Hard Probes theory

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Hard Probes (theory)
N. Armesto
International School on Quark-Gluon Plasma and
Heavy Ion Collisions past, present,
future Torino, May 11th-17th 2005
Néstor Armesto Departamento de Física de
Partículas and Instituto Galego de Altas
Enerxías Universidade de Santiago de Compostela
Acknowledgements F.Arleo, R.Baier, A.Capella,
A.Dainese, D.dEnterria, E.G. Ferreiro, P.Jacobs,
A.Morsch, C.Pajares, C.A.Salgado, J.Schukraft and
U.A.Wiedemann.
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Contents
N. Armesto
1. Introduction. 2. Basics of pQCD. 3.
Medium-induced gluon radiation. 4. Quarkonium
(very brief). 5. Final remarks.

• I will concentrate on point 3 (see also Peter
  Jacobs' lectures). Other hard
• probes as open and hidden heavy flavor will be
  treated in other lectures.
• See Yellow Report on Hard Probes in HIC at the
  LHC, CERN-2004-009
• (hep-ph/0308248,0310274,0311048)
  http//event-hardprobes04.web.cern.ch.

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Hard Probes (theory)
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1. Introduction
N. Armesto

• Hard probes (of the medium created in a HIC)
  those whose
• benchmark (result of the probe in cold nuclear
  matter) can be
• studied using perturbative QCD, for which a hard
  scale is
• required (pT, mQ,...gtgt1/Rh).

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Hard Probes (theory)
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Summary of probes
N. Armesto
Jet quenching/heating
Quarkonium suppression
Control of the benchmark DY, prompt photons
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Hard Probes (theory) 1. Introduction
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2. Basics of pQCD
N. Armesto

• Fields quarks and gluons.
• Coupling constant asymptotic freedom.
• Confinement.
• Factorization in hard processes.
• Initial state ingredients.
• Hard scattering elements.
• Final state fragmentation in vacuum.

See e.g. Ellis et al, QCD and Collider Physics,
Cambridge Univ. Muta, Foundations of QCD, World
Scientific Yndurain, The theory of quark and
gluon interactions, Springer-Verlag Pich,
hep-ph/9505231.
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Hard Probes (theory)
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Fields quarks and gluons
N. Armesto

• QCD quantum field theory with SU(NC3) as local
  gauge group.
• The fields in the QCD Lagrangian are
• A) Matter fields NC quarks being point-like
  spin-½ particles.

Evidences quark model, DIS experiments, two-jet
events,...
B) Exchange bosons NC2-1gluons being massless
spin-1particles.
Evidences three-jet events, scaling
violations,...
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Hard Probes (theory) 2. Basics of pQCD
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Coupling constant asymptotic freedom
N. Armesto
Renormalization fields, masses and the coupling
constant acquire a dependence on a (momentum)
scale.
Due to gluon self-interactions (absent in QED),
the coupling constant decreases with increasing
momenta large/ small at small /large momenta.
,
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Hard Probes (theory) 2. Basics of pQCD
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Confinement
N. Armesto

• The fields q, g in the Lagrangian are not the
• particles in Nature (pions, protons,...).
• The strong interaction is short range but QCD
• gluons (as QED photons) are massless.

(106 ) problem of confinement

• Hadrons colorless combinations.
• Valence description 'dressed'
• constituent quarks.
• Mass dynamically generated.
• Q-Qbar potential (until Vgt2mq)

• Looking for deconfinement in HIC
• QGP search.
• K?0 at large T bound states (quarkonium) are
  dissolved (H.Satzs lecture).

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Hard Probes (theory) 2. Basics of pQCD
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Factorization in hard processes I
N. Armesto

• Asymptotic freedom allows the use of pQCD for
  processes with a
• large scale (m, transverse momentum,...)
  involving the QCD fields q,g.
• For inclusive processes, factorization (Collins,
  Soper, Sterman, '85) is
• the tool which makes it possible to use pQCD for
  hadronic processes.

Basis very different scales in h (1/Rh) and in
the hard scattering.
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Hard Probes (theory) 2. Basics of pQCD
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Factorization in hard processes II
N. Armesto

• Hard scattering elements computable in
  perturbation theory.

