Pomeron vertices in perturbative QCD in diffractive scattering

We analyze the momentum space triple pomeron vertex in perturbative QCD. In addition to the standard form of this vertex which is used in the context of total cross sections at high energies and in the QCD reggeon field theory, there exists an alternative form which has to be used in the study of high-mass diffraction. We review and analyze the relation between these two versions. We discuss some implications for the BK equation. In the second part of our paper we extend this analysis to the pomeron-odderon-odderon vertex.Received: 11 January 2005, Revised: 24 January 2005, Published online: 3 March 2005     

Extended iterative scheme for QCD: three-point vertices

In the framework of a generalized iterative scheme introduced previously to account for the non-analytic coupling dependence associated with the renormalization-group invariant mass scale Λ, we establish the self-consistency equations of the extended Feynman rules (Λ-modified vertices of zeroth perturbative order) for the three-gluon vertex, the two ghost vertices, and the two vertices of massless quarks. Calculations are performed to one-loop-order, in Landau gauge, and at the lowest approximation level (r=1) of interest for QCD. We discuss the phenomenon of compensating poles inherent in these equations, by which the formalism automatically cancels unphysical poles on internal lines, and the role of composite-operator information in the form of equation-of-motion condensate conditions. The observed near decoupling of the four-gluon conditions permits a solution to the 2-and-3-point conditions within an effective one-parameter freedom. There exists a parameter range in which one solution has all vertex coefficients real, as required for a physical solution, and a narrower range in which the transverse-gluon and massless-quark propagators both exhibit complex-conjugate pole pairs. Received: 1 September 1998 / Revised version: 1 December 1998     

Two-loop anomalous dimensions of timelike cut vertices in QCD

The two-loop corrections to the anomalous dimensions of timelike cut vertices in QCD are presented for the non-singlet case. We check that cut vertices are renormalizable to two-loop order.     

Lattice QCD thermodynamic results with improved staggered fermions

We present results on the QCD equation of state, obtained with two different improved dynamical staggered fermion actions and almost physical quark masses. Lattice cut-off effects are discussed in detail as results for three different lattice spacings are available now, i.e. results have been obtained on lattices with temporal extent of N _τ =4,6 and 8. Furthermore we discuss the Taylor expansion approach to non-zero baryon chemical potential and present the isentropic equation of state on lines of constant entropy per baryon number.     

Renormalization group improved perturbative QCD

The results of perturbative QCD calculations are reformulated as renormalization-scheme independent predictions; in so doing, we obtain a renormalization group improvement of perturbation theory. As an application, we show that asymptotic freedom alone does not give the correct quantitative relation between pseudoscalar charmonium decay and the scaling violations in deep inelastic scattering.     

Non-linear QCD dynamics and exclusive production in ep collisions

The exclusive processes in electron–proton (ep) interactions are an important tool to investigate the QCD dynamics at high energies as they are in general driven by the gluon content of proton which is strongly subject to parton saturation effects. In this paper we compute the cross sections for the exclusive vector meson production as well as the deeply virtual Compton scattering (DVCS) relying on the color dipole approach and considering the numerical solution of the Balitsky–Kovchegov equation including running coupling corrections. We show that the small-x evolution given by this evolution equation is able to describe the DESY-HERA data and is relevant for the physics of the exclusive observables in future electron–proton colliders and in photoproduction processes to be measured in coherent interactions at the LHC.     

Non-linear QCD dynamics in two-photon interactions at high energies

Perturbative QCD predicts that the growth of the gluon density at high energies should saturate, forming a Color Glass Condensate (CGC), which is described in mean field approximation by the Balitsky–Kovchegov (BK) equation. In this paper we study the γγ interactions at high energies and estimate the main observables which will be probed at future linear colliders using the color dipole picture. We discuss in detail the dipole–dipole cross section and propose a new relation between this quantity and the dipole scattering amplitude. The total γγ, γ ^? γ ^? cross sections and the real photon structure function $F_{2}^{\gamma }(x,Q^{2})$ are calculated using the recent solution of the BK equation with running coupling constant and the predictions are compared with those obtained using phenomenological models for the dipole–dipole cross section and scattering amplitude. We demonstrate that these models are able to describe the LEP data at high energies, but predict a very different behavior for the observables at higher energies. Therefore we conclude that the study of γγ interactions can be useful to constrain the QCD dynamics.     

Improved evolution equations for QCD

Evolution equations based on probabilistic interpretation of QCD are derived. The main improvement is the inclusion of exact off mass shell kinematics in parton branching, which permits a realistic Monte Carlo simulation of the jet evolution.     

Perturbative chiral violations for domain-wall QCD with improved gauge actions

We investigate, in the framework of perturbation theory at finite Ns$N_s$, the effectiveness of improved gauge actions in suppressing the chiral violations of domain-wall fermions. Our calculations show substantial reductions of the residual mass when it is compared at the same value of the gauge coupling, the largest suppression being obtained when the DBW2 action is used. Similar effects can also be observed for a power-divergent mixing coefficient which is chirally suppressed. No significant reduction instead can be seen in the case of the difference between the vector and axial-vector renormalization constants when improved gauge actions are used in place of the plaquette action. We also find that one-loop perturbation theory is not an adequate tool to carry out comparisons at the same energy scale (of about 2 GeV), and in fact in this case even an enhancement of the chiral violations is frequently obtained.     

