Multifractal dimensions in QCD cascades

Particle production in small rapidity or angular intervals have fractal structures similar to a Cantor dust. In this paper we present analytical result for multifractal dimensions valid for high energies. For high moments the dimension is given by \(\sqrt {6\alpha _s /\pi } \) . The scaling properties seen in the partonic state are not so well reflected in the hadronic multiplicity moments or factorial moments. We show how to define new observables on the final hadronic state, which do scale well. This means that the multifractal dimensions can be well determined and compared with results from QCD.     

Gluonic regge singularities and anomalous dimensions in QCD

The Regge calculus results on the perturbative pomeron are applied to deep inelastic scattering. Explicit expressions are given for the anomalous dimensions γ_GGⁿ and γ_GFⁿ at n ? 1 to the lowest order in α and all orders in α/(n ? 1).     

Three-loop anomalous dimensions for squarks in supersymmetric QCD

In this Letter we evaluate the renormalization constants and anomalous dimensions for the squark wave function and mass within supersymmetric QCD. These results complement the ones obtained in Harlander et al. (2009) [1] and thus provide further confirmation on the applicability of dimensional reduction to supersymmetric QCD at three-loop order. The three-loop anomalous dimension constitute important input to precision predictions of the supersymmetric mass spectrum as obtained from the evolution from the GUT to the TeV energy scale.     

Broken conformal invariance and spectrum of anomalous dimensions in QCD

Employing the operator algebra of the conformal group and the conformal Ward identities, we derive the constraints for the anomalies of dilatation and special conformal transformations of the local twist-2 operators in Quantum Chromodynamics. We calculate these anomalies in the leading order of perturbation theory in the minimal subtraction scheme. From the conformal consistency relation we derive then the off-diagonal part of the anomalous dimension matrix of the conformally covariant operators in the two-loop approximation of the coupling constant in terms of these quantities. We deduce corresponding off-diagonal parts of the Efremov-Radyushkin-Brodsky-Lepage kernels responsible for the evolution of the exclusive distribution amplitudes and non-forward parton distributions in the next-to-leading order in the flavour singlet channel for the chiral-even parity-odd and -even sectors as well as for the chiral-odd one. We also give the analytical solution of the corresponding evolution equations exploiting the conformal partial wave expansion.     

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.     

Color decoherence in in-medium QCD cascades

The talk, based on [1], analyzes the consequences of the combined effect of the consequences of the assumption that the effects of quantum coherence and the resulting angular ordering in QCD cascades are disrupted within the finite-sized hot fireball created in ultrarelativistic heavy ion collisions and of the collisional energy losses of the cascade gluons and final hadronic clusters.     

Dipole formulation of QCD cascades

The formulation of a QCD parton cascade in terms of colour dipoles or colour antennae is applied to e⁺e⁻-annihilation. In this formulation the destructive interference for soft-gluon emission has a very natural interpretation, and it is easy to construct a Monte Carlo simulation program. At PEP and PETRA energies the results agree very well with experimental data, and thus also with results from conventional parton cascades. However, at higher energies observable differences emerge, which can discriminate between the models.     

Fluctuations and the QCD phase diagram

In this contribution the role of quantum fluctuations for the QCD phase diagram is discussed. This concerns in particular the importance of the matter back-reaction to the gluonic sector. The impact of these fluctuations on the location of the confinement/deconfinement and the chiral transition lines as well as their interrelation are investigated. Consequences of our findings for the size of a possible quarkyonic phase and location of a critical endpoint in the phase diagram are drawn.     

Phenomenological irrelevance of coherence effects in QCD cascades

A quantitative assessment is presented of the actual possibility of detecting soft gluon interference effects in experimental studies of jets. It is found that the effects are too small to be appreciated in calorimetric data, and that in general their magnitude is well within the uncertainties associated with the choice of the parton mass cutoff, needed in perturbative calculations.     

