RELATING THE QCD POMERON TO AN EFFECTIVE GLUON MASS

We construct the Pomeron as an exchange of two nonperturbative gluons, where the nonperturbative gluon propagator is described by an approximate solution of the Schwinger-Dyson equation which contains a dynamically generated gluon mass. We compute the total and elastic differential (dsigma/dt) cross sections for pp scattering, obtaining agreement with the experimental data for a gluon mass m = 370 MeV for LAMBDA(QCD) = 300 MeV. In particular, the Pomeron effectively behaves like a photon-exchange diagram with a coupling determined by the glucon mass.

DIFFRACTION AND THE GLUON MASS

We recently proposed a QCD Pomeron described by the exchange of two nonperturbative gluons characterized by a dynamically generated gluon mass. It is shown here that data on elastic scattering, exclusive rho production in deep inelastic scattering, and the J/psi-nucleon total cross section can be successfully described in terms of a single gluon mass m(g) congruent-to 0.37 GeV. We observe that the total cross sections of hadrons with small radii, such as J/psi, have a marked dependence on the effective gluon mass.

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed. © SISSA 2006.

Analyzing dynamical gluon mass generation

We study the necessary conditions for obtaining infrared finite solutions from the Schwinger-Dyson equation governing the dynamics of the gluon propagator. The equation in question is set up in the Feynman gauge of the background field method, thus capturing a number of desirable features. Most notably, and in contradistinction to the standard formulation, the gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. Various subtle field-theoretic issues, such as renormalization group invariance and regularization of quadratic divergences, are briefly addressed. The infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is presented.

On dynamical gluon mass generation

The effective gluon propagator constructed with the pinch technique is governed by a Schwinger-Dyson equation with special structure and gauge properties, that can be deduced from the correspondence with the background field method. Most importantly the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions, a property which allows for a meanigfull truncation. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles. The resulting integral equation, subject to a properly regularized constraint, is solved numerically, and the main features of the solutions are briefly discussed.

Negative differential conductance and effective electron mass in highly asymmetric ballistic bilayer graphene nanoribbon

We present a simplified theory of the effective momentum mass (EMM) and ballistic current–voltage relationship in a degenerate two-folded highly asymmetric bilayer graphene nanoribbon. With an increase in the gap, the density-of-states in the lower set of subbands increases more than that of the upper set. This results in a phenomenological population inversion of carriers, which is reflected through a net negative differential conductance (NDC). It is found that with the increase of the ribbon width, the NDC also increases. The population inversion also signatures negative values of EMM above a certain ribbon-width for the lower set of subbands, which increases in a step-like manner with the applied longitudinal static bias. The well-known result for symmetric conditions has been obtained as a special case.

On the two dimensional effective electron mass in quantum wells, inversion layers and NIPI superlattices of Kane type semiconductors in the presence of strong light waves: Simplified theory and relative comparison

An attempt is made to study the two dimensional (2D) effective electron mass (EEM) in quantum wells (Qws), inversion layers (ILs) and NIPI superlattices of Kane type semiconductors in the presence of strong external photoexcitation on the basis of a newly formulated electron dispersion laws within the framework of k.p. formalism. It has been found, taking InAs and InSb as examples, that the EEM in Qws, ILs and superlattices increases with increasing concentration, light intensity and wavelength of the incident light waves, respectively and the numerical magnitudes in each case is band structure dependent. The EEM in ILs is quantum number dependent exhibiting quantum jumps for specified values of the surface electric field and in NIPI superlattices; the same is the function of Fermi energy and the subband index characterizing such 2D structures. The appearance of the humps of the respective curves is due to the redistribution of the electrons among the quantized energy levels when the quantum numbers corresponding to the highest occupied level changes from one fixed value to the others. Although the EEM varies in various manners with all the variables as evident from all the curves, the rates of variations totally depend on the specific dispersion relation of the particular 2D structure. Under certain limiting conditions, all the results as derived in this paper get transformed into well known formulas of the EEM and the electron statistics in the absence of external photo-excitation and thus confirming the compatibility test. The results of this paper find three applications in the field of microstructures. (C) 2011 Elsevier Ltd. All rights reserved.

