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.     

Solution of non-singlet DGLAP evolution equation in leading order and next to leading order at small-x

The non-singlet structure functions have been obtained by solving Dokshitzer, Gribove, Lipatov, Alterelli, Parisi (DGLAP) evolution equations in leading order (LO) and next to leading order (NLO) at the small x limit. Here a Taylor Series expansion has been used and then the method of characteristics has been used to solve the evolution equations. We have also calculated t and x-evolutions of deuteron structure function and the results are compared with the New Muon Collaboration (NMC) and E665 data.     

Next-to-next-to-leading order Higgs production at Hadron Colliders

The Higgs-boson production cross section at pp and pp colliders is calculated in QCD at next-to-next-to-leading order (NNLO). We find that the perturbative expansion of the production cross section is well behaved and that scale dependence is reduced relative to the NLO result. These findings give us confidence in the reliability of the prediction. We also report an error in the NNLO correction to Drell-Yan production.     

QCD analysis of non-singlet neutrino structure functions

We present a systematic analysis of all available neutrinoxF ₃ data, using an analytic parametrisation which incorporates second order QCD predictions forQ ² evolution. We find $$\Lambda _{\overline {MS} } = 0.30 \pm 0.13{\rm{ }}GeV$$ where the error is statistical, and both Fermi andW-boson propagator corrections have been made to the data. Neglect of the former has negligible effects, but neglect of the latter would increase Λ by ～0.1 GeV. We find that higher-twist effects are small and negative, and estimate their effect on the determination of Λ. We are unable to fit the data with higher-twist terms alone.     

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)     

QCD analysis of non-singlet electromagnetic structure functions

A direct analysis of all data on the nonsinglet combination of electromagnetic structure functionsF ₂ ^p ?F ₂ ⁿ is shown to yield a value of the QCD scale-breaking parameter \(\Lambda _{\overline {{\rm M}S} } = 0.36 \pm 0.16\) Gev, in good agreement with that obtained from non-singlet neutrino data. The ratiod _v /u _v , extracted using the results of a previous neutrino analysis, shows an excess of up-quarks to down-quarks of about a factor of five at largex.     

Next-to-next-to-leading order corrections to three-jet observables in electron-positron annihilation

I report on a numerical program, which can be used to calculate any infrared safe three-jet observable in electron-positron annihilation to next-to-next-to-leading order in the strong coupling constant alpha(s). The results are compared to a recent calculation by another group. Numerical differences in three color factors are discussed and explained.     

Processes involving fragmentation functions beyond the leading order in QCD

We point out that the electron propagator, calculated from a truncated Johnson-Baker-Willey equation, suffers from the following defects: lack of renormalizability gauge dependence of the electron electromagnetic mass, as well as unacceptable analytic structure.     

Evolution of parton densities beyond leading order: The non-singlet case

We develop a technique, based explicitly on the factorization properties of mass singularities, which allows one to calculate the evolution of parton densities beyond leading order. We present the results for the evolution of hadronic structure functions as well as for parton fragmentation functions into hadrons. Within our scheme the predictions for a particular process are obtained by convoluting a universal parton density with a “short-distance” cross section specific to the process. As an application, we calculate the QCD predictions for the Q² dependence of deep inelastic lepton-hadron scattering and of one-particle iclusive e⁺ e^? annihilation cross sections. Our results for electroproduction agree with those obtained with the operator product expansion technique. Physical quantities in scattering are related to the corresponding ones in annihilation by analytic continuation, whereas the Gribov-Lipatov relation is strongly violated.     

Modified DGLAP evolution for fragmentation functions in nuclei and QGP

Within the framework of generalized factorization of higher-twist contributions, including modification to splitting functions of both quark and gluon, we get and numerically resolve the medium-modified DGLAP (mDGLAP) evolution equations. With Woods-Saxon nuclear geometry and Hirano 3D ideal hydrodynamic simulations of hot medium, we study the medium modified fragmentation functions (mFF) in DIS and Au+Au collisions in RHIC. Our calculations imply that the parton density in the hot medium produced in RHIC is about 30 times larger than in a cold nucleus.     

Generalizing the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of fragmentation functions to the smallest values

An approach valid to any order which unifies the fixed order Dokshitzer-Gribov-Lipatov-Altarelli-Parisi evolution of fragmentation functions at large x with soft gluon logarithmic resummation at small x is proposed. At lowest order, this approach, implemented with the double logarithmic approximation, reproduces exactly the modified leading logarithm approximation but is more complete due to the degrees of freedom given to the quark sector and the inclusion of the fixed order terms. We find that data from the largest x values to the peak region can be better fitted than with other approaches.     

An analysis of non-singlet structure function in next-to-next-to-leading order at small-x

A more general form of non-singlet structure function in Next-to-Next-to-leading order (NNLO) by solving Dokshitzer, Gribov, Lipatov, Altarelli, Parisi (DGLAP) equation at small-x is obtained. Results are compared with Fermi Lab Experiment E665 data.     

(Medium-modified) fragmentation functions

We discuss some of the recent advances in the field of parton fragmentation processes into hadrons as well as their possible modifications in QCD media. Hadron-production data in e ⁺ e ⁻, deep inelastic scattering and hadronic collisions are presented, together with global analyses of fragmentation functions into light and heavy hadrons and developments on parton fragmentation in perturbative QCD at small momentum fraction. Motivated by the recent RHIC data indicating a significant suppression of large-p _⊥ hadron production in heavy-ion collisions, several recent attempts to model medium-modified fragmentation, e.g. by solving “medium” evolution equations or through Monte Carlo studies, have been proposed and are discussed in detail. Finally, we mention the possibility to extract medium-modified fragmentation functions using photon–hadron correlations.     

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.     

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.     

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.