Light-quark and heavy-quark fragmentation functions

We discuss the shape of the leading-fragment momentum distribution function in light- and heavy-quark fragmentation. The features of the u-quark and s-quark leading fragmentation functions extrapolated to higher quark masses lead to the conclusion that as the quark mass increases the average momentum 〈z〉 carried by the heavy meson increases and the fragmentation function becomes narrower. This result fully supports Bjorken's proposal for heavy quark decay. Predictions are given for the shape of the c, b, … quark fragmentation functions.     

Gluon fragmentation functions from quark jets

The analysis of events with a fixed, different from unity, fraction of energy flowing into a solid angle ΔΩ can be used to extract the probability functions related to the scaling violations of deep inelastic scattering. One can obtain from the study of a quark jet, both the gluon and the quark fragmentation functions into hadrons.     

Dynamical connections between quark fragmentation functions

Assuming that the quark kicked by a virtual photon emits pions one by one, integral equations connecting the fragmentation functions D_u^π+ (z) and D_u^π? (z) are obtained. It is shown that they have a plateau the height of which can be determined from the multiplicity difference N_p^π+ (z) ? N_p^π? (z). Comparison with experiment is made.     

Spin structure of baryon fragmentation functions

The valence part of the quark fragmentation function resulting in the octet of baryons together with their spin structure are parametrised, using a model for the hadronisation and the available experimental data on baryon products in e⁺e^? annihilation and μp deep inelastic scattering. Spin correlations are predicted.     

Momentum sum rules for fragmentation functions

Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schäfer–Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.     

Modelling quark distribution and fragmentation functions

The representation of quark distribution and fragmentation functions in terms of non-local operators is combined with a simple spectator model. This allows us to estimate these functions for the nucleon and the pion ensuring correct crossing and support properties. We give estimates for the unpolarized functions as well as for the polarized ones and for subleading (higher twist) functions. Furthermore, we can study several relations that are consequences of Lorentz invariance and of C, P, and T invariance of the strong interactions.     

Charmed-meson fragmentation functions with finite-mass corrections

We elaborate the inclusive production of single heavy-flavored hadrons in e⁺e⁻ annihilation at next-to-leading order in the general-mass variable-flavor-number scheme. In this framework, we determine non-perturbative fragmentation functions for D⁰, D⁺, and D^*+ mesons by fitting experimental data from the Belle, CLEO, ALEPH, and OPAL Collaborations, taking dominant electroweak corrections due to photonic initial-state radiation into account. We assess the significance of finite-mass effects through comparisons with a similar analysis in the zero-mass variable-flavor-number scheme. Under Belle and CLEO experimental conditions, charmed-hadron mass effects on the phase space turn out to be appreciable, while charm-quark mass effects on the partonic matrix elements are less important.     

Medium-modified average multiplicity and multiplicity fluctuations in jets

The energy evolution of average multiplicities and multiplicity fluctuations in jets produced in heavy-ion collisions is investigated from a toy QCD-inspired model. In this model, we use modified splitting functions accounting for medium-enhanced radiation of gluons by a fast parton which propagates through the quark–gluon plasma. The leading contribution of the standard production of soft hadrons is enhanced by a factor while next-to-leading order (NLO) corrections are suppressed by , where the parameter N _s >1 accounts for the induced soft gluons in the medium. Our results for such global observables are cross-checked and compared with their limits in the vacuum.     

Quark and gluon fragmentation functions into photons

The fragmentation functions of quarks and gluons into photons are studied beyond the Leading Logarithm approximation. We address the nature of the initial conditions of the evolution equation solutions and study problems related to factorization scheme invariance. The possibility of measuring these distributions in LEP experiments is discussed, and a comparison with existing data is made. Received: 28 May 1997 / Published online: 20 February 1998     

Dihadron fragmentation functions for large invariant mass

Using perturbative quantum chromodynamics, we compute dihadron fragmentation functions for a large invariant mass of the dihadron pair. The main focus is on the interference fragmentation function H(1)(?), which plays an important role in spin physics of the nucleon. Our calculation also reveals that H(1)(?) and the Collins fragmentation function have closely related underlying dynamics. By considering semi-inclusive deep-inelastic scattering, we further show that collinear factorization in terms of dihadron fragmentation functions and collinear factorization in terms of single-hadron fragmentation functions provide the same result in the region of intermediate invariant mass.     

Next-to-next-to-leading order evolution of non-singlet fragmentation functions

We have investigated the next-to-next-to-leading order (NNLO) corrections to inclusive hadron production in e⁺e⁻$e^{+}{e}^{-}$ annihilation and the related parton fragmentation distributions, the ‘time-like’ counterparts of the ‘space-like’ deep-inelastic structure functions and parton densities. We have re-derived the corresponding second-order coefficient functions in massless perturbative QCD, which so far had been calculated only by one group. Moreover we present, for the first time, the third-order splitting functions governing the NNLO evolution of flavour non-singlet fragmentation distributions. These results have been obtained by two independent methods relating time-like quantities to calculations performed in deep-inelastic scattering. We briefly illustrate the numerical size of the NNLO corrections, and make a prediction for the difference of the yet unknown time-like and space-like splitting functions at the fourth order in the strong coupling constant.     

Test of the universality of naive-time-reversal-odd fragmentation functions

We investigate the "spontaneous" hyperon transverse polarization in e+ e- annihilation and semi-inclusive deep inelastic scattering processes as a test of the universality of the naive-time-reversal-odd transverse momentum dependent fragmentation functions. We find that universality implies definite sign relations among various observables. This provides a unique opportunity to study initial or final state interaction effects in the fragmentation process and test the associated factorization.     

Next-to-leading order fragmentation functions for pions and kaons

We present new sets of fragmentation functions for charged pions and kaons, both at leading and next-to-leading order. They are fitted to TPC data taken at energy =29 GeV and describe excellently a wealth of othere ⁺ e ^– data on charged-hadron production, ranging from =5.2 GeV way up to LEP 1 energy. They also agree with data on the production of neutral pions and kaons, if one makes the natural assumption that the respective fragmentation functions are related to the charged counterparts bySU(2) symmetry. We also list simple parameterizations of thex andQ ² dependence of our results, which may be implemented conveniently in applications.Supported by Bundesministerium für Forschung und Technologie, Bonn, Germany, under Contract 05 6 HH 93P (5), and by EEC ProgramHuman Capital and Mobility through NetworkPhysics at High Energy Colliders under Contract CHRX-CT93-0357 (DG12 COMA)