Strong coupling constant from scaling violations in fragmentation functions

We present a new determination of the strong coupling constant alpha(s) through the scaling violations in the fragmentation functions for charged pions, charged kaons, and protons. In our fit we include the latest e+e- annihilation data from CERN LEP1 and SLAC SLC on the Z-boson resonance and older, yet very precise, data from SLAC PEP at center-of-mass energy sqaure root of s = 29 GeV. At next-to-leading order, we find alpha(s)(5)(M(Z)) = 0.1170+/-0.0073. A new world average of alpha(s) is given.     

On the difference of scaling violations for proton and neutron targets

It is shown that the different Q² dependence for F₁^ep and F₁^ep, as recently observed at SLAC, is compatible with field theoretic expectations.     

Testing QCD scaling violations in the HERA energy range

High energy electron-proton colliders open new kinematical domains for the investigation of scaling violations in nucleon structure functions. Focussing on HERA as a definite study case we explore the precision which can be expected in determinations of the QCD scale parameter Λ and the running coupling constant α _s (Q ²). Our results provide a quantitative basis for discussions of the possibilities and requirements of QCD tests in inclusive deep inelastic scattering at HERA energies.     

Energy conservation and scaling violations in particle production

We use a simple Colour Glass Condensate/String Percolation Model argument to show the existence, due to energy conservation, of bounds to the violation of Feynman scaling and limiting fragmentation.     

On the fragmentation functions of heavy quarks into hadrons

An explicit form for the charmed quark fragmentation function D^C_c(z) into hadrons has been obtained with the help of the “reciprocity relation” and the c-quark distribution function in charmed mesons (the function calculated in terms of the Kuti-Weisskopf model). D^C_c(z) turns out to peak mainly at z close to 1. The analysis of new data on muon pair production in neutrino reactions points to such a behaviour of the D^C_c(z) function. The obtained fragmentation function, contrary to those, used earlier, leads to a charmed particle (average) multiplicity in e⁺e^?-annihilation independent of energy.     

On the next-to-next-to-leading order evolution of flavour-singlet fragmentation functions

We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon- and Higgs-exchange structure functions in deep-inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions.     

Subleading long-range interactions and violations of finite size scaling

We study the behavior of systems in which the interaction contains a long-range component that does not dominate the critical behavior. Such a component is exemplified by the van der Waals force between molecules in a simple liquid-vapor system. In the context of the mean spherical model with periodic boundary conditions we are able to identify, for temperatures close above T _c, finite-size contributions due to the subleading term in the interaction that are dominant in this region decaying algebraically as a function of L. This mechanism goes beyond the standard formulation of the finite-size scaling but is to be expected in real physical systems. We also discuss other ways in which critical point behavior is modified that are of relevance for analysis of Monte Carlo simulations of such systems. Received 21 November 2000 and Received in final form 28 February 2001     

On the origin of approximate KNO scaling ine + e − annihilation

KNO scaling of the multiplicity distribution in hadronic final states was originally derived as a consequence of Feynman scaling. We show that in iterative models of hadron production in jets, incorporating Feynman scaling, KNO scaling obtains only in the limit when the width of the multiplicity distribution tends to zero. Within the context of the models currently employed to describee ⁺ e ^? annihilation into hadrons, the apparent KNO scaling observed is an accidental consequence of effects which violate Feynman scaling.     

Where is the origin of CP violations?

If experimentally b → c is more suppressed than b → u, the Kobayashi-Maskawa mechanism of CP violation may not work. In the SU (2) × U(1) × S₃ model, which gives all elements of the KM matrix naturally by the quark masses, this is the case and CP violations originate mainly from the Yukawa sector.     

Detailed description of the violations of Bjorken scaling in QCD (including higher-order corrections)

We present a compendium of formulae and parameters required to study the violations of Bjorken scaling, up to and including the subleading (i.e. O(α_S)) corrections.     

Perturbative vs. non-perturbative scaling violation in quark fragmentation

We investigate the approach to scaling for non-perturbative quark fragmentation in the frame-work of the uncorrelated jet model. It is found that subasymptotic kinematic scale breaking is comparable in size to scaling violations from hard gluon emission a la QCD. Experimental data available at present do allow for such non-perturbative scale breaking effects.     

Singular scaling functions in clustering phenomena

We study clustering in a stochastic system of particles sliding down a fluctuating surface in one and two dimensions. In steady state, the density-density correlation function is a scaling function of separation and system size. This scaling function is singular for small argument — it exhibits a cusp singularity for particles with mutual exclusion, and a divergence for noninteracting particles. The steady state is characterized by giant fluctuations which do not damp down in the thermodynamic limit. The autocorrelation function is a singular scaling function of time and system size. The scaling properties are surprisingly similar to those for particles moving in a quenched disordered environment that results if the surface is frozen.     

Correlation functions of descendants in the scaling Lee-Yang model

Correlation functions of the composite field \(T\bar T\) in the scaling Lee-Yang model are studied. Using the analytic expression for form factors of this operator recently proposed by Delfino and Niccoli hep-th/0407142 [1], we show numerically that the constraints on the \(T\bar T\) expectation values obtained by Zamolodchikov hep-th/0401146