Quarkonia: theoretical overview

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Quarkonia theoretical overview
III Convegno Nazionale sulla Fisica di
ALICE Frascati, 12-14 Novembre 2007

• Marzia Nardi
• INFN Torino

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• CGC effects on J/y 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)
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Hadron scattering at high energy
From HERA
At high energies hadrons appear dense.
A new phenomenon is expected parton
saturation
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Gluon density in hadrons
McLerran, hep-ph/0311028
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Saturation scale in nuclei

• 
  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 as/Q2
• If many partons interact SNpartons
• In a nucleus NANpartonA Nparton
  xG(x,Q2)
• The parton density saturates when SpRA2
• Saturation scale Qs2 as(Qs2)NA/pRA2 A1/3
• At saturation NA is proportional to 1/as
• Qs2 is proportional to the (transverse) density
  of participating nucleons nANA/pRA2 larger for
  heavy nuclei.
• NA Qs2 /as(Qs2)

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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.

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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, vsNN20200
  GeV
• Pb-Pb and p-Pb collisions at LHC, vsNN 5500 GeV
• total multiplicity
• centrality dependence
• rapidity dependence

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J/y production

• The production mechanism of J/y 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

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• mc gt LQCD ? perturbative QCD, but
  non-perturbative effects are not negligible
• In A-A collisions J/y 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.
  Qs2(x2) gtgt LQCD.
• For heavy quarks
• Qs lt m Q production is incoherent, pQCD
• Qs gt m Q production is coherent, the projectile
  interacts with the whole nucleus.

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Time scales in p-A collisions

• tp c-cbar production time
• in the pair rest frame tp0 1/2mc .
• in the nucleus rest frame (gEg/2mc) tp
  Eg/(2mc)2
• Eg x1 Ep
• s(x1ppx2pt)22x1x2EpM2x2EgM
• s(2mc)2
• tp 1/(2x2M)
• x2mce-y/sqrt(s)
• at RHIC x26.5x10-3 e-y ? tp 15 ey fm

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• tint interaction time RA/c
• at high energies tp gt tint
• or lctp c gt 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

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• tf J/y formation time
• in the pair rest frame tf0 2/(my-my)
• in the nucleus rest frame (gEg/My)
  tf 2Eg/(my-my) My
• tf00.45 fm ? tfRHIC41 ey fm

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• At ygt1, at RHIC
• tf gt tp gt tint
• J/y is formed outside the nucleus, no nuclear
  effects !

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• At -1ltylt0 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/y production. Correction for
  nuclear absorption.

A-A as6A2/3
p-A as5A1/3
For large A, diagram (a) dominates
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• At ylt-2 the coherence is lost.
• The production of J/y in p-A is similar to the
  one in pp collisions
• J/y can be formed inside the nucleus.
• c-cbar and J/y interact with nuclear matter.

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J/y production cross-section
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• Probability of gluon radiation by a valence q
  
• with
• J/y wave function (NR approximation)

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• The saturation properties are contained in the
  amplitude
• with

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Total cross-section

• where zmr .
• If MygtQs
• and
• If MyltQs
• and

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Results for d-Au
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Results for Au-Au (RHIC)