• f flux of 'initial' partons in the hadron or
  nucleus
• (DGLAP) evolution with scale computable in
  perturbation theory.

• D projection of 'final' partons onto the
  observed particle
• (DGLAP) evolution with scale computable in
  perturbation theory.

Note 1 separation initial-final meaningless if
there is cross-talk.
Note 2 this factorization is called collinear,
other schemes exist.
Note 3 corrections to factorization in the form
of powers 1/scale.
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Hard Probes (theory) 2. Basics of pQCD
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Initial state ingredients I(see Marzia Nardi's
talk Roberts, The structure of the proton,
Cambridge Univ.)
N. Armesto
Parton fluxes (densities) measured in DIS
scale, large for pQCD.
Momentum fraction of the parton in the hadron
Densities at initial scale parameterized, evolutio
n with scale given by DGLAP global LO and NLO
fits to nucleon data (MRST, CTEQ, GRV) gluon
at small x rather uncertain, problem
for extrapolations for LHC.
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Hard Probes (theory) 2. Basics of pQCD
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Initial state ingredients II
N. Armesto
Strategy parameterize ratios at initial scale,
evolution with scale given by DGLAP global fits
to nuclear data (EKS (LO), HKM (NLO), dFS
(NLO)) (YR hep-ph/0308248).
Nuclear case
so partons fluxes in nuclei are not the
superposition of those in hadrons (even isospin
corrected).
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Hard Probes (theory) 2. Basics of pQCD
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Hard scattering elements
N. Armesto
Fixed order, collinear hard scattering elements
available (at NLO, at least) for
Available Monte Carlo simulators (PYTHIA,
HERWIG,...) use LO hard scattering elements
parton showers (i.e. parton radiation
from initial and final state partons they
correspond to no fixed order in PT) (see e.g.
Frixione, Webber, hep-ph/0202244 Nagy, Soper,
hep-ph/0503053). Note most HIC simulators (e.g.
HIJING) use PYTHIA for hard processes.
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Hard Probes (theory) 2. Basics of pQCD
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Final state fragmentation in vacuum I
N. Armesto
Define a (collinear and IR) safe observable at
partonic level (e.g. jets) (Sterman, Weinberg,
PRL39(77)1436), OR use
D(z,Q) fragmentation function, gives the
probability parton k ---gt hadron a with a
momentum fraction z, at a scale Q whitening of a
parton by radiation.
a
Strategy parameterize at some low scale, evolve
with scale using DGLAP, fit to available
(electron-positron) data (NLO KKP, Kretzer) ff
harder for massive (leading takes more than
70) than for massless quarks (less than 40).
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Hard Probes (theory) 2. Basics of pQCD
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Final state fragmentation in vacuum II
N. Armesto
If there are no final state medium effects, for
scales large enough initial state effects and
power suppressed contributions vanish
As the number of nucleon-nucleon collisions is
proportional to AB times the nuclear overlap, at
large enough scales we expect collision scaling,
any deviation should be due to medium effects.
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Hard Probes (theory) 2. Basics of pQCD
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3. Medium-induced gluon radiation
N. Armesto

• History.
• Qualitative arguments.
• Formalism.
• Effects of radiation.
• Features versus (RHIC) data.
• To explore further.

Reviews Baier, Schiff, Zakharov,
hep-ph/0002198 Gyulassy, Vitev, Wang, Zhang,
nucl-th/0302077 Kovner, Wiedemann,
hep-ph/0304151. Recent Wiedemann,
hep-ph/0503119 Vitev, hep-ph/0503221.
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Hard Probes (theory)
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History I
N. Armesto

• 1982 Bjorken (FERMILAB-PUB-82-059-THY)
  postulates the energy
• degradation of leading particles in jets and
  their disappearance in a
• dense medium, by elastic scattering (collisional
  energy loss).

• Later works showed that elastic scattering lead
  to small energy loss
• e.g. dE/dx0.1 GeV/fm for a 20 GeV parton for
  Tplasma250 MeV.
• Radiative energy loss (inelastic scattering) was
  proposed (Gyulassy,
• Plumer, PLB243(90)432) Bethe-Heitler to
  Bethe-Bloch in QED.

