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Register a new userA model density of states for Quarks and Gluons in QGP
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We propose an algebraic form for the density of states of quarks and gluons in a Quark-Gluon Plasma (QGP) fireball in quasi-equilibrium with a hadronic medium as $rho(k)= frac {alpha}{k} + {beta}k + {delta}k^{2}$, and determine the parameters $alpha$, $beta$ and $delta$ using Lattice Gauge results on the velocity of sound in QGP. The behaviour of the resulting $rho(k)$ can be easily compared with the thermodynamic data on QGP that is expected from LHC and other RHIC experiments. Our numerical result shows a linear rise of the value of $rho(k)$ for $ksim T approx 160 to 180 MeV$, which is significant, and throws light on the evolution of the QGP phase.
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A general approach to the construction of bound states in quantum field theory, called the renormalization group procedure for effective particles (RGPEP), was applied recently to single heavy-flavor QCD in order to study its utility beyond illustration of its general features. This heavy-flavor QCD is chosen as the simplest available context in which the dynamics of quark and gluon bound states can be studied with the required rigor using Minkowski-space Hamiltonian operators in the Fock space, taking the advantage of asymptotic freedom. The effective quarks and gluons differ from the point-like canonical ones by having a finite size $s$. Their size plays the role of renormalization group parameter. However, instead of integrating out high-energy degrees of freedom, our RGPEP procedure is based on a transformation of the front-form QCD Hamiltonian from its canonical form with counterterms to the renormalized, scale-dependent operator that acts in the Fock space of effective quanta of quark and gluon fields, keeping all degrees of freedom intact but accounting for them in a transformed form. We discuss different behavior of effective particles interacting at different energy scales, corresponding to different size s. Namely, we cover phenomena ranging from asymptotic freedom at highest energies down to the scales at which the formation of bound states occurs. We briefly present recent applications of the RGPEP to quarks and gluons in QCD, which have been developed using expansion in powers of the Fock-space Hamiltonian running coupling. After observing that the QCD effective Hamiltonian satisfies the requirement of producing asymptotic freedom, we derive the leading effective interaction between quarks in heavy-flavor QCD. An effective confining effect is derived as a result of assuming that the non-Abelian and non-perturbative dynamics causes effective gluons to have mass.
In this review article, we develop the perturbative framework for the calculation of hard scattering processes. We undertake to provide both a reasonably rigorous development of the formalism of hard scattering of quarks and gluons as well as an intuitive understanding of the physics behind the scattering. We emphasize the importance of logarithmic corrections as well as power counting of the strong coupling constant in order to understand the behavior of hard scattering processes. We include rules of thumb as well as official recommendations, and where possible seek to dispel some myths. Experiences that have been gained at the Fermilab Tevatron are recounted and, where appropriate, extrapolated to the LHC.
We use perturbation theory to construct perfect lattice actions for quarks and gluons. The renormalized trajectory for free massive quarks is identified by blocking directly from the continuum. We tune a parameter in the renormalization group transformation such that for 1-d configurations the perfect action reduces to the nearest neighbor Wilson fermion action. The fixed point action for free gluons is also obtained by blocking from the continuum. For 2-d configurations it reduces to the standard plaquette action. Classically perfect quark and gluon fields, quark-gluon composite operators and vector and axial vector currents are constructed as well. Also the quark-antiquark potential is derived from the classically perfect Polyakov loop. The quark-gluon and 3-gluon perfect vertex functions are determined to leading order in the gauge coupling. We also construct a new block factor $n$ renormalization group transformation for QCD that allows to extend our results beyond perturbation theory. For weak fields it leads to the same perfect action as blocking from the continuum. For arbitrarily strong 2-d Abelian gauge fields the Manton plaquette action is classically perfect for this transformation.
The collisional energy gain of a heavy quark due to chromo-electromagnetic field fluctuations in a quark-gluon plasma is investigated. The field fluctuations lead to an energy gain of the quark for all temperatures and velocities. The net effect is a reduction of the collisional energy loss by 15-40% for parameters relevant at RHIC energies.
We propose a simple statistical model for the density of states for quarks and gluons in a QGP droplet, making the Thomas-Fermi model of the atom and the Bethe-model for the nucleons as templates for constructing the density of states for the quarks and gluons with due modifications for the `hot relativistic QGP state as against the `cold non-relativistic atom and nucleons, which were the subject of the earlier `forebears of the present proposal.We introduce `flow-parameters $gamma_{q,g}$ for the quarks and the gluons to take care of the hydrodynamical (plasma) flows in the QGP system as was done earlier by Peshier in his thermal potential for the QGP. By varying $gamma_{g}$ about the `Peshier-Value of $gamma_{q} = 1/6$, we find that the model allows a window in the parametric space in the range $8gamma_{q} leq gamma_{g} leq 12gamma_{q}$, with $gamma_{q} =1/6$ (Peshier-Value), when stable QGP droplets of radii $sim$ $6 fm$ appear at transition temperatures $100 MeV leq T leq 250 MeV$. The smooth cut at the phase boundary of the Free energy vs. droplet radius suggests a First - Order phase transition .On the whole the model offers a robust tool for studying QGP phenomenology as and when data from various ongoing experiments are available .
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