2 + 1 flavor simulations of QCD with improved staggered quarks

The MILC Collaboration has been performing realistic simulations of full QCD with 2 + 1 flavors of improved staggered quarks. Our simulations allow for controlled continuum and chiral extrapolations. I present results for the light pseudoscalar sector: masses and decay constants, quark masses and Gasser-Leutwyler low-energy constants. In addition I will present some results for heavy-light mesons, decay constants and semileptonic form factors, obtained in collaboration with the HPQCD and Fermilab lattice Collaborations. Such calculations will help in the extraction of CKM matrix elements from experimental measurements.     

Non-linear superposition in non-linear evolution equations

Special non-linear evolution equations are discussed and classified in integrable and non-integrable partial differential equations. Important methods of solution are sketched. An interesting task is the calculation of the so-called superposition functions permitting to construct from a few known solutions whole chains of further solutions. For integrable partial differential equations they are computed with the help of BÄcklund transformations providing a rather general superposition rule for special types of solutions. At present however a consistent treatment of non-linear evolution equations is only possible in 1 + 1 space and time dimensions. The extension to higher space dimensions brings many problems. An insight into the results and problems in the one-dimensional case is given together with an outlook indicating the conceptual difficulties for a treatment in higher space dimensions.Presented at the International Conference Selected Topics in Quantum Field Theory and Mathematical Physics, Bechyn, Czechoslovakia, June 23–27, 1986.     

Space- and time-like cut vertices in QCD beyond the leading order—The singlet sector

The analytic continuation relation found in the non-singlet structure of the processes e⁺h→e^?X and e^?e⁺→hX up to the next-to-the-leading-logarithm approximation, is shown to be true also for the singlet case. This relation is used to find the two-loop anomalous dimensions for the singlet time-like cut vertices from the anomalous dimension of the singlet space-like cut vertices. We give also the singlet time-like coefficient functions.     

Effective Hamiltonian for QCD evolution at high energy

We construct the effective Hamiltonian which governs the renormalization group flow of the gluon distribution with increasing energy and in the leading logarithmic approximation. This Hamiltonian defines a two-dimensional field theory which involves two types of Wilson lines: longitudinal Wilson lines which describe gluon recombination (or merging) and temporal Wilson lines which account for gluon bremsstrahlung (or splitting). The Hamiltonian is self-dual, i.e., it is invariant under the exchange of the two types of Wilson lines. In the high density regime where one can neglect gluon number fluctuations, the general Hamiltonian reduces to that for the JIMWLK evolution. In the dilute regime where gluon recombination becomes unimportant, it reduces to the dual partner of the JIMWLK Hamiltonian, which describes bremsstrahlung.     

Space-time evolution of bulk QCD matter at RHIC

We introduce a combined fully three-dimensional macroscopic/microscopic transport approach employing relativistic 3D-hydrodynamics for the early, dense, deconfined stage of the reaction and a microscopic non-equilibrium model for the later hadronic stage where the equilibrium assumptions are not valid anymore. Within this approach we study the dynamics of hot, bulk QCD matter, which is being created in ultra-relativistic heavy-ion collisions at RHIC. In particular, we perform a detailed analysis of the reaction dynamics, hadronic freeze-out, transverse flow and elliptic flow. PACS 25.75.-q; 24.10.Nz; 24.10.Lx     

Statistical physics in QCD evolution towards high energies

The concepts and methods used for the study of disordered systems have proven useful in the analysis of the evolution equations of quantum chromodynamics in the high-energy regime: Indeed, parton branching in the semi-classical approximation relevant at high energies and at a fixed impact parameter is a peculiar branching-diffusion process, and parton branching supplemented by saturation effects(such as gluon recombination) is a reaction-diffusion process. In this review article, we first introduce the basic concepts in the context of simple toy models, we study the properties of the latter, and show how the results obtained for the simple models may be taken over to quantum chromodynamics.     

Deconfinement and gluon plasma dynamics in improved holographic QCD

The thermodynamics of 5D dilaton gravity duals to confining gauge theories is analyzed. We show that they exhibit a first order Hawking-Page type phase transition. In the explicit background of improved holographic QCD of [U. Gursoy and E. Kiritsis, J. High Energy Phys. 02 (2008) 03210.1088/1126-6708/2008/02/032] [U. Gursoy, E. Kiritsis, and F. Nitti, J. High Energy Phys. 02 (2008) 01910.1088/1126-6708/2008/02/019], we find T_{c}=235 MeV. The temperature dependence of various thermodynamic quantities such as the pressure, entropy, and speed of sound is calculated. The results are in agreement with the corresponding lattice data.     

Analysis of the vertices DDV and D<Superscript>*</Superscript>DV with light-cone QCD sum rules

In this article, we study the vertices DDV and D^*DV with the light-cone QCD sum rules. The strong coupling constants g_DDV and f_D*DV play an important role in understanding the final-state re-scattering effects in the hadronic B decays. They are related to the basic parameters β and λ respectively in the heavy quark effective Lagrangian; our numerical values are smaller than the existing estimations. PACS 12.38.Lg; 13.20.Fc     

Meson screening masses at high temperature in quenched QCD with improved Wilson Quarks

We report on a lattice investigation of improved quenched Wilson fermions above and below the confinement-deconfinement phase transition. Results on meson screening masses as well as spatial wave functions are presented. Moreover, the meson dispersion relation is studied. Below the critical temperature we do not observe any significant temperature effect while above the data are consistent with a leading free quark behavior. Received: 2 April 2001 / Published online: 8 June 2001