• Gyulassy and Wang (NPB420(94)583) multiple
  collisions of partons
• with the medium in a QED form interference in
  radiation (LPM effect).

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Hard Probes (theory) 3. Medium-induced gluon
radiation
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History II
N. Armesto

• Baier-Dokshitzer-(Mueller-)Peigne-Schiff
  (PLB345(95)277) identified
• the dominant role in QCD of the rescattering of
  the gluon.

• A general path-integral formalism was developed
  (Zakharov,
• JETPL63(96)952) the BDMPS results and the
  opacity expansion were
• recovered (Wiedemann, NPB588(00)303 Gyulassy,
  Levai, Vitev, NPB594(01)371
• also the twist expansion in Wang, Guo,
  NPA696(01)788).

• RHIC discovers high transverse momentum particle
  suppresion
• (PHENIX, PRL88(02)022321 STAR, PRL91(03)172302
  PHOBOS, PLB578(04)297
• BRAHMS, PRL91(03)072305 STAR, PRL90(03)082302).

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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments
N. Armesto
I vacuum definitions. II phase
arguments. III regimes of radiation. IV
energy loss.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments I(Baier, Schiff,
Zakharov, hep-ph/0002198 Baier, NPA715(03)209)
N. Armesto
xw/Eltlt1

• Vacuum

• Take a medium of length L and density r (usually
  modelled as a collection
• of Yukawa-type potentials with Debye screening
  mass m GW model).

• Definitions s proportional to aS the cross
  sections with the medium.
• l1/(rs) the mean free
  path.
• m2 the typical squared
  momentum transferred from
• the medium to the
  parton.
• qhatm2/l the BDMPS
  transport coefficient.

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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments II
N. Armesto

• In high-energy multiple scattering, the
  rescattered particle acquires a phase

• What matters is the phase accumulated by the
  gluon to decohere from
• the radiating particle jaccumulatedgt1, so wltwc
  is the dominant region, but
• small w are suppressed by oscillations in the
  phase.

• From the phase the time to decohere the gluon

and the number of coherent scatterings is
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments III
N. Armesto
Take Egtwc (LltlE/ELPM1/2), and
ELPMm2l2wc(l/L)2 and ignore logs and constants.
We have three regimes in the spectrum
A) wltELPM or tcohltl Bethe-Heitler, incoherent
regime, 1 scattering.
B) ELPMltwltwc or llttcohltL LPM regime, Ncohlt1,
suppression from Bethe-Heitler.
C) wgtwc or tcohgtL factorization regime,
enhancement from LPM.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments IIIb
N. Armesto
tcoh(w/qhat)1/2 time to liberate the
gluon, lt(E/qhat)1/2.
l
L
A) wltELPM or tcohltl Bethe-Heitler, incoherent, 1
scattering.
C) wgtwc or tcohgtL factorization regime.
Difference QED/QCD in QED, just the radiating
parton accumulates, through rescattering, phase
to decohere the radiated photon in QCD, the
radiated gluon also accumulates phase ?
additional factor L.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Qualitative arguments IV
N. Armesto
Now the energy loss
The dominant contribution is wltwc
so we get the BDMPS result
so the energy loss becomes independent of E and
proportional to CF and L2.
Note in QED
so
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Formalism
N. Armesto
I, II formula and ingredients. III
limitations. IV what we can compute.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Formalism I
N. Armesto
The most complete formalism (Zakharov, Wiedemann)
uses a path integral

• It resums all nuclear
• corrections LO in ,

leading (NL) in 1/E in the norm (phase).
indicates the opacity which characterizes the
medium.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Formalism II
N. Armesto

• The strength of the medium-induced radiation is
  determined by the
• displacement of the radiating charge.

FT of the elastic cross section (high energies,
so only transverse coordinates).

• Interference and mass effects

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Hard Probes (theory) 3. Medium-induced gluon
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Formalism III
N. Armesto

• Limitation I except for a (1/E)-NL contribution
  allowed in the phase, this
• is an eikonal formalism, so DEltltE (the radiating
  parton does not deviate).
• Kinematical restrictions kTltw and wltE imposed a
  posteriori.

