dN/d pt (CT , CT+Shad)

pA @ 10 TeV: reduction by 10 % (or 1.1) in the total cross section (linear-p)

pA @ 10 TeV: reduction by 1.7 in dN/dy at large y (linear–p)

CT (overestimates linear regime)

CT+ShadLinear p (underestimates linear regime)

)( XQQpp

F2c: large suppression factors (3 – 4) with (CT , CT+Shad)

F2c: almost no suppression with (linear-p)

Rc: no sign of saturation F2c: large suppression factors (2) in other approaches

Different ways to estimate the linear predictions in eA and pA:

x

xQAQs

020

3/1222

0 0.1 GeVQ 4

0 10267.0 x

253.0

pp

Very small r

})(4

1{exp1),( 22

sQrrxN

)(4

1{exp1),( 22

sQrrxN }

GBW )(4

1),( 22

sQrrxN

)(4

1),( 22

sQrrxN

0r

rcBK (?)

Not so small r

Discussion

On charm production in pp and AA :Merino,Pajares,Ryzhinskiy, Shabelski,Shuvaev, arXiv:0910.2364

NLO QCD

KT factorization

KT factorization

NLO QCD

FONLL

STAR data

Will we have data on total cross section from Tevatron?

Disagreement between PHENIX and STAR is gone ?

KT factorization

NLO QCD

Tevatron data

Fragmentation ?

If STAR was right enhanced production might have non-pert. origin: strong fields

Should we prefer KT factorization?

pp

Cazaroto, Gonçalves, Navarra in progress

PHENIX

UA2

C-Rays Merino et al. (2009)

Merino et al. (2009)

Merino,Pajares,Ryzhinskiy, Shabelski,Shuvaev, arXiv:0910.2364

KT factorization

NLO QCD

R = full / linearF2

Charm structure function in the KLN model

),(),(2

)(),,(

1 212

222

xgy

xC

y

dyemQxF

x xa

scc

c

2

2

1Q

ma c

),( zC Coefficient function from pQCD

222 4 Qmc 22 4 cm

),( 2xgx

422

0 )1()(

xQSQss

422

0 )1()(

xQSQ s

ss

22sQQ

22sQQ linear

saturation

)( 020

2

x

xQQs

Glück, Reya, Stratmann (1994)

Glück, Reya, Vogt (1995)

Kharzeev, Levin, Nardi (2001)

GeVmc 2.1

2RS

ep

220 34.0 GeVQ

30 103 x

25.0

Carvalho, Durães Navarra, Szpigel (2009)

eA

),(),( 22 xgxg A

SASS A 3/2

23/122s

Ass QAQQ

pc

Ac

c FA

FR

2

2

linear

fullRFL

Charm production in pA collisions

Kopeliovich, Tarasov (2002)

Back ups

Introduction

NLO collinear factorization

Fixed Order plus Next to Leading Log (FONLL)

KT factorization

Color dipole formalism

pA

pA

Rapidity distribution

Saturation: reduction by 1.7 at y = 6