Singularity structure of massless QCD at finite temperature

A complete relativistic calculation to first order in the strong coupling constantα _s is presented for deep inelastic scattering of leptons off a heat bath of quarks and gluons. The singularity structure is studied and the cancellation of all collinear and infrared divergences is proven. It is shown that it is necessary to include all processes of a given order (i.e. not only the gluon emission and absorption as usually stated). We show that for non-equilibriumn _F andn _B distributions the collinear singularities do not cancel.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c����

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c???? the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitary??*?? amplitude of the eikonal form.     

The bootstrap condition for many reggeized gluons and the photon structure function at lowx andN c→∞

The bootstrap condition is generalized ton reggeized gluons. As a result it is demonstrated that the intercept generated byn reggeized gluons cannot be lower than the one forn=2. Arguments are presented that in the limitN _c→∞ the bootstrap condition reduces then gluon chain with interacting neighbours to a single BFKL pomeron. In this limit the contribution fromn gluons leading at high energies corresponds ton/2 non-interacting BFKL pomerons (then/2 pomeron cut). The sum overn leads to a unitaryγ*γ amplitude of the eikonal form.     

Quasi-confinement in theSU(3)-gluon plasma

We investigate a phenomenological equation of state for the gluon plasma, which differs from the ideal gluon gas equation of state in three aspects: (a) it is assumed that gluons withlow momentum are subject to confining interactions anddo not contribute to the energy spectrum of free gluons; (b)only gluons withhigh momentum are considered as an ideal gas with perturbative corrections of orderO(α_s); (c) a non-perturbative vacuum pressure is included. We show that feature (a) allows for a reasonable perturbative treatment of the interaction between gluons with high momentum. The equation of state reproduces lattice data for the thermodynamical functions of theSU(3) pure gauge theory above the deconfinement transition temperatureT _c. This result suggests that a possible way to describe the gluon plasma is in terms of perturbatively interacting gluons and non-perturbative “glueball” states.     

Simple models of the contribution of intermediate stage gluons to J/ψ suppression at the CERN SPS

We construct three simple scenarios of the time dependence of density of intermediate stage gluons in nuclear collisions in the CERN SPS energy range. Gluons with energy of about 0.6–1.0 GeV are assumed to be produced in nucleon-nucleon collisions in a Glauber type model. The rate of gluon production is given by the parameter n _g/nn equal to the average number of gluons produced per nucleon-nucleon collision. The value of this parameter determines the behaviour of the gas of gluons. The number of gluons increases due to gluon branching and processes like g+g → g+g+g and decreases due to the hadronization. Gluons are assumed to be able to dissociate J/ψ in g+J/ψ collisions, the dissociation cross-section σ _gγ is taken as a free parameter. In the first scenario, the energy density of the gas of gluons never reaches the critical energy density ε _c ≈ 0.7 GeV/fm³ and gluons rapidly hadronize. In the second scenario, the critical energy density is reached but the system of gluons is unable to reach thermalization. In the third scenario gluons reach thermalization and the thermalized system suppresses J/ψ by the Matsui-Satz mechanism. The third scenario under the assumption of a small value of σ _gψ is able to describe qualitatively the data on J/ψ suppression in Pb?Pb interactions obtained by the NA50 Collaboration. Other scenarios have problems with getting the rather abrupt onset of J/ψ suppression.     

Unusual initial state interactions and Kinoshita diagram identities in perturbative QCD

Unlike in QED, algebraic identities for individual single-cut Kinoshita diagrams with all soft gluons are generally violated by initial state spectator interactions in light-cone time-ordered perturbation theory. At g⁴ order, identities insuring IR cancellation for the real graphs considered by Bodwin, Brodsky and Lepage for ππ→μ⁺μ^?+X when all gluons are soft can be obtained by summing over several of the corresponding single-cut diagrams. Although this fails for the two-loop virtual's diagrams considered by BBL, summing over a larger class of possible two-loop virtual spectator interactions having two Glauber singularities does restore IR finiteness when both gluons are soft.For individual single-cut Kinoshita diagrams with an arbitrary number ladder exchanges, algebraic identities for the (C_F)^n/2 contribution from the initial state are derived.     