• Limitation II exact solution to the path
  integral does not exist, just
• two approximations

saddle point (BDMPS), Brownian motion.
Opacity expansion (in powers of (ns)N) first
terms usually dominate (GLV) and give corrections
to Brownian motion.

• Approaches numerically similar (Salgado,
  Wiedemann, PRD68(03)014008).

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Hard Probes (theory) 3. Medium-induced gluon
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Formalism IV
N. Armesto
Within these limitations, we can compute
everything 1) Double differential spectrum of
radiated gluons gluon number and energy
distributions associated with a high energy
radiating parton. 2) Energy spectrum 3)
Energy loss influence over single particle
spectra.
Note 1 what we get are partons (gluons), not
hadrons, so either study 'safe' observables
(jets) or go to hadrons with LPHD or ff. Note 2
dilution of the medium due to expansion taken
into account by the redefinition
,
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation
N. Armesto
I, II degradation of the leading particle how
to compute single particle spectra. III
jet heating and jet shapes. IV effect of the
mass of the radiating parton. V effect of the
color charge of the parent parton. VI dilution
of the medium. VII flow effects?
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation I
N. Armesto
Gluon radiation implies an energy degradation of
the leading particle.
To compute single-inclusive particle spectra two
ways
A)
(BDMS, JHEP 0109(01)033). It clearly shows the
influence of the spectrum the harder it is, the
stronger the quenching effects.
The spectrum also determines the high pT
behavior for fixed DE(pT at h0),
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation II
N. Armesto
B)
(Wang, Guo, NPA696(01)788). It shows
the influence of the ff at z--gt1 the harder it
is (e.g. for heavy flavor), the stronger the
effect.

• Quenching weights (BDMS,
• JHEP 0109(01)033 SW, PRD'03) probability
• to lose a fraction of energy e,
• computed under the assumption
• of multiple independent emissions

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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation III
N. Armesto
Jet heating increase of associated hadron
multplicity and broadening of the associated
parton shower (BDMS, PRC64(01)057902
SW, PRL93(04)042301).
RHIC particle multiplicity associated with a
high pT trigger (see Peter Jacobs' lectures).
LHC energy distribution within a cone of size R,
still unclear whether the jet will survive (full
Monte Carlo simulations needed).
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation IV
N. Armesto
Mass effects on radiation in vacuum we have the
dead cone effect

• Dokshitzer, Kharzeev (PLB519(01)199)
• proposed that the same effect should
• suppress medium-induced radiation.

• Technically dead cone rescattering,
• numerical results (Djordjevic, Gyulassy,
• NPA733(04)265 Zhang, Wang, Wang, PRL93
• [phone] ASW, PRD69(04)114003).

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Hard Probes (theory) 3. Medium-induced gluon
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Effects of radiation V
N. Armesto

• Color effect gluons, CF3, lose more energy
  than quarks, CF4/3
• --gt look for particle ratios sensitive to this,
  as pbar/p or Lbar/L
• (Wang, PRC58(98)2321 Wang, Wang,
  PRC71(05)014903) or heavy-to-light
• ratios (e.g. D/h) (Dainese et al,
  PRD71(05)054027).

• Several effects to be
• taken into account in
• realistic predictions
• Color charge.
• Mass effects on partonic
• spectrum.
• Id. on fragmentation.
• Id. on energy loss.

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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Effects of radiation VI
N. Armesto

• Dilution of the medium
• due to expansion redefinition

(SW, PRL89(02)092303 BDMS, PRC58(98)1706
Gyulassy, Vitev, Wang, PRL86(01)2537).

