Quark-Gluon Interactions at High Temperature and Large Distances

Continuum fourdimensional Quantum Chromodynamics (QCD) including quarks in the regime of high temperature and large distances (the HT regime) is studied to all perturbative orders. The imaginary time (τ) formalism is used. Then, as shown in previous works, QCD is described by a new generating functional Z_HT, in which quark fields retain their dependences on τ, while gluon and ghost fields are τ-independent. The invariance of Z_HT under BRST transformations in the HT regime is exhibited: it closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT. Infinite sets of non-abelian Ward identities for the closed quark and electric gluon loops in the HT regime are obtained. The electric mass terms in Z_HT are shown to be infrared finite. We prove to all perturbative orders that one can regard as subdominant, and, hence, neglect consistently the contributions of :i) all closed electric gluon loops, ii) all closed quark loops with three or more vertices in diagrams having an even number of electric gluons (or none) in the external lines. In the HT regime, the axial anomalies are obtained: their expressions in terms of τ-independent gluon fields are similar to those for zero temperature. A non-trivial renormalization group (RG) equation in the HT regime, specifically due to the quark-gluon interaction, is presented. A positive beta function is obtained, and it is argued that interactions are not weak in that regime. The RG and the perturbative analysis to all orders appear to indicate that quarks and gluons may be confined in the HT regime (and, in particular in the Early Universe), due to the infrared divergent magnetic gluon sector. Other possibilities are also discussed.     

Light Quark Hadron Mass Scale

With a symmetry procedure based on Noether's theorem, the field equation of motion is obtained from the Dirac Hamiltonian H(D_μ) of a massless quark interacting with a gluon. The equation of motion is the Yang-Mills equation with external current which is spin-dependent and follows from the group algebra. In addition to the pure gauge solution we find a gauge covariant solution which follows from current conservation and sets the mass scale m₀/M = g². This gluon field is due to the density of dipole moments squared and represents four harmonic oscillators with quadratic constraints; the gluon can be written as a string potential or as a 1/x potential with a sharp cutoff. The chiral symmetry group G^spin × G^D gives the light quark hadron degenerate multiplet mass spectrum in terms of m₀[SU(2) × SU(2)] with the spinorial decomposition and the multipole breaks into dipoles. Scaling from atomic lengths it is found that g = em₀/nM for light quarks is the quark charge e/3 renormalized by m₀/M and g is magnetic. Thus quarks occur at the ends of spinning magnetic strings with dipole lengths ∼m₀⁻¹. The mass scale is that of a degenerate magnetic multipole with charge n = 3, 4… .     

Can quarks always be confined by a linear potential?

It is demonstrated on the basis of the Dirac equation that quarks cannot be confined by a vector gluon potential of the form(r/r ₀)^a or[ln(r/r ₀]^a, a>0, if the quark-gluon interaction conserves parity. In order to confine quarks with the parity-conserving interaction, the effective gluon potential must be a pseudovector or a scalar. These are shown in a simple Yang-Mills field with theSU(2) group.     

Effective Lagrangian and equations for valence quark and gluon Green's functions

Starting from the QCD Lagrangian and separating background and valence degrees of freedom, one arrives at the effective Lagrangian for valence quarks and gluons. Each term in the Lagrangian contains a product of valence quark and gluon operators acting at the end of the fundamental or adjoint string, made of the background field. A simple procedure is described how to obtain from the Lagrangian self-coupled equations for quark and gluon Green's function.     

The Magnetic Mass of Transverse Gluon, the B-Meson Weak Decay Vertex and the Triality Symmetry of Octonion

With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion make an octonion which possesses the triality symmetry, I calculate the magnetic mass of the transverse self-dual gluon from three loop diagram, in which a heavy quark pair is created and two self-dual gluons are interchanged. The magnetic mass of the transverse gluon depends on the mass of the pair created quarks, and in the case of charmed quark pair creation, the magnetic mass m _mag becomes approximately equal to T _c at ${T=T_c\sim 1.14\Lambda_{\overline{MS}} \sim 260}$ MeV. A possible time-like magnetic gluon mass from two self-dual gluon exchange is derived, and corrections in the B-meson weak decay vertices from the two self-dual gluon exchange are also evaluated.     

Spectator interactions and theK-factor in the Drell-Yan process

The precise value of theO(α _s perturbative QCD correction to the Drell-Yan cross-section seems to depend on the calculational procedure. We show how this ambiguity is removed when proper account is taken of the additional interactions involving spectator quarks. Explicit calculations in the scalar quark model reveal that the important contributions come from values of the gluon momentum that are very soft.