Decoherence and energy loss in QCD cascades in nuclear collisions

The paper analyzes the consequences of the assumption that the effects of quantum coherence and the resulting angular ordering in QCD cascades are disrupted within the hot fireball created in ultrarelativistic heavy ion collisions. The effects of decoherence are taken into account by switching off angular ordering for the vertices of MC-generated cascade that lie within the fireball of some given size. We show that decoherence exerts a pronounced influence on the spatiotemporal pattern of a cascade. Related effects due to non-radiative losses of cascade gluons and those of final prehadrons are discussed. We show that decoherence leads to a substantial increase in the yield of cascade particles hadronizing inside the hot zone thus exerting a strong influence on the properties of final hadrons and amplifying the effects of collisional energy losses of cascade partons and final prehadrons that take place inside the fireball.     

Nucleon resonances and anomalous dimensions

It is studied whether duality analogous to that of Bloom and Gilman holds in the case in which the non-canonical scaling proves to be true. The data show that such duality holds well, independently of Q².     

Consistent massive anomalous dimensions

We re-evaluate the O(g²) momentum-subtracted anomalous dimensions of QCD with massive quarks. The QCD equations of motion are used to relate operator matrix elements with different tensor structures. This procedure yields explicitly gauge-invariant anomalous dimensions. Our results differ slightly from those in the literature. The forward Compton amplitude for scattering of massive quarks and a scalar current is examined. The large Q² behavior of this amplitude is shown to be simply related to the momentum-subtracted, mass-dependent anomalous dimension.     

Fluctuations of Goldstone modes and the chiral transition in QCD

We provide evidence for the influence of thermal fluctuations of Goldstone modes on the chiral condensate at finite temperature. We show that at fixed temperature, T<T_c, in the vicinity of the chiral transition temperature this leads to a characteristic dependence of the chiral condensate on the square root of the light quark mass (m_l), which is expected for 3-dimensional models with broken O(N) symmetry. As a consequence the chiral susceptibility shows a strong quark mass dependence for all temperatures below T<T_c and diverges like in the chiral limit.     

Warm cascades and anomalous scaling in a diffusion model of turbulence

A phenomenological turbulence model in which the energy spectrum obeys a nonlinear diffusion equation is analyzed. The general steady state contains a nonlinear mixture of the constant-flux Kolmogorov and fluxless thermodynamic components. Such "warm cascade" solutions describe a bottleneck phenomenon of spectrum stagnation near the dissipative scale. Transient self-similar solutions describing a finite-time formation of steady cascades are analyzed and found to exhibit nontrivial scaling behavior.     

Solutions of anomalous Ward identities in a QCD framework

The anomalous Ward identities are solved in the framework of QCD. An important outcome of this calculation is the possibility of an extremely small width for ι→γγ decay mode.     

Leading logarithms in the anomalous sector of two-flavour QCD

We add the Wess–Zumino–Witten term to the N=3$N=3$ massive nonlinear sigma model and study the leading logarithms in the anomalous sector. We obtain the leading logarithms to six loops for π⁰→γ^?γ^?${\pi }^0\to {\gamma }^{?}{\gamma }^{?}$ and to five loops for γ^?πππ${\gamma }^{?}\pi \pi \pi$. In addition we extend the earlier work on the mass and decay constant to six loops and the vector form factor to five loops. We present numerical results for the anomalous processes and the vector form factor. In all cases the series are found to converge rapidly.     

Scaling exponents and multifractal dimensions for independent random cascades

This paper is concerned with Mandelbrot's stochastic cascade measures. The problems of (i) scaling exponents of structure functions of the measure, (q), and (ii) multifractal dimensions are considered for cascades with a generator vector (w ₁...w _c) of the general type. These problems were previously studied for independent strongly bounded variablesw _i: 0<a _ic. Consequently, a broad class of models used in applications, including Kolmogorov's long-normal model in turbulence, long-stable universal cascades in atmospheric dynamics, has not been covered. Roughly speaking, problems (i), (ii) are here solved under the condition that the scaling exists; the -function is calculated for all arguments (previously this was done for positiveq) and a new effect emerges: the -function can generally involve discontinuities in the first derivative as well as in the second.