Particle flow in a jet

The angular distribution of hadrons in a jet is evaluated in perturbative QCD. The predictions are restrictive in the sense they do no depend on the details of the non-perturbative process. The distribution depends on only one phenomenologically adjustable parameter, a cutoff massQ ₀ (in addition to the universal QCD mass-scale ). The fit of the leading order prediction to the TASSO data is obtained withQ ₀270 MeV.The low value ofQ ₀ supports the hypothesis of local partonhadron duality. The particle flow in a gluon jet is also analysed.     

Corrections to angular ordering in multiple hadroproduction

One of the key ideas in describing the multiparticle production at high energies in the perturbative QCD is the angular ordering in successive soft-gluon emission. We analyse the angular distribution of particles in a jet, and investigate the corrections to the angular ordering. At a small angle from the jet direction, the angular ordering is exact at the next-to-leading order. At a large angle, the angular ordering overestimates the angular particle density by a factor (1?γln cos²(γ/2)), whereγ is the anomalous dimension of the multiplicity. TheO(γ) correction restores the boost invariance of the cross section.     

Rapidity distribution ine + e − annihilation

A method to systematically calculate the rapidity distribution of hadrons in a high-energy jet is formulated in terms of an integral equation for the multiplicity. The distribution has the following properties at high energies: (i) a translational invariance; (ii) an increasingly steep distribution with a width proportional to \(\sqrt {\ln s} \) , but without a widening “central plateau”; (iii) if the rapidity is scaled by \(\sqrt {\ln s} \) , it approaches to a universal exponential curve. In the large rapidity region, however, the translational invariance is broken because of the recoil of the quark by the emission of soft gluons. It is also discussed that a gluon jet has a wider angular distribution.     

Short-distance dominance in the elastic form factors of hadrons

The renormalization group analysis is applied to the high-energy behavior of the pion form factor in QCD. The anomalous dimension of the form factor is directly related to the short-distance behavior of the Bethe-Salpeter wave function with suitable choice of normalization. Absence of infrared singularities and short-distance dominance are proven by the use of a power counting argument in the axial gauge. The relation between our method and the “factorization” method is clarified. The applicability of our method to other elastic form factors is discussed.     

Thrust ine + e −-annihilation

The thrust distribution ine ⁺ e ^–-annihilation is analysed in perturbative QCD. Proper account is taken of multiple emission of gluons. Scaling holds for this quantity in the sense that its energy dependence comes only through the change in the QCD effective coupling. It thus provides an ideal means to determine the value of the QCD mass scale experimentally. From the data atW=91 GeV by the ALEPH collaboration at LEP, we obtain .     

Multiplicity with a thrust cut

We evaluate the multiplicity of hadrons in thee ⁺ e ^–-annihilation at a given thrustT in the modified leading-log approximation, including corrections. The calculation is done at a large value of =1–T by the use of the factorisation which takes place in the one-particle-inclusive cross section at a given . At a small , a different type of factorisation takes place, which also enable us to evaluate the multiplicity. Two approaches are compared numerically. Measuring this quantity near =1/3, we can determine the multiplicity ratio between a gluon-jet and a quark-jet.     

Recoil effect on multiplicity correlation

The kinematical constraint due to energymomentum conservation reduces the multiplicity correlation ine ⁺ e ^–-annihilation (recoil effect). The correction starts at the second order in the expansion in powers of [i.e.O(_s)]. TheO(_s) correction to the squared dispersionr ₂ of the scaled multiplicity distribution is evaluated. It is found so large that the truncated expansion is inadequate at current energies. An evaluation without the expansion gives a reduced correction, with which the prediction remains positive down to low energies. The recoil effect makes the prediction closer to the experimental data.     

Resummed multiplicity moments

The multiplicity distribution of hadrons in a jet is reanalysed. The \(\mathcal{O}(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} )\) correction to the double-log summation is so large that its addition makes the value of the multiplicity moments unphysical at the current energies ofe ⁺ e ^? annihilation. This implies the necessity of systematic resummation of the whole series in powers of \(1/\sqrt {\ln (W^2 /\Lambda _{QCD}^2 )} \) . In this article we perform this resummation. In fact, a formal exact solution of the integral equation, which gives recursion relations among the multiplicity moments, takes the form of a geometric series. The resummation reduces the correction substantially.