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The subject of Quark Gluon Plasma is introduced and a discussion of the theoretical aspects is presented. The significance of quark-gluon-plasma studies, and signatures for the evidence of its existence are discussed.
The experiments looking for quark-gluon-plasma, their results and the latest news on the topic is presented. The report then summarizes the findings from the survey of the topic and adds concluding remarks.
The theory of strong interactions, QCD (Quantum Chromodynamics) predicts a new state of matter that might have existed in the very early stages of the Big Bang. This new state of matter is called
"Quark-Gluon-Plasma", and is expected to have the properties of a plasma state with free, mobile charges a ideal fluid like behavior. However there is more to this state of matter; as in, it has some peculiar properties compared to normal plasma that we know of, and rightly so.
Matter in a highly dense state behaves differently. Highly dense nuclear matter called Quark matter expected to exist at the cores of highly dense neutron stars, which is a degenerate Fermi gas of quarks .
Let us consider a kinematical situation where we collide two particles (at least one of them is a hadron) at very high energies that the momentum transfer is very large; so the interaction between them takes place within a distance less than the diameter of a hadron. In such condition the interaction between colliding particles mainly occur due to the quark and gluon components of the hadron. At higher and higher energies scattering occurs not only from the valence quarks but also from the sea-quarks and gluons.
We know that Quarks are always found in a confined state within hadrons.
The reason being the nature of the strong force. However the quarks are found to be free at very small separations from each other (within the diameter of a hadron) ; this is usually referred to as asymptotic freedom.
In the Quark-Gluon-Plasma however ; at very high temperatures and extremely high densities of Quarks over a large volume, greater than the volume of a hadron the Quarks are expected to enter a De-confined phase where the quarks are no more a part of a single nucleon, but are now a part of a highly dynamic medium of free quarks and gluons. Quark gluon plasma is also expected to have properties of quasi-neutrality and a state in
which Chiral symmetry is restored ( Which is a broken symmetry for matter in its normal state).
We intend to study this state of matter in order to gain insights into the very
early stages (~ few microseconds to first couple minutes) of the Big Bang.
These studies will help us understand the transition and evolution of this
early-hot-cosmic-soup into baryonic matter we know of today. However, Baryogenesis and Matter-antimatter asymmetry are still not understood well. Accurate quantitative details from these studies are hard to acquire due to the nature of strong interactions. However a qualitative understanding would be helpful to begin with. In the following sections, the nature of strong interactions is described in brief and the tools used for research in different QCD regimes is introduced.
The nature of strong interaction
The force which holds together protons and neutrons in the atomic nucleus is found to be a residual of the interaction between Quarks which compose them. In all hadrons the composite quarks exchange force carriers called gluons. In a simplified picture, the hadrons contain massive constituent quarks and massless exchange force particles, gluons. The strong interaction is explained using a non-abelian gauge theory (Quantum Chromodynamics) which says quarks have an additional SU(3) gauge degree of freedom (the color charge) to which other the strongly interacting (colored) objects couple using massless colored bosons (Gluons).
In nature only color neutral or white objects are observed and colored objects remain confined within the bounds of these white objects which could be baryons which are composed of three quarks or mesons which are made of quark antiquark pairs.
Confinement means that the force between quarks does not diminish as they are separated. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easily demonstrated using lattice QCD .
Asymptotic freedom is a property of QCD that causes interactions between colored particles to become arbitrarily weak at energy scales that become arbitrarily large, or, equivalently, at length scales that become arbitrarily small.
Deep Inelastic Scattering (DIS) experiments probe the internal structure of nucleons by bombarding high speed projectiles (e.g.. electrons) against nucleons. These experiments have not only confirmed the existence of structure at lower scales, but also helped us gain insight into the nature of strong interaction. It is very interesting to note that particles that appear point-like turn out to be composite when studied more closely (Just like atomic nuclei in Rutherford scattering with low-energy Î± particles). In deep in-elastic scattering, however, a new phenomenon is observed. With an increasing resolution, quarks and gluons turn out to be composed of more quarks and gluons; which themselves, at even higher resolutions, turn out to be composite as well. The quantum numbers (spin, flavor, color etc) of these particles remain the same; only the mass, size, and the effective coupling change. Hence one finds that, there appears to be a self similarity in some sense in the internal structure of strongly interacting particles.
