f.s.n., v.p. gonçalves and e. cazaroto
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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
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