• In principle, the transport coefficient
• measures the energy density of the
• medium

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Hard Probes (theory) 3. Medium-induced gluon
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Effects of radiation VII
N. Armesto

• If hard partons are not produced in a frame
  comoving with the
• medium, radiative energy loss may be sensitive to
  more than energy density

(for e3p) can be large (5p for h1).
Momentum exchanges becomes anisotropic
Space-time picture of the medium? (ASW,
PRL93(04)242301 hep-ph/0411341).
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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data
N. Armesto
I. Where to look for. II. Problems at RHIC and
LHC energy of the parent. III, IV. Description
of the medium. V. Full formula. VI. Single
particle spectra for light flavors. VII. What
about the transport coefficient? VIII. Heavy
flavors.
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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data I
N. Armesto
Where to look for all this? Which pT is high
enough? (Wiedemann, QM04)
V
Hadronization outside medium, partonic dynamics
inside, tomography?
Multiplicities, saturation?
Hadronization inside medium, particle species
dependence
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Features versus data II
N. Armesto

• Problem how to determine the energy of the
  radiating parton?
• At the LHC try to reconstruct the jet energy or
  considers jets
• balanced by a particle which can be identified
  (e.g. g-jet configuration).
• At RHIC low energy jets do not stand over
  background, energy
• reconstruction problematic, so look at the
  hardest particle. But this
• implies a trigger bias

a) The hardest fragmentation b) Surface
emission (small L) c) Low energy loss for
fixed L d) Initial pT broadening towards
the trigger (not collinear)
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Features versus data III
N. Armesto
Two parameters describe the medium geometry and
product density times cross section, given
generically by L and qhat, or combinations like
wcL2qhat/2 and RwcL.
Until now, the most discussed observable
is single-particle ratios
Geometry to test the L2 dependence proper of the
LPM effect (different from the linear dependence
in absorption models) a) Centrality evolution
of the ratios. b) Dependence with the azimuth.
Density times cross section to test our
understanding of the created medium that we try
to characterize a) Magnitude of the
suppression. b) Evolution of the suppression
with collision energy.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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Features versus data IV
N. Armesto
(GVW, PRL86(01)2537 Dainese et al,
EPJC38(05)461 Eskola et al, NPA747(05)511)
Production point s(x0,y0) sampled according to
TA(s)TB(b-s) i.e. number of nucleon-nucleon collis
ions. Trajectory

• Then

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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data V
N. Armesto
Full formula (also ADSW, PRD71(05)054027)

• Geometry one parameter (fixed e.g. in central
  AuAu) give full results.

• Quenching weights publicly available they may
  give DEgtE (they were
• deduced in the high-energy approximation). Two
  recipes to mend this give
• the most extreme cases (see Dainese et al and
  Eskola et al) and guarantee

a) Renormalize to DEltE or b) Set DEgtE
to DEE.
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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data VI
N. Armesto
4.5ltpTlt10 GeV
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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data VII
N. Armesto
Medium is opaque at RHIC 4ltqhatlt14 GeV2/fm
surface emission (Muller, PRC67(03)061901 see
Arleo, JHEP0211(02)044 for qhat).
Extrapolation to other energies according to
multiplicities from top RHIC dNch/dhh0600,
factor 2.5 to 7 (even 15) to LHC.
Now
So for e(t0)100 GeV/fm3, L10t0, 0.75ltalt1.5,
c8-19gtgt2 --gt non-ideal QGP, links with the
thermalization/viscosity problems.
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Hard Probes (theory) 3. Medium-induced gluon
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Features versus data VIII
N. Armesto
What about heavy flavor production?
RHIC data in AuAu electron spectra, weak
correlation in pT with D/B (Batsouli et al,
PLB557(03)23), and possible contribution from B
decays the region pTDlt7 GeV is to be taken with
care.
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Hard Probes (theory) 3. Medium-induced gluon
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To explore further
N. Armesto
I. RHIC heavy flavors. II. RHIC jet-like
shapes. III. RHIC v2 at large pT. IV. LHC jet
shapes. V. LHC heavy flavors. VI. Other
alternatives.
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Hard Probes (theory) 3. Medium-induced gluon
radiation
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To explore further I
N. Armesto

• Run IV at RHIC enormous increase
• in statistics (factor 40), so new studies
• become possible
• Extend the study of electron spectra
• to large pT.
• Look for topological decays D-gtKp
• (as STAR in dAu).
• ADSW, PRD71(05)054027
• the region 7ltpTDlt12 GeV should be
• safe from hadronization uncertainties
• and sensitive to color and mass effects
• (but contamination from B decays has
• to be considered).