The coupling of strong interaction depends on the interaction energy or the momentum transfer. QCD is studied using different techniques in different energy regimes. Perturbative QCD is a subfield in which QCD is studied by using the fact that the strong coupling constant Î±s is small in high energy or short distance interactions, thus allowing perturbation theory techniques to be applied. In most circumstances, making testable predictions with QCD is extremely difficult, due to infinite number of topologically inequivalent interactions possible. Over short distances, the coupling is small enough that this infinite number of terms can be approximated accurately by a much more manageable number of terms. Although limited in scope, this approach has resulted in the most precise tests of QCD to date.
The QCD factorization which separates the cross sections into two parts: the process dependent Perturbative QCD with its calculable short-distance Parton cross section, and the universal long-distance functions. Those universal long-distance functions can be measured with global fit to experiments. In this way we have been able to obtain a partly calculable prediction to particle interactions. These so called universal long-distance functions include : Parton Distribution functions , Fragmentation functions, Multi-Parton Correlation functions , Generalized Parton distribution, and many kinds of form factors.
A first-order perturbative calculation in QCD gives us the the above analytical relation for the strong coupling Î±s a function of Q2 (the momentum transfer squared) and number of quark types involved (nf) in the interaction. The number of quark types involved is higher for greater energies since there is enough energy to create heavier quarks. Alternatively a heavy virtual quark-antiquark pair has a very short lifetime and range, and hence it can be resolved only at very high Q2. A Plot of
Î±s (strong coupling) as a function of the energy in GeV (Î¼ is just a
re-parametrized energy scale used in QCD ).
Fig.1 Plot of Î±s vs energy. (From Particle Data Group)
Here Î› is the only free parameter of QCD ; it is determined by comparing predictions with experimental data to be Î› â‰ˆ 250 MeV/c. The application of perturbative expansion procedures in QCD is valid only if Î±s << 1. This is satisfied for Q2 >> Î›2 â‰ˆ 0.06 (GeV/c)2. The Q2-dependence of the coupling strength relates to a dependence on separation. For very small distances i.e high values of Q2, the coupling decreases, vanishing asymptotically .
Analytical or perturbative solutions in low energy QCD are hard to provide due to the non-linear nature of the strong force. Lattice QCD rescues the situation by allowing us to make meaningful calculations by defining the fields representing quarks to be at lattice sites and the links joining the adjacent sites to be gluon fields. This however introduces momentum cut of the order of 1/a where a is the lattice spacing. The computational cost of numerical calculations being too high these are extrapolated to a=0 by simulating at various smaller of a .
While it is a slow and resource-intensive approach, it has wide applicability, giving insight into parts of the theory inaccessible by other means. Lattice computations also predict the existence of QGP.
Quark Gluon Plasma ; Theoretical aspects
Hadronic interactions give an abundant resonance production, and the resulting number hadron species Ï(m), increases exponentially as a function of the resonance mass m, (Ï(m) âˆ¼ exp (bm)). In hadron thermodynamics, this exponential increase in the resonance degeneracy results in an upper limit for the temperature of hadronic matter, Tc = 1/b â‰ƒ 150-200 MeV .Hadronic matter, can turn at high temperatures and/or densities into a quark-gluon plasma of point-like coloured quarks and gluons as .
At T = 0, in vacuum, quarks dress themselves with gluons to form the constituent quarks which make up hadrons. As a result, the bare quark mass mq âˆ¼ 0 is replaced by a constituent quark mass Mq âˆ¼ 300 MeV. At higher temperatures, this dressing melts and Mq â†’ 0. Since the QCD Lagrangian for mq= 0 is chirally symmetric, Mq =Ì¸ implies spontaneous chiral symmetry breaking. And Mq â†’ 0 thus corresponds to a restoration of this symmetry .