Simple theoretical analysis of the effective electron mass in semiconductor nanowires

In this paper we study the effective electron mass (EEM) in Nano wires (NWs) of nonlinear optical materials on the basis of newly formulated electron dispersion relation by considering all types of anisotropies of the energy band constants within the framework of k . p formalism. The results for NWs of III-V, ternary and quaternary semiconductors form special cases of our generalized analysis. We have also investigated the EEM in NWs of Bi, IV-VI, stressed Kane type materials, Ge, GaSb and Bi2Te3 by formulating the appropriate 1D dispersion law in each case by considering the influence of energy band constants in the respective cases. It has been found that the 1D EEM in nonlinear optical materials depend on the size quantum numbers and Fermi energy due to the anisotropic spin orbit splitting constant and the crystal field splitting respectively. The 1D EEM is Bi, IV-VI, stressed Kane type semiconductors and Ge also depends on both the Fermi energy and the size quantum numbers which are the characteristic features of such NWs. The EEM increases with increase in concentration and decreasing film thickness and for ternary and quaternary compounds the EEM increases with increase in alloy composition. Under certain special conditions all the results for all the materials get simplified into the well known parabolic energy bands and thus confirming the compatibility test.

Dynamical gluon mass corrections in heavy quarkonia decays

Using the expression of the dynamical gluon mass obtained through the operator product expansion we discuss the relevance of gluon mass effects in the decays V --> hadrons (V = J/psi, Y), Relativistic and radiative corrections are also introduced to calculate alpha(s)(m(c)) and alpha(s)(m(b)) comparing them with other values available in the literature. The effects of dynamical gluon masses are negligible for Y decay but important for J/psi decay. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Schwinger-Dyson equations and dynamical gluon mass generation

We obtain a solution for the gluon propagador in Landau gauge within two distinct approximations for the Schwinger-Dyson equations (SIDE). The first, named Mandelstam's approximation, consist in neglecting all contributions that come from fermions and ghosts fields while in the second, the ghosts fields are taken into account leading to a coupled system of integral equations. In both cases we show that a dynamical mass for the gluon propagator can arise as a solution.

A dynamical gluon mass solution in Mandelstam's approximation

We discuss the pure gauge Schwinger-Dyson equation for the gluon propagator in the Landau gauge within an approximation proposed by Mandelstam many years ago. We show that a dynamical gluon mass arises as a solution. This solution is obtained numerically in the full range of momenta that we have considered without the introduction of any ansatz or asymptotic expression in the infrared region. The vertex function that we use follows a prescription formulated by Cornwall to determine the existence of a dynamical gluon mass in the light cone gauge. The renormalization procedure differs from the one proposed by Mandelstam and allows for the possibility of a dynamical gluon mass. Some of the properties of this solution, such as its dependence on A(QCD) and its perturbative scaling behavior are also discussed.

gamma p and gamma gamma scattering from (p)over-bar-p, pp forward amplitudes in a QCD eikonal model with a dynamical gluon mass

We examine the gamma p photoproduction and the hadronic gamma gamma total cross sections by means of a QCD eikonal model with a dynamical infrared mass scale. In this model, where the dynamical gluon mass is the natural regulator for the tree level gluon-gluon scattering, the gamma p and gamma gamma total cross sections are derived from the pp and (p) over barp forward scattering amplitudes assuming vector meson dominance and the additive quark model. We show that the validity of the cross section factorization relation sigma(pp)/sigma(gamma p)=sigma(gamma p)/sigma(gamma gamma) is fulfilled depending on the Monte Carlo model used to unfold the hadronic gamma gamma cross section data, and we discuss in detail the case of sigma(gamma gamma -> hadrons) data with W-gamma gamma> 10 GeV unfolded by the Monte Carlo generators PYTHIA and PHOJET. The data seems to favor a mild dependence with the energy of the probability (P-had) that the photon interacts as a hadron.

Aspects of a dynamical gluon mass approach to elastic hadron scattering at LHC

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Relating a gluon mass scale to an infrared fixed point in pure gauge QCD

The condition for the global minimum of the vacuum energy for a non-Abelian gauge theory with a dynamically generated gauge boson mass scale which implies the existence of a nontrivial IR fixed point of the theory was shown. Thus, this vacuum energy depends on the dynamical masses through the nonperturbative propagators of the theory. The results show that the freezing of the QCD coupling constant observed in the calculations can be a natural consequence of the onset of a gluon mass scale, giving strong support to their claim.

A dynamical gluon mass solution in a coupled system of the Schwinger-Dyson equations

We study numerically the Schwinger-Dyson equations for the coupled system of gluon and ghost propagators in the Landau gauge and in the case of pure gauge QCD. We show that a dynamical mass for the gluon propagator arises as a solution while the ghost propagator develops an enhanced behavior in the infrared regime of QCD. Simple analytical expressions are proposed for the propagators, and the mass dependency on the ΛQCD scale and its perturbative scaling are studied. We discuss the implications of our results for the infrared behavior of the coupling constant, which, according to fits for the propagators infrared behavior, seems to indicate that α s(q2) → 0 as q2 → 0. © SISSA/ISAS 2004.