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To explore further II
N. Armesto
Increasing interest at RHIC on particles
distributions associated with a high pT trigger
(see P. Jacobs' lectures).

• Several ideas
• Soft particles shift the
• radiation (Voloshin,
• nucl-th/0312065).
• Flow may induce asymmetry
• in radiation (ASW, PRL93(04)
• 242301 hep-ph/0411341).
• Difficult studies need of
• Monte Carlo simulation
• (Hirano, Nara, PRC66(02)041901
• PRC69(04)034908) coupled to
• the medium to be quantitative.

STAR Magestro at HP04
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Hard Probes (theory) 3. Medium-induced gluon
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To explore further III
N. Armesto
v2 at RHIC at large pT too large to be explained
by jet quenching models (even by absorption
models Drees, Feng, Jia, PRC71(05)034909).
Dainese et al, EPJC38(05)461

• Push by low pT partons? (Molnar,
• nucl-th/0503051).

• The introduction of a component of qhat
  proportional to the flow field
• (ASW, hep-ph/0411341) increases v2, but also
  mimics a higher energy density
• --gt flow may be very important for the
  interpretation of high pT at RHIC.

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To explore further IV
N. Armesto
Jets at LHC (see Peter Jacobs' lectures) huge
background, so define jets by an small cone in
the hXf-plane.

• ppbar 75 of the energy of
• the parent parton lies within a
• cone of R0.3, R2h2f2.
• It is not clear yet whether it is possible to
  use a small cone and still
• determine the energy of the parent the
  degradation is what you want to
• study but you need to know how much energy has
  been redistributed...
• --gt need more quantitative tools to account where
  induced radiation goes.
• Use jets balanced by well determined particle
  (e.g. g, Z0) determine
• neutrals (EMcal in ALICE?),...

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To explore further V
N. Armesto
LHC will extend the measurements of heavy flavor
(either of electron or by topological decays) to
much larger pT (20-30 GeV?) both flavor-tagged
jet shapes and heavy-to-light ratios
RD,B/hRAAD,B/RAAh will be very useful.
10ltpTlt20 GeV charm sensitive to color (g at low
x), bottom to mass effects on radiation
(ADSW, PRD71(05)054027).
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To explore further VI
N. Armesto
Other alternatives (far from complete) a)
Absorption models, either hadronic (Cassing,
Gallmeister, Greiner, NPA735(04)277) or
prehadronic (Capella, Ferreiro, Kaidalov, Sousa,
EPJC40(05)129 Drees, Feng, Jia,
PRC71(05)034909) not very different from
radiative energy loss, they provide a picture of
the medium with which hard partons interact. b)
Entension of low and intermediate pT models like
recombination (Hwa, Yang, PRC70(04)024905),
percolation (Braun, Del Moral, Pajares, PRC65(02)0
24907), saturation (Kharzeev, Levin, Mclerran,
PLB561(03)93),...
To distinguish Role of elastic scattering (e.g.
Molnar, nucl-th/0503051).
Compatibility with dAu.
L2 dependence (in DIS, Wang, Wang,
PRL89(02)162301
Accardi, Grunewald, Muccifora, Pirner,
hep-ph/0502072).
Associated particle distribution (Kharzeev,
Levin, Mclerran,
NPA748(05)627 Majumder, Wang,
PRD70(04)014007...).

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radiation
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4. Quarkonium
N. Armesto

• Production in pp.
• Production in pA/AB initial state.
• Production in pA/AB nuclear absorption.

All this fixes the benchmark to observe anomalous
effects, to be treated in some other lectures.

• Mechanisms for anomalous behavior (schematic).

See the heavy flavor chapter of the Yellow Report
on Hard Probes in HIC at the LHC, CERN-2004-009
(hep-ph/0311048) also other lectures
(F.Antinoris).
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Production in pp I
N. Armesto

• Historically, the understanding of the
  charmonium spectrum was
• one of the first phenomenological successes of
  QCD (De Rujula,
• hep-ph/0404215). The large mass offers a hard
  scale for a small coupling
• and also a low L/mQ as a parameter to develop an
  effective theory.