Another kind of transition would set in if the attractive interaction between quarks leads in the de-confined phase to the formation of coloured bosonic diquark pairs.With Baryo-chemical potential Î¼ as a measure for the baryon density of the system, we expect the QCD phase diagram to to be of the form shown in Fig.2.
Fig. 2 The phase diagram of QCD. Figure borrowed from:
Satz, H.: The Thermodynamics of Quarks and Gluons.
Thermodynamic calculations from finite-temperature lattice QCD at vanishing baryon densities shows that:
â€¢ There is a transition leading to color de-confinement coincident with chiral symmetry restoration at Tc â‰ƒ 0.15-0.20 GeV.
And this transition is accompanied by a sudden increase in the energy density (Could be called "latent heat of de-confinement") from a small value in normal hadrons, to a much larger value, about 10% below that of ideal quark-gluon plasma.
-> In the limit of (bare quark mass)mq â†’ âˆž for all quark species, we recover pure SU(3) gauge theory, with a de-confinement phase transition provided by spontaneous Z3 breaking.
-> For mq â†’ 0 for all quark masses, the Lagrangian becomes chirally symmetric, and we have a phase transition corresponding to chiral symmetry restoration.
-> For Intermediate bare quark masses (0 < mq < âˆž), there is neither spontaneous Z3 breaking nor a chiral symmetry restoration. There is no singular behavior as such, apart from transient disappearance of the first-order discontinuities on a line of second-order transitions.Beyond this stage, there is no genuine phase transition; only a "rapid cross-over" from confinement to de-confinement can happen .
Fig. 3 The nature of thermal critical behavior in QCD (From )
-> The nature of the transition depends very much, on the number of Quark flavors (Nf) involved and the quark masses: it can either be a genuine phase transition (i.e first order or continuous), or just a rapid cross-over. The "physical point", corresponding to small u, d masses and a larger s-quark mass is fairly certain to fall into the cross-over region. The above figure (Fig.2) summarizes the above mentioned points.
Some theoretical and experimental analysis have shown the production of QGP (Quark Gluon Plasma) in the Earth's atmosphere from the interaction of cosmic rays with heavy ions . QGP is expected to be present inside the core of neutron stars of mass ~1030 kg with radius ~10 km. It is also expected to be produced in laboratory through the collision of high energy particles.QGP can be studied in two energy regimes :
e < 10 GeV/nucleon and (ii) e > 10 GeV/nucleon.
When e < 10 GeV/nucleon, a projectile is stopped by targets which are usually heavy nuclei like lead, gold, and uranium. Most of the kinetic energy before collision is converted into thermal and compression energy right after the collision. The energy density becomes 1-1.5 GeV/fm3 ; very close to the critical energy density of quark matter, and the hadronic density becomes four times its normal value (~0.6 fm-3). Thus QGP is produced with extra quark-antiquark (qq) pairs .
For collisions where the energy becomes greater than 10 GeV/nucleon, the
number of baryons after collisions becomes negligible when compared to the qq( Quark antiquark) pairs and gluons. In this collision process, the nuclei behave as they were transparent to each other .
An interesting aspect called inside-outside cascade is expected to occur. What happens is that the nuclear scattering cross-section saturates around 40 mb and the mean free path of a nucleon in nuclear matter becomes ~1.5-2 fm. In the reference frame of a nucleon, the nucleon covers a long distance in nuclear matter before materialization. The point of materialization will be outside the nucleus in such a scenario. In this process many mesons are produced and re-scattered .
Using Lattice QCD Quark Gluon Plasma has been studied in three regimes
T <= 0.9 Tc, (ii) T Â» Tc, and (iii) T => 3Tc.