     

Gluon condensation and the bag model of hadrons

Migdal's scheme for gluon condensation is applied to a model where gluons are dynamically confined by coloured Higgs fields and are also subjected to ac-number colour field due to external “semiclassical” quarks. We show that, no matter how strong the external field becomes, stabilization of the gluonic ground state is guaranteed by the formation of an inhomogeneous gluon condensate. The contribution to the total energy from the condensate is computed semiclassically using a variational approximation. A physical interpretation of the results obtained is given in terms of a renormalization of the MIT bag model input parameters in particular the zero point energy coefficientZ and the bag constantB.

     

Gluon condensates,quark matter equation of state and quark stars

We consider here quark matter equation of state including strange quarks and taking into account a nontrivial vacuum structure for QCD with gluon condensates. The parameters of condendsate function are determined from minimisation of the thermodynamic potential. The scale parameter of the gluon condensates is fixed from the SVZ parameter in the context of QCD sum rules at zero temperature and zero baryon density. The equation of state for strange matter at zero temperature as derived is used to study quark star structure using Tolman Oppenheimer Volkoff equations. Stable solutions for quark stars are obtained with a large Chandrasekhar limit as 3.2M and radii around 17 kms.     

Hadron resonance gas and nonperturbative QCD vacuum at finite temperature

Nonperturbative QCD vacuum with two light quarks at finite temperature was studied in a hadron resonance-gas model. Temperature dependences of the quark and gluon condensates in the confined phase were obtained. It is shown that the quark condensate and one-half (chromoelectric component) of the gluon condensate are evaporated at the same temperature corresponding to the quark-hadron phase transition. With allowance for the temperature shift of hadron masses, the critical temperature was found to be T _c ?190 MeV.     

Quark strong interactions as a possible mechanism of symmetry breaking in weak interactions

A new mechanism for symmetry breaking is suggested which is connected with the negative contribution of quark loops to the vacuum energy and with the strong interactions of quarks with gluons diminishing this effect. The “gluon mechanism” of symmetry breaking makes it possible to estimate the mass of the heaviest quark (～ 60 GeV) and the mass of the Higgs boson (～ 7 GeV).     

Self-energy of heavy quark

We demonstrate that to calculate the selfenergy of a heavy quark in the heavy quark limit (or the heavy fermion limit in what is called the Baryon Chiral Perturbation Theory), the use of standard dimensional regularization provides only the quantum limit: opposite to the heavy quark (or classical) limit that one wishes to obtain. We thus devised a standard ultraviolet/infrared regularization procedure in calculating the one- and two-loop contributions to the heavy quark self-energy in this limit. Then the one-loop result is shown to provide the standard classical Coulomb self-energy of a static colour source that is linearly proportional to the ultraviolet cutoff Λ. All the two-loop contributions are found to be proportional to Λ In (Λ/γ) where γ is the infrared cutoff. Often only the contribution from the bubble (light quarks, gluon and ghost) insertion to the gluon propagator has been considered as theO(α _s ) correction to the Coulomb energy to this order. Our result shows that other contributions are of the same magnitude, thus have to be taken into account.     

Semileptonic decays of heavy quarks in quantum chromodynamics

We investigate the semileptonic decays of heavy quarks in the leading non-trivial order in quantum chromodynamics. Effects of gluon corrections and the initial quark Fermi motion on the semileptonic rates and decay distributions are calculated. The resulting lepton energy spectrum for the charm semileptonic decay is compared with data to extract the mass of the charm quark. This is combined with the semileptonic branching ratio to predict the charm-quark lifetime. We find the lepton energy spectrum very stable with respect to gluon corrections. Expected spectra from the semileptonic decays of bottom and top quarks are presented. We also study the semileptonic decay process Q → q?v_? + G, involving the emission of a single hard non-collinear gluon. This process should be observable with a branching ratio of a few percent in the decays of top (and heavier) quarks.     

<Emphasis Type="Italic">Z</Emphasis><Superscript>0</Superscript>-tagged quark jets at the large hadron collider

The Large Hadron Collider will allow studies of hard probes in nucleus-nucleus collisions which were not accessible at the Relativistic Heavy Ion Collider—even the study of small cross-section Z ⁰-tagged jets becomes possible. Going beyond the measurement of back-to-back correlations of two strongly interacting particles to measure plasma properties, we replace one side by an electromagnetic probe which propagates through the plasma undisturbed and therefore provides a measurement of the energy of the initial hard scattering. We show that at sufficiently high transverse momentum the Z ⁰-tagged jets originate predominately from the fragmentation of quarks and anti-quarks while gluon jets are suppressed. We propose to use lepton-pair tagged jets to study medium-induced partonic energy loss and to measure in-medium parton fragmentation functions to determine the opacity of the quark gluon plasma.     

