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1 Signals of Quark-Gluon Plasma production J. Magnin CBPF

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2 Basics: What the QGP is ? The deconfinement/chiral transition (toy model) Heavy ion collisions, why ? Signals for QGP production The mass Conclusions Outline

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3 What QGP is ? QCD has the property that the coupling constant tends to zero as the inverse of the logarithm of the energy scale: Asymptotic freedom

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What QGP is ?4 Consequently: In hard processes (means large Q 2 ) we can treat quarks and gluons as if they were free (non-interacting) entities. At a low Q 2 scale is large and perturbative calculations are not allowed (soft processes). Examples: DIS is a hard process Low energy properties of hadrons (mass spectrum, resonance widths, etc) are soft processes

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What QGP is ?5 But… The situation may change if the temperature if high enough ! In this case the scale parameter is T and Quark-Gluon Plasma The same situation may occur at zero temperature for sufficiently large chemical potentials, or increasing both, the temperature and the chemical potential (or, equivalently, the pressure) Above some critical temperature T c (~ 150 MeV) it is possible to have a gas of almost free quarks and gluons:

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What QGP is ?6

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7 The deconfinement/chiral transition The bag model: The bag model has two main features of QCD: asymptotic freedom and confinement Hadrons are bubbles of (perturbative) vacuum in a confining medium Inside the bag quarks are free Outside the bag quarks cannot appear as free particles

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The deconfinement/chiral transition8 Approach: Solve Dirac equation for massles free fermions in a spherical cavity Solve matrix equation and get wavefunction for massless fermion Solutions in terms of spherical Bessel functions Boundary condition at the surface of the bag due to confinement (r = R) Evaluate wavefunction with boundary conditions Then…

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The deconfinement/chiral transition9 Hadron energy: Radius of the hadron: Hadron mass: Pressure: Volume termKinetic energy Contribution from the vacuum (-B) balanced by the quark kinetic energy

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The deconfinement/chiral transition10 Look at the grand potential For a boson gas: for a fermion gas: and for a gas of quarks and gluons: gluons vacuum quarks

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The deconfinement/chiral transition11 Equality of the pressure in the plasma and hadron phases gives the critical temperature T c For a pion gas: with

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The deconfinement/chiral transition12

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The doconfinement/chiral transition13

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14 Heavy ion collisions, why ? Picture of a nuclei-nuclei collision Two Lorentz contracted nuclei (transverse radius R and longitudinal extension d L ~2Rm N /E cm ) collide during a time t~d L /c. The two nuclei cross each other and two Lorentz contrac- ted hadronic systems recede from each other in opposite di- rections carrying the initial baryonic number. They leave behind them exited hadronic matter with zero baryonic number.

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Heavy ion collisions, why?15 Typical numbers: Pb-Pb collision al LHC energies: E cm = 2 TeV d L /c~7x10 -3 fm/c

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Heavy ion collisions, why ?16 The central hadronic system Zero baryonic number. It could be assumed to be a perfect relativistic fluid (hydro- dynamical picture) It is a closed system (then entropy is conserved) For E cm ~ 2TeV, in the case of an ideal QGP with N f =2 T 0 ~300 MeV and ~12.8 GeV/fm 3

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17 Once the QGP was produced then: 1- the expanding system reaches thermal equilibrium (~ 1fm) 2- temperature falls with expansion of the system 3- when T=T c mixed plasma-hadronic phase 4- chemical freeze-out particle abundances preserved 5- thermal freeze out all interactions between hadrons cease (~10 fm)

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18 Signals for QGP production Changes in the intrinsic properties of hadrons. Increase in the multistrange particle production. Changes in the dilepton spectrum. J/ suppression. Increase in the production of hadronic resonances. Transverse and longitudinal hadronic flux outside of the production plane. Etc…

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19 The mass mesons play a special role due to its short lifetime (~1.3 fm) as compared to the lifetime of the system formed in the collision (~10 fm). Two possible approach: 1- Study of the electromagnetic decay channels 2- Study of the hadronic decay channels Mass of the 0 meson in ultra-relativistic heavy-ion collisions A. Ayala, J.G. Contreras, J. Magnin; Phys. Lett. B603 (2004) 165

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The rho mass20 electromagnetic decay channels Reconstruction of the spectrum by looking at particles with small probability of interaction with the surrounding hadronic medium. Typical studies including the VDM hypothesis to look at the low mass dilepton spectrum. Studies are still inconclusive: part of the problem is that one is looking at dileptons which are produced in different stages of the reaction (changes in the properties in a time integrated manner). l+l+ l-l-

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The rho mass21 hadronic decay channels Allows to look at the decay, regeneration and re-scattering of the meson within a dilute hadronic system STAR (RHIC) reported a shift of ~70 MeV for the peak of the invariant mass distribution of the decay in Au+Au collisions at GeV. m ~ 40 MeV

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The rho mass22 The is a resonance, then changes in the distribution of its decay products can be divided into 1- phase space distortions of the decay products. 2- intrinsic changes in the properties (mass and width) of the resonance in the heat bath. A quantitative description of the later is linked to model dependent considerations. Models are built to represent the interactions of the mesons with other mesons and baryons. These models respect the basic symmetries of the strong interactions (current conservation and parity invariance). Thermal modification of intrinsic properties are computed by evaluating the one-loop modification of its self-energy.

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The rho mass23 at one-loop The self-energy is related to the intrinsic properties by is calculated using a covariant formalism. m mass of the in vacuum M and tot are temperature and/or density dependent quantities

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The rho mass24 Use is done of Thermal Field Theory in the imaginary-time formulation (Matsubara) Details to take care of 1-We take the z axis as the direction of motion of the meson, then the thermal mass can be computed from the thermal part of the component 11 in the limit of vanishing three-momentum. 2- Recalculate coupling constants if necessary by adjusting theoretical expressions to experimentally measured branching ratios

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The rho mass25 Interactions of with baryons Look for baryonic resonances decaying into -nucleon RJPJP vac N (MeV ) vac tot (MeV) f JP f NR JP N(1520)3/2-251209.77 N(1720)3/2+10015077.8 (1700) 3/2-1203004.45 (1905) 5/2+21035012.912.2

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The rho mass26

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The rho mass27 and also look at the contribution from interactions - Nucleon

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29 Interactions of with mesons R h decay JPJP vac h (MeV) vac tot (MeV) g hR (782) 1-~58.4325.8 h 1 (1170) 1+seen~36011.37 a 1 (1260) 1+dominant~40013.27 K 1 (1270) KK 1+~60~909.42 ’(1300) 0-seen~4007.44

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31 and add also the - interaction

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33 Finally, sum all the contributions to the mass

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34 Conclusions We shown that it is possible to achieve a shift of ~40 MeV for a reasonable range of temperatures of the hadronic phase of a relativistic heavy ion collisions. Chemical potential should help to increase the shift of the mass. The overall change in the mass of the + - distribution is also affected by phase space distortions due to thermal motion of the decay products and changes in the width. These results underline the importance of meson and baryon scattering to decrease the intrinsic mass of the .

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