For the cases (i) and (ii), calculations are very difficult, and reveal a highly non-trivial behavior for the plasma. But in case (iii) the QGP is expected to show an ideal gas behavior. Lattice gauge theory predicts that for SU(2) gauge fields, the phase transition from normal matter to de-confined matter is of second order. For SU(3) gauge fields, it predicts that the phase transition is of first order .
Karsch et.al, in their pioneer works have shown that for QCD with SU(3) as the gauge group, the transition temperature for various cases are as follows :
(i) Tc (gauge) = 271 Â± 2 MeV , (ii) Tc (2 flavors) = 173 Â± 4 MeV ,
(iii) Tc (3 flavors) = 154 Â± 8 MeV .
They calculated the equation of state (EOS) and energy density for various quark flavors. Also, below Tc they have shown that the screening effects increase significantly due to the spontaneous creation of qq and gluon pairs. Various physical quantities like the energy density, the entropy density , the speed of sound, the specific heat, and the quark matter susceptibilities have been obtained through the quenched approximation to QCD. All these quantities show ideal gas behavior of QGP at high temperature . The energy densities that are obtained are shown in the plot below (Fig.4)
Fig.4 : Energy density Îµ/T4 vs. temperature T/Tc for QCD with 3 light quark flavors. RHIC and LHC refer to the regimes attainable at the Relativistic Heavy Ion and Large Hadron Colliders.
(Fig adopted from  F. Karsch et.al)
From Fig.3, it is seen the energy density is rising very steeply at T â‰ƒ 170MeV, and rapidly reaching a plateau at roughly 80% of the Stefan-Boltzmann value for a relativistic non-interacting plasma . This is strong evidence for QGP formation at Tc â‰ƒ 170MeV, Îµc â‰ƒ 600MeV/fm3.
The Hunt for QGP
Since QGP is expected to Hadronize within 5-10 fm, its important need to look for strong and clean signals. Hence we look for particles that do not interact very strongly, but are also sensitive to the properties of plasma.
Photons from QGP : These carry information of the thermodynamic state of matter. at RHIC have studied these signals in detail. Typical reactions :
However, It is difficult to analyze these results kinematically. And the back-grounds due to decay of different hadrons are very large.
For example :
Di-lepton production : Leptons produced provide better signal than photons which is very sensitive to temperature. They also carry information of the thermodynamic state of the system at the time of production. A typical reaction would be:
But even this has background issues arising from Di-lepton production from other processes like Drell-Yan process caused by sea quarks, hadrons, and other resonances. For Example:
3) Strangeness production : It was proposed that strangeness production could be a signal for QGP. SInce the fireball lifetime is too short for weak interactions to be of importance, baryons with strangeness produced in these reactions may be good signals for QGP. Reactions of the type:
The dominant mechanism here, of strangeness production, involves gluons only present when matter has changed into the QGP phase. When QGP Hadronizes, the high availability of strange antiquarks helps to produce antimatter containing multiple strange quarks, which is otherwise rarely made. For this reason, it is expected that the yield of multi-strange antimatter particles produced in such a state is enhanced compared to conventional series of reactions. [2,8]. For example :
4) Charmonium suppression : Matsui and Satz proposed (J/psi) suppression as a signal of QGP formation. The concept is explained as follows: cc-bar pairs are produced at the very early stage of QGP formation. High gluon density resulting from color De-confinement causes Debye screening for the color interaction between c and c quarks. The Debye screening length becomes much smaller than the radius of charmonium and its other states. Eventually charm quarks and anti charm quarks find light quark partners to make hadrons, which leads to the suppression of charmonium. Charmonium suppression has been observed at RHIC (Relativistic heavy Ion Collider) by the PHENIX collaboration.
Charmonium suppression can be classified into two types :
a) Normal J/y suppression : This happens due to collision of charmonium with other particles, and absorption of J/Psi by nuclear matter etc. This does not provide a great deal of information about QGP.
