Lectures on the Near-Side Ridge, Landau Hydrodynamics, and Heavy Quarkonia in High Energy Heavy-Ion Collisions

Abstract. We give an introduction to three different topics that are of current interest in heavy-ion collisions. Particles associated with the near-side jet are found to exhibit a Δφ-Δη correlation in the form of a ridge in the Δη direction but a peak at Δφ ∼ 0. The experimental data support the description that the ridge particles are medium partons kicked by the jet. The measurement of the characteristics of the ridge provides a unique tool to probe the nature of the (jet parton)-(medium parton) collision and the momentum distribution of dense matter formed in the early stage of the heavy-ion collision. We find that the magnitude of the longitudinal momentum kick along the jet direction acquired by a medium parton in collision with the jet is about 1 GeV, and the early parton momentum distribution is in the form of a rapidity plateau with a thermal-type transverse momentum distribution. In the second lecture, we re-examine the validity of Landau hydrodynamics which provides a reasonable description of the space-time dynamics of the hot matter produced in high-energy heavy-ion collisions. We find that the rapidity distribution of produced particles should be more appropriately modified from Landau’s result. Past successes of the Gaussian distribution in explaining experimental rapidity data can be understood, not because it is an approximation of the original Landau distribution, but because it is in fact a close representation of the modified distribution. In the final lecture, we give an introduction to the development of the potential model for quarkonia, using thermodynamical quantities obtained in lattice gauge calculations. We find that the potential model is consistent with the lattice gauge spectral function analysis, if the color-singlet heavy quark-antiquark potential is a linear combination of the color-singlet free energy F1 and internal energy U1, with coefficients that depend on the equation of state. We find that the effects of dynamical quark modifies only slightly the stability of J/ψ and the quark drip line limits possible quarkonium states with light quarks to temperatures close to, and slightly greater than, the critical phase transition temperature.

correlation Probability distribution P( , ) in -is in the form of (i) a "jet component" (ii) a "ridge component".The width in depends on the magnitude of q.Boost invariant distribution corresponds to a=0.
The shape in around =0 depends weakly on a.
The shape in around large depends strongly on a.
The ridge shape in The pp near-side jet data can be described by  Unanwsered questions: • Is Landau's formula for y or ?• Landau rapidity distribution is actually The Gaussian Landau distribution is only an approximation  • The quantitative agreement of Landau hydrodynamics supports its use in other problems of heavy ion collisions, such as J/psi suppression, jet quenching, and ridge jetmedium interaction,….

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Experimental information about the ridge • (i) Ridge yield correlated with N_participants • (ii) Ridge yield nearly independent of pt, flavor, baryon, meson characters of the jet trigger • (iii) Tjet>>Tridge > Tinclusive • (iv) Ridge particles have ~0 • (v) Ridge particles nearly uniform in Dense Matter In Heavy Ion Collisions and Astrophysics (DM2008) the ridge phenomenon occur?• What is the momentum distribution of the early medium partons?• What is the dominant mechanism of jet momentum loss?These questions are linked together and can be answered by the momentum kick model: Ridge particles are medium partons kicked by the jet.The kicked partons carry direct information on the medium parton momentum distribution and the magnitude of the momentum kick .The momentum kick is related to the jet momentum loss.medium partons kicked by the jet • (i) Ridge yield correlated with N_participants • (ii) Ridge yield nearly independent of pt trigger, flavor, baryon, meson characters of the jet • (iii) T jet >>T ridge > T inclusive • (iv) ~ 0 implies that the ridge particles acquire their azimuthally properties from the jet • (v) jet-(medium parton) interactions are short-ranged because of non-

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The kicked final partons subsequently materialize as hadrons by parton-hadron duality •The ridge particle distribution depends on the initial parton momentum distribution and the momentum kick q.Heavy Ion Collisions and Astrophysics (DM2008) 01006-p.11 dN/dy ~ (1-x) a (05) & J. Phy.G34, S679 (07) pp near-side jet data (open blue circles) side data (black solid points) described well by the momentum kick model around ~0 Data from STAR Collaboration PRL95,152301(05) & J. Phy.G34, S679 (07) Dense Matter In Heavy Ion Collisions and Astrophysics (DM2008) 01006-p.15AA near-side data (black solid points) described well by the momentum kick model around | |~3.3 Data from STAR Col. F. Wang et al. arXiv:0707.0815('07) 30 Momentum kick model gives the correct prediction EPJ Web of Conferences 01006-p.16Shape of early parton momentum distribution 32 Possible evolution scenario of medium partons Dense Matter In Heavy Ion Collisions and Astrophysics (DM2008)01006-p.17

Conclusions••
The ridge particles can be described as medium partons kicked by the jet, and they carry information on the early parton momentum distribution and the momentum kick.•The parton momentum distribution at the moment of jet-parton collision is relatively flat in rapidity with a thermal-like transverse momentum distribution and sharp kinematic boundaries.• The magnitude of the momentum kick gained by the parton is 1 GeV, which is also the momentum loss by the jet in a jet-parton collision.It gives a good description of experimental data • It gives a simple description of the space-time dynamics of the dense hot matter produced in heavy-ion collisions • Dense hot matter evolution is needed in many problems • It is very simple • L.D.Landau, Izv.Akad.Nauk SSSR, 17, 51 (1953)   •Belenkij and L.D.Landau,Usp.Fiz.Nauk.56, 309 (1955)    3 Recent revived interest in Landau hydrodynamics• BRAHM dN/dy data agree with Landau hydrodynamics Murray, J. Phys.G30, S667 (2004) N ch /(N part /2) agrees with experiment Dense Matter In Heavy Ion Collisions and Astrophysics (DM2008) s prediction on N ch agrees with data • The rapidity distribution in Landau hydrodynamics should be modified.The modified rapidity distribution gives better agreement with experimental data than the Landau distribution EEA5;3F;A@ ;@ 5A>>;E;A@ I;F: 9>GA@E (982 !# Dense Matter In Heavy Ion Collisions and Astrophysics (DM2008)

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Does the original Landau distribution agree with data?
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