Diamagnetic susceptibility near the surface or twinning plane at the transition to the superconducting state

Besides the well-known bulk fluctuation contribution to the diamagnetic susceptibility there is an additional surface contribution with the singularity at T_SH exceeding the superconducting bulk transition temperature T_c(H). The results obtained allow to explain the anomalous behavior of the diamagnetic susceptibility found by Khaikin and Khlyustikov.     

Gluon recombination and shadowing at small values of x

We determine the recombination probabilities for gluons to go into gluons or into quarks in a low-density limit. A modified Altarelli-Parisi equation expressing this recombination is given. We find recombination is very small compared to normal evolution in all interesting circumstances except that of nuclear shadowing. Thus, for evolution above Q₀ ≈ 2 GeV, the gluon density remains far below saturation except at unusually small values of x.     

Flavor singlet contribution to the structure functiong 1 at small-x

The singlet contribution to theg ₁(x, Q ²) structure function is calculated in the double-logarithmic approximation of perturbative QCD in the regionx?1. Double logarithmic contributions of the type (α _s ln²(1/x)) ^k which are not included in the GLAP evolution equations are shown to give a power-like rise at small-x which is much stronger than the extrapolation of the GLAP expressions. The dominant contribution is due to the gluons which, in contrast to the unpolarized case, mix with the fermions also in the regionx?1. The two main reasons why the small-x behavior of the double logarithmic approximation is so much stronger than the usual GLAP evolution are: the larger kinematical region of integration (in particular, no ordering in transverse momentum) and the contributions from non-ladder diagrams.     

Anomalous mass dependence of glueball exclusive decay rates

Exclusive decays such as G → ππ are studied in the framework ofperturbative QCD. We discuss the possibility of the constituent gluons' virtualness scaling as the glueball mass M_G, which is a picture equivalent to a glueball containing a few slow-moving, heavy gluons. In this case, the decay rate exhibits a pinch singularity which enhances it by a factor of order (M_G²/m_q²)² over the dimensional scaling expectation. This singularity is partially suppressed by Sudakov effects which reduce the enhancement factor to $\text{(M}{}_{\mathrm{<mtext>G</mtext>}}{}^2\text{/m}{}_{\mathrm{<mtext>q</mtext>}}{}^2\text{)}{}^{\mathrm{2n}}\text{,}\text{where}\text{n ? 0.4}$.     

Gluon-exchange currents: The nucleon axial-vector coupling constant and magnetic moments in bag models

Possible numerical importance of the two-body currents arising from exchange of one hard gluon between two constituent quarks is investigated by studying the evaluation of the nucleon axial-vector coupling constantg _A and magnetic moments μ _p ^tot , μ _n ^tot in the context of the MIT bag model. The double counting problem is resolved only to the extent that, in accord with the standard wisdom, hard gluons have nothing to do with the formation of bags (quark confinement) and so are not included in bag-model wave functions. For reasonable choices of the parameters, we find that (1) the contribution tog _A arising from one-gluon-exchange currents (OGEC) could account for the discrepancy between the observed value and the one-body bag-model prediction, and that (2) whereas the OGEC contribution to μ _n ^tot is negligible, the contribution to μ _p ^tot could be important but does not allow further understanding of the observed μ _p /μ _n ratio.     

Charged spin-1 gluons,parton model and the Archimedes effect

In a gauge theory of (SU(2)×U(1))_flavour×SU(3)_colour with un-confined integer-charged quarks and massive integer-charged gluons both quarks and gluons contribute to electro- and neutrino-production. The gluon parton contribution to the lepto-production of colour is considered. Supported in part by NSF Grant No. GP43662X, and in part by UGC Research Assistantship, U.K.; Supported in part by a Senior Visiting Fellowship awarded by the Science Research Council, U.K., and by NSF Grant No. GP43662X;     

Perturbative thermalisation in nuclear collisions at very high energies?