Anomalous J/y suppression : Occurs when the collision impact parameter is less than 8 fm; which corresponds to energy density greater than 2.2 GeV/fm3. For example in Pb-Pb collision at 158 GeV/c per nucleon. This has been observed by the NA50 collaboration. Figure 8 shows anomalous J/y suppression in various experiments. The anomalous J/y suppression is the actual signal for QGP. However, It should be noted that there are several other mechanisms proposed to explain the J/y suppression. Some of them even do not require the existence of QGP. But when there are large number of nuclei involved which are at considerably higher energies, the J/y suppression is expected to be due to the formation of QGP.  .
Although charmed quarks are too heavy (decay too quickly) to be abundant in thermal equilibrium, they can be pair-produced in the initial high-energy collisions to form cc Ì„ mesons, of which the J/Ïˆ at 3097MeV is the lightest - in the vacuum it is relatively long-lived.
In Fig. 5 The data used for the plot involve proton-nucleus, sulphur-uranium and lead-lead collisions. The inset shows the number of muon pairs produced in an ion collision as a function of energy, clearly showing the peak due to J/Ïˆ decay at âˆ¼3GeV, as well as a high energy tail due to the Drell-Yan mode of production. Where the suppression factor is plotted against the number of nucleons Npart ; participating in the ion collision, which is proportional to the energy density reached. This effect can be modeled by assuming a uniform decay rate integrated along the length of nuclear material traversed by J/Ïˆ before it emerges into the vacuum.
Other signals :
Production of anti particles , lack of charge correlation between pions of neighboring momenta , radial flow , elliptic flow, jet quenching, Hanbury Brown-Twiss (HBT) effect etc are also usually listed among the other signals for QGP.
Fig.5 : J/Ïˆ suppression at SPS. (From  ; Simon Hands )
Space-time evolution of QGP:
Fig.6 shows QGP produced soon after the collisions is initially in a non-equilibrium phase. It thermalizes eventually. As the fireball expands the plasma Hadronizes. The collisions among these hadrons cause a chemical freezeout in which the quark composition of hadrons is changed and we get various kind of hadrons. As the expansion of the hadronic gas continues there is another thermal freeze-out around 100 MeV after which the hadrons de-couple from one another and expand as a free gas.
Fig.6 Space-time evolution of QGP ( Figure adopted From )
Modeling the dynamics of QGP :
For studying the QGP dynamics we need a careful modeling based on QCD. It can be described by the following two ways
String picture : This based on soft hadronic interactions, (non-perturbative QCD) . According to this picture the deformed nucleons in a collision, draw color-flux tubes (strings) between each other. This is described by the color-flux tube (CFT) model. At high energy the strings overlap with each other. It makes the formulation complicated. Concerning the issue of QGP formation it appears inconsistent to assume that the establishment of a truly perturbative quantum chromodynamics (pQCD) phase should proceed via non-perturbative dynamics.
Parton picture : This is founded on the Parton model of hadronic interactions under the pQCD formulation. At low beam energy this approach becomes invalid.
Evolution of QGP
The QGP produced in the collisions is initially in a non-equilibrium state. It is important to study the evolution towards an equilibrium state. It is mainly studied in kinetic theory framework. A classical approach and a quantum mechanical approach to this is possible.
Classical approach: In this approach we solve the transport equation for colour charge numerically. This allows us to calculate different physical quantities. It should be noted that the treatment of color as a classical variable becomes exact only for higher dimensional representations of the gauge group. Still, the classical treatment of color and the associated transport theory remain very useful.The main challenge here is to determine the form of distribution function. It is mostly assumed as a perturbative expansion around equilibrium distribution function.
Quantum mechanical approach: The quantum mechanical analogue of the classical distribution function is Wigner distribution function. Quantum transport theory can also be used to calculate the response functions and the transport coefficients of QGP.
