Quarkonia: theoretical overview

Marzia Nardi

INFN Torino

III Convegno Nazionale sulla Fisica di ALICE

Frascati, 12-14 Novembre 2007

CGC effects on J/ production in nuclear collisions

p(d)-A : D. Kharzeev, K. Tuchin, hep-ph/0510358 (published)

A-A : D. Kharzeev, E. Levin, M.N., K. Tuchin (in preparation)

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Hadron scattering at high energy

A new phenomenonis expected : parton saturation

From HERA:

At high energies hadrons appear dense.

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Saturation scale in nuclei [D.Kharzeev, E.Levin, M.Nardi][D.Kharzeev, E.Levin, M.Nardi]•Consider a nucleus or hadron interacting with an external probe, exchanging Q• Transverse area of a parton ~ 1/Q2

• Cross section parton-probe : ~ s/Q2

• If many partons interact : S~Nparton• In a nucleus : NA=NpartonA [Nparton = xG(x,Q2)]• The parton density saturates when S~RA

2

• Saturation scale : Qs2 ~ s(Qs

2)NA/RA2 ~A1/3

• At saturation NA is proportional to 1/s

• Qs2 is proportional to the (transverse) density of participating

nucleons nA=NA/RA2; larger for heavy nuclei.

• NA~ Qs2 /s(Qs

2)

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Color Glass Condensate

Classical effective theory : high density limit of QCD

• color : partons are colored

• glass : they evolve slowly compared to their natural time-scale

• condensate : their density is proportional to the inverse of the coupling constant, typical of a Bose condensate.

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Hadron production from the CGC

Hadron multiplicities can be described in a parton saturation model, based on the Color Glass Condensate theory. In particular :

• Au-Au and d-Au collisions at RHIC, √sNN=20÷200 GeV

• Pb-Pb and p-Pb collisions at LHC, √sNN= 5500 GeV

– total multiplicity – centrality dependence – rapidity dependence

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

J/ production

The production mechanism of J/ in nuclear collisions at RHIC energies is different from that in pp collisions, because of gluon saturation in the nucleus.

In p-A:

• at forward y more suppression

• at backward y weak enhancement

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

mc > QCD perturbative QCD, but non-perturbative effects are not negligible

In A-A collisions: J/ suppression is a signature of QGP formation it is important to understand the production mechanism.

At RHIC : experimental data on hadron multiplicity can be explained by CGC, parton (gluon) saturation in the nuclear wave function. Qs

2(x2) >> QCD.

For heavy quarks :

• Qs < m : Q production is incoherent, pQCD

• Qs > m : Q production is coherent, the projectile interacts with the whole nucleus.

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Time scales in p-A collisions• tp = c-cbar production time

– in the pair rest frame tp0 = 1/2mc .

– in the nucleus rest frame (=Eg/2mc) : tp =Eg/(2mc)2

Eg = x1 Ep

s=(x1pp+x2pt)2=2x1x2EpM=2x2EgM

s=(2mc)2

tp =1/(2x2M)

x2=mce-y/sqrt(s)

at RHIC : x2=6.5x10-3 e-y tp =15 ey fm

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

• tint = interaction time = RA/c

at high energies tp > tint

or lc=tp c > RA

tp =15 ey fm : at forward y tp is very large

– the projectile interacts with the whole nucleus– eikonal approximation for the calculation of

scattering amplitude

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

• tf = J/ formation time

– in the pair rest frame tf0= 2/(m’-m)

– in the nucleus rest frame (=Eg/M) : tf = 2Eg/(m’-m) M

– tf0=0.45 fm tf

RHIC=41 ey fm

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

At y>1, at RHIC :

tf > tp > tint

J/ is formed outside the nucleus, no nuclear effects !

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

At -1<y<0 the production time at RHIC becomes smaller than he nuclear size : the c-cbar pair is produced in the interaction with a few nucleons: enhancement of J/ production. Correction for nuclear absorption.

A-A : s6A2/3 p-A : s

5A1/3

For large A, diagram (a) dominates

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

At y<-2 the coherence is lost.

The production of J/ in p-A is similar to the one in pp collisions

J/ can be formed inside the nucleus.

c-cbar and J/interact with nuclear matter.

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

J/ production cross-section

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

• Probability of gluon radiation by a valence q:

with

• J/ wave function (NR approximation)

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

• The saturation properties are contained in the amplitude

with

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Total cross-section

where =mr .

• If M>Qs :

and

• If M<Qs :

and

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Results for d-Au

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

III Conv. Naz. ALICE, Frascati, 12-14 Nov. 2007 Marzia Nardi

Results for Au-Au (RHIC)