According to lowest order perturbation theory more than one hundred gluons and quarks with p_T > p₀ ≈2 GeV are produced per unit rapidity within a time of 0.1 fm in an average collision of two large nuclei at a CMS energy/particle in the few 100 GeV range. We show, including longitudinal expansion and QCD branching, that before a time of about 0.4 fm each of these will experience more than one collision with one of the other gluons and quarks. Without any assumptions concerning soft QCD one thus concludes that the quark-gluon subsystem is driven towards thermalisation.     

Monte Carlo study of three-dimensional QCD at finite temperature

Three-dimensional QCD at finite temperature is analyzed using Monte Carlo calculations. It is shown that confinement at low temperature is lost through a second-order phase transition. At high temperature, static quarks are liberated and screened and it is argued that timelike (A₀) gluons are liberated. Just above the critical temperature electric correlation functions seem to be dominated by a resonance of two timelike gluons, whose existence is suggested by perturbation theory. The influence of an external magnetic field close to the critical point is considered.     

Nonforward color-octet kernel of the Balitsky-Fadin-Kuraev-Lipatov equation

The contribution to the kernel of the nonforward Balitsky-Fadin-Kuraev-Lipatov equation from two-gluon production is calculated for the case of the antisymmetric color-octet state of two Reggeized gluons in the t channel. The one-gluon contribution to the kernel in the one-loop approximation is also obtained by using the one-loop expression for the effective vertex of the one-gluon production in Reggeon-Reggeon collisions. An explicit form of the total kernel is presented.     

Diffractive production of dijets at HERA

We investigate the production of a quark-antiquark pair in diffractive photon-proton scattering, approximating soft pomeron exchange by the exchange of two nonperturbative gluons. In deep inelastic scattering at HERA, events with two jets and the scattered proton in the final state are predicted to be observable, with an important contribution from charm production. For photoproduction of light quark jets with high transverse momentum we find that both exchanged gluons must have a large invariant mass, so that the cross section is very small, whereas for charm quarks it is quite appreciable. From our calculation we also extract the quark structure function of the pomeron for the scaling variablez no too close to 0 or 1, finding a strong flavour dependence and a behaviour somewhat harder thanz(1?z) for light quarks.     

Limits on the scalar-leptoquark and scalar-gluon masses from the parameters <Emphasis Type="Italic">S</Emphasis>, <Emphasis Type="Italic">T</Emphasis>, and <Emphasis Type="Italic">U</Emphasis> in the minimal model based on four-color symmetry

The contributions to the parameters S, T, and U of radiative corrections from the doublets of scalar leptoquarks and scalar gluons are analyzed within the minimal model based on four-color symmetry of the Pati-Salam type. It is shown that current experimental data on the parameters S, T, and U admit the existence of relatively light scalar leptoquarks and scalar gluons (of mass lower than 1 TeV), the best fit to experimental data being attained at mass values not greater than 400 GeV. In particular, the existence of scalar leptoquarks of mass below 300 GeV is found to be compatible with data on the parameters S, T, and U at χ² < 3.1 (3.2) for m_H = 115 (300) GeV as against χ _SM ² = 3.5 (5.0) in the Standard Model. The mass of the lightest scalar gluon is then predicted to be less than 850 (720) GeV. It is emphasized that the aforementioned doublets of scalar leptoquarks and scalar gluons can play a significant role in processes involving a t quark at LHC.     

Transverse momentum of jets in electroproduction from quantum chromodynamics

Detailed predictions of QCD on transverse momentum distributions of jets in leptoproduction are presented. The average p_⊥² is found to be asymptotically proportional to W² (the hadronic invariant mass squared) with a coefficient function that depends little on x and y. Contributions from gluons in the nucleon are relatively smaller than for σ_L/σ_T.     

Largep ⊥ jets at small angles

It is pointed out that study of largep _⊥ jets produced at small angles will provide easy tests for the QCD gluons as partons active in hard hadronic collisions.