Experiments For QGP :
A natural place to look for QGP is immediately after the Big Bang, when the energy density in the early universe considerably higher than any found naturally today. In the first moments, energies were so high that all matter was highly relativistic. However, this is beyond the range of direct observation, which cannot penetrate beyond the epoch when the cosmic microwave background radiation was formed about t âˆ¼ 105 years ago.
In recent years, however, most attention has been focussed on the possibility of recreating the QGP in terrestrial laboratories in relativistic heavy-ion collisions, i.e. high energy collisions between nuclei such as sulphur (S), lead (Pb) and gold (Au).
The Relativistic heavy ion collider at BNL is known as Relativistic Heavy Ion Collider (RHIC). Thee highest collision energy, in the centre of mass frame, for RHIC is sNN = 200 GeV. The RHIC circumference is 3833.845 m long. The main goal of RHIC is to get an understanding of the description of the initial Partonic configuration of the system .
It has the following components: The Fig.7 gives a birds eye view of the collider at BNL.
PHOBOS: We can measure quantities such as the temperature, size and density of the fireball produced in the collision. We can also study the ratios of the various particles produced. Using these it is possible to both detect and study a phase transition that might occur between QGP and ordinary matter.
PHENIX: Has tracking chambers which record hits along the fight path to measure the curvature and this way we determine each particle's momentum.
BRAHMS: is smaller detector which is used to study charged hadrons.
STAR : its main component is the Time Projection chamber which tracks and identifies particles emerging from heavy ion collisions. It is used to search for signatures of QGP.
AGS : Alternating Gradient Synchrotron (AGS) mainly used as an injector at RHIC.
The results from RHIC tell us :
Partons created in a hard scattering process can act as a very efficient probe of QGP.
For the charmonium sector, the predictions on what to expect at RHIC vary widely from total suppression to a strong enhancement of the J/y and yÂ¢ yields.
This J/Ïˆ suppression is confirmed in data from RHIC. The results from RHIC also match very well with calculations made using a fluid model. This is significant, because a fluid implies strong interactions.
Fig.7 A birds eye view of the collider at RHIC. (adopted from )
The BRAHMS collaboration suggests the biggest indicator of quark gluon plasma is the transverse momentum suppression. This transverse suppression/Bremsstrahlung effect indicates that the particles are interacting with color charges over length scales longer than nucleons. Free color charges imply free quarks, which is a fundamental property of quark gluon plasma. A plot making a comparison of the results from STAR and PHENIX with hydrodynamic calculations from theory is shown in Fig.8
FIG. 8: Comparison of hydrodynamic calculations plotted against experimental data from RHIC. Notice how good the fit is. Taken from
ALICE at CERN.
At CERN the Super Proton Synchrotron (SPS) accelerator is used to accelerate Pb-ions for QGP experiments. SPS results tell us that no single observable or measurement is capable of giving an unambiguous evidence for the onset of de-confinement.
Highly dense nuclear matter was created in these reactions and the energy densities could be measured which indicated the kind of temperatures required for creation of Quark gluon plasma. The collective fluid-like behavior and the radiation from the plasma(Photons and thermal di-leptons) also indicate the same.
There are a number of experimental obstacles which make it hard to directly observe the phase transition. It is important to realize that the timescales over which the collisions at RHIC take place are on the order âˆ¼ 10fm/c. Hence, its hard to be sure if a phase transition is taking place between two states in thermal equilibrium. This, unfortunately, obscures the signatures of the phase transition.
However from what has been observed, a new state of matter highly fluid-like, has been found. To our surprise it is quite strongly interacting over distances greater than a single nucleon. This gives something to think about for the theorists. Some believe that the quark gluon plasma has been observed , but some are reluctant to make that claim. None of the signals gives a deterministic prediction or exclusive evidence about the existence of QGP. Study of response functions has plays a key role in understanding the physics of QGP. This field has a long way to go. And improvement in lattice simulations for finite temperature. Improvements are needed on all the three fronts, theoretical refinement according to observations, lattice simulations at finite temperature and chemical potential and making the experiments more effective.