• Two models most commonly used
• A) Color Evaporation Model (Fritzsch,
  PLB67(77)217 Halzen, PLB69(77)105)

FC is a constant for each quarkonium state no
attention is paid to color or spin.
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Hard Probes (theory) 4. Quarkonium
56
Production in pp II
N. Armesto
B) Non-relativistic QCD (Bodwin, Braaten, Lepage,
PRD51(95)1125)

• operators classified by the quantum numbers and
  the velocity of QQbar
• in cms (v20.3 for c and 0.1 for b) fitted to
  data or computed on lattice.
• Both color singlet (QQbar color state) and color
  octet contributions.

• NLO not yet completed polarization,
• production associated with D's?

• Both CEM/NRQCD have successes/
• failures e.g. CSM in photoproduction,
• CEM for polarization,... (Bodwin, Braaten,
• Lee, hep-ph/0504014).
• 60 J/y are direct, 30 come from
• c decays and 10 from y' decays.

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Hard Probes (theory) 4. Quarkonium
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Production in pA/AB initial state
N. Armesto

• Heavy flavor production test of gluon at small
  x, uncertainties already
• in nucleon, larger in A (g at small x is
  constrained in DGLAP analysis
• indirectly by evolution - scaling violations,
  Eskola et al, PLB532(02)222).

• At SPS energies, x1,20.1 for c at y0 --gt
• no deviation from 1 (no nuclear effect on g).
• At RHIC, x1,20.01 for c, region indirectly
• constrained by existing nuclear data.
• At LHC, x1,20.0001 for c, no constrain from
• data enhancement due to non-linear effects
• (Eskola et al, PLB582(04)157), saturation
  (Kharzeev,
• Tuchin, NPA735(04)248 Marzia Nardi's
  lecture),...?

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Hard Probes (theory) 4. Quarkonium
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Production in pA/AB nuclear absorption I
N. Armesto

• Historically suppression
• already seen in pA, xFx1-x2 (LO relation).

• Scales in quarkonium production
• QQbar production 1/mQ.
• QQbar-g system 1/(mQL)1/2, it may be absorbed
  by nuclear matter.
• Quarkonium 1/LgtRA for large enough xF
  interactions with comovers.

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Hard Probes (theory) 4. Quarkonium
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Production in pA/AB nuclear absorption II
N. Armesto

• Different regimes according to the energy
• Low energies absorption formula - production
  at z, then absorption.

sabs a few mb, is not a quarkonium-nucleon
cross section close to threshold, but that of a
pre-resonant state.

• High energies uncertainties due to new
• possibilities for the production mechanism
• (Braun et al, NPB509(98)357 Kopeliovich,
• Tarasov, Hufner, NPA696(01)669)

Rosati at HP04
larger than sabs, no longer absorption
or no nuclear effect (but on pdf's) at all.
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Mechanisms for anomalous behavior
N. Armesto
Two basic possibilities a) Absorption from
non-equilibrated strong matter i.e. partons
co-moving with the pre-resonance (times scales
too short, densities too high for hadronic
matter). Cross sections uncertain (Barnes,
nucl-th/0306031), and no threshold or
discontinuity in any variable. b) Dissociation by
QGP. Discontinuities may appear in some 'good'
variable, still to see whether these thresholds
appear in measurable variables. Both mechanisms
effective at high densities/T, not easy to
discriminate but for thresholds in the
suppression of different quarkonium states
(Helmut Satzs lecture).
PHENIX Rosati at HP04
Opposite enhancement due to recombination
(100s ccbar pairs per PbPb central collision at
the LHC).
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Hard Probes (theory) 4. Quarkonium
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5. Final remarks
N. Armesto
Hard probes have a twofold interest a) As
computable in pQCD, they offer the possibility to
investigate new QCD phenomena applications of
pQCD in high density/temperature, multiple
partonic scattering,... They allow a relation
with the pQCD community in more
elementary collisions. b) They offer a
characterization of the medium densities, cross
sections and, eventually, flow. They already
have a bright present at RHIC, with new analysis
coming, and will be very abundantly produced at
the LHC, so they are and will continue to be a
central part of the HIC program.
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