On finite lattice corrections to gauge field thermodynamics

We consider the ideal gas limit of lattice Yang-Mills with fermions. Recently, such a system has been considered in great detail in the literature. We discuss possible finite lattice corrections to the energy density of the quarks and gluons due to the constraint of the quark-gluon gas being in colour singlet state. In the case of pure Yang-Mills theory at finite temperature, we find that Monte Carlo data agree very well with the asymptotically free gluon gas being a colour singlet. In the presence of quarks, in the quenched approximation, we find that Monte Carlo data seem to agree with a distribution where the quarks themselves form a colour singlet.     

The ferromagnetic phase of quark matter in the framework of one gluon exchange and thermodynamics with the density-temperature-dependent particle mass model

In the current work we examine the possibility of ferromagnetism phase of quark matter by using the one gluon exchange interaction and the thermodynamics with the density-temperature-dependent particle masses as well as the normal thermodynamics (with constant masses). We calculate the free energy per particle of the polarized and unpolarized states to discuss the difference between these two phases at various densities and temperatures. In our calculations we assume that the QCD coupling, α_c, is constant (the simple model) or varies with the temperature and the density (the asymptotic freedom); but we keep α_c less than one, because we intend to use the perturbation method to calculate the exchange energy. We also assume that the up and down quarks are massless and do not interact. Only the strange quarks interact with each other via the one gluon exchange interaction. The free and internal energies as well as the effective masses and the pressure are calculated at different densities and temperatures. The results are discussed and a comparison is made with those of Tatsumi. Finally it is shown that the present models do not predict any transition for the strange quark matter to its ferromagnetic phase.     

Quark potentials at finite temperatures

We scan the quark-antiquark potential and the meson-meson potential for static quarks in aSU ₃ gluon field from strong coupling to weak coupling. The breakdown of the confinement between quark and antiquark at the phase transition is observed. There is no interaction between pointlike mesons in the whole coupling regime. It is pointed out that the interaction mechanism between two quark clusters can be classified by these two fundamental examples.     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

Baryon spectrum and the forces between quarks

We study the effect of confinement on gluon bremsstrahlung. A natural infrared cutoff emerges both at small gluon momenta and at small angles. If the confinement potential is of the linear “string” type, the cutoff is controlled by the tension parameter and is thus about 1GeV for the transverse momentum of a hard gluon relative to its parent quark. We propose that this confinement effect may remove the necessity for introducing ad hoc cutoffs by a large “intrinsic partonp _T ” in phenomenological applications of perturbative QCD.     

Constituent quark masses from modified perturbative QCD

A recently proposed modified perturbative expansion for QCD incorporating gluon condensation is employed to evaluate the quark and gluon self-energy corrections in first approximation. The results predict mass values of 1/3 of the nucleon mass for the light quarks u, d, and s and a monotonously growing variation with the current mass. The only phenomenological input is that is evaluated up to order as a function of the unique parameter C defining the modified propagator, and then C is fixed to give a current estimate of . The light quarks u and d as a result are found to be confined and the s, c, b and t ones show damped propagation modes, suggesting a model for the large differences in stability between the nucleons and the higher resonances. The above properties of quark modes diverge from the fully confinement result following from the similar gluon propagator previously considered by Munczek and Nemirovski. On the other hand, the condensate effects on the gluon self-energy furnish a tachyonic mass shell as predicted by the Fukuda analysis of gluon condensation in QCD. Received: 28 September 2001 / Revised version: 15 November 2001 / Published online: 8 February 2002     

A Minimal Dynamical Scheme for “Understanding” Hadronic Widths

Using a quark model scheme of ‘least Dynamics’, an inclusive determination of the total widths of mesons and baryons is proposed via the following mechanism: There exists a short (breathing) mode for the temporary dissociation of a hadron into a pair of “qausi-free” quarks and/or diquarks which eventually hadronize with certainty, so that the requisite widths correspond to this “first stage” dissociation itself. A detailed model (described elsewhere) based on the momentum dependence of the quark's mass function m(p) suggests a significant mass reduction of these quasi-free quarks w.r.t their “constituent” values m(O). Using this logic, a phenomenological coupling scheme for the meson-(quasifree)quark-vertex function is derived from Schwinger's Partial (broken chiral). Symmetry which incorporates the conservation of isospin, baryonic charge and hypercharge with respective ‘gauge mesons’ rho, omega, phi. A very similar structure is found for baryon couplings to quark (q)-diquark (D) pairs, with the same overall coupling constant (gs) for both systems. Its tentative identification with the QCD value yields a surprisingly good pattern of agreement with data for both hadron types, using two “quasi-free” masses (m_ud and m_s) as inputs, with the corresponding diquark masses determined additively.