Parton-hadron Duality Research Articles

Can multiparticle correlations be described by present analytical QCD calculations?

Previous experimental studies of various correlation functions in angular intervals and their comparison with QCD calculations are summarized. A good description is only obtained for a globally normalized function ( r ). The hypothesis of Local Parton Hadron Duality (LPHD) seems to be well fulfilled in this case. For all differentially normalized functions, however, several disagreements are observed and the validity of LPHD is in question. It is argued (using Monte Carlo calculations) that LPHD could still be valid also in this case — after improving the perturbative QCD calculations. Only after the inclusion of full energy-momentum conservation in the calculations one will have a better handle to estimate, how far non-perturbative effects are spoiling the agreement with the data.

Evidence of color coherence effects in W+jets events from [formula omitted] collisions at [formula omitted] TeV

We report the results of a study of color coherence effects in p p collisions based on data collected by the DØ detector during the 1994–1995 run of the Fermilab Tevatron Collider, at a center of mass energy s =1.8 TeV. Initial-to-final state color interference effects are observed by examining particle distribution patterns in events with a W boson and at least one jet. The data are compared to Monte Carlo simulations with different color coherence implementations and to an analytic modified-leading-logarithm perturbative calculation based on the local parton-hadron duality hypothesis.

Multiplicity fluctuations in one- and two-dimensional angular intervals compared with analytic QCD calculations

Multiplicity fluctuations in rings around the jet axis and in off-axis cones have been measured by the DELPHI collaboration in e + e − annihilations into hadrons at LEP energies. The measurements are compared with analytical perturbative QCD calculations for the corresponding multiparton system, using the concept of Local Parton Hadron Duality. Some qualitative features are confirmed by the data but substantial quantitative deviations are observed.

Energy dependence of inclusive spectra in e+e− annihilation

Inclusive charged hadron distributions as obtained from the DELPHI measurements at 130, 136, 161, 172 and 183 GeV are presented as a function of the variables rapidity, ξp, p and transversal momenta. Data are compared with event generators and with MLLA calculations, in order to examine the hypothesis of local parton hadron duality. The differential momentum spectra show an indication for coherence effects in the production of soft particles. The relation between the energy dependence of the charged multiplicity and the rapidity distribution is examined.

ϒ photoproduction at HERA compared to estimates of perturbative QCD

We estimate the cross section for γp→ ϒp by two independent methods. First, by studying the corrections to the naive leading-order QCD formula and, second, by using parton-hadron duality. The estimates are in good agreement with each other and with the recent measurements of the cross section at HERA.

Production ofπ+,K+,K0,K*0,φ,pandΛ0in hadronicZ0decays

We have measured the differential production cross sections as a function of scaled momentum x_p=2p/E_cm of the identified hadron species pi+, K+, K0, K*0, phi, p, Lambda0, and of the corresponding antihadron species in inclusive hadronic Z0 decays, as well as separately for Z0 decays into light (u, d, s), c and b flavors. Clear flavor dependences are observed, consistent with expectations based upon previously measured production and decay properties of heavy hadrons. These results were used to test the QCD predictions of Gribov and Lipatov, the predictions of QCD in the Modified Leading Logarithm Approximation with the ansatz of Local Parton-Hadron Duality, and the predictions of three fragmentation models. Ratios of production of different hadron species were also measured as a function of x_p and were used to study the suppression of strange meson, strange and non-strange baryon, and vector meson production in the jet fragmentation process. The light-flavor results provide improved tests of the above predictions, as they remove the contribution of heavy hadron production and decay from that of the rest of the fragmentation process. In addition we have compared hadron and antihadron production as a function of x_p in light quark (as opposed to antiquark) jets. Differences are observed at high x_p, providing direct evidence that higher-momentum hadrons are more likely to contain a primary quark or antiquark. The differences for pseudoscalar and vector kaons provide new measurements of strangeness suppression for high-x_p fragmentation products.

Momentum spectra in the current region of the Breit frame in deep inelastic scattering at HERA

The production of charged particles has been measured in deep inelastic scattering with the ZEUS detector. The evolution of the moments of the scaled momenta distributions in Q2 and x has been investigated in the current fragmentation region of the Breit frame. The results in the current region are compared to e+e- data and QCD analytical calculations. The results are consistent with the universality of single-particle spectra in DIS and e+e- annihilation at high Q2. The results at low Q2 disagree with analytical calculations based on the modified leading log approximation and local parton hadron duality.

Perturbative QCD description of mean jet and particle multiplicities in e+e− annihilation

A complete numerical solution of the evolution equation for parton multiplicities in quark and gluon jets with initial conditions at threshold is presented. Data on both hadron and jet multiplicities in e + e − annihilation are well described with a common normalization, giving further support to the picture of Local Parton Hadron Duality. Predictions for LEP-II energies are presented. Furthermore we study the sensitivity to the cutoff parameter Q 0 and the scale of α s .

Perturbative QCD description of multiparticle correlations in quark and gluon jets

The QCD evolution equations in Modified Leading Log Approximation for the factorial moments of the multiplicity distribution in quark and gluon jets are numerically solved with initial conditions at threshold by fully taking into account the energy conservation law. After applying Local Parton Hadron Duality as hadronization prescription, a consistent quantitative description of available experimental data for factorial cumulants and factorial moments of arbitrary order and for their ratio both in quark and gluon jets and in e + e − annihilation is achieved.

$\pi^{\pm}$ , ${\rm K}^{\pm}$ , p and $\overline p$ production in ${\rm Z}^0 \rightarrow q\overline{q}$ , ${\rm Z}^0 \rightarrow b\overline{b}$ , ${\rm Z}^0 \rightarrow u\overlineu$ , $d\overline{d}$ , $s\overline{s}$

The DELPHI experiment at LEP uses Ring Imaging Cherenkov detectors for particle identification. The good understanding of the RICH detectors allows the identification of charged pions, kaons and protons, covering the full momentum range from $0.7 < p < 45.6$ GeV/c. The $\pi^{\pm}$ , ${\rm K}^{\pm}$ , p and $\overline{\rm p}$ normalised production rates, their differential cross sections, multiplicities and the maxima $\xi_{p}^{*}$ of the $\xi_{p}=\ln(1/X_{p})$ distributions are measured for three event samples ${\rm Z}^0 \rightarrow q\overline{q}$ , ${\rm Z}^0 \rightarrow b\overline{b}$ , ${\rm Z}^0 \rightarrow u\overlineu$ , $d\overline{d}$ , $s\overline{s}$ , selected from $\sim 1\,400\,000\,\rm Z^{0}$ decays collected by DELPHI in 1994. The results are compared to the predictions of the JETSET string fragmentation model and the HERWIG cluster fragmentation model. The Modified Leading Logarithm Approximation with Local Parton-Hadron Duality is tested. The $\xi_{p}^{*}$ dependence on the primary quark flavour is investigated and quantified for the different particle distributions. The $\pi^{\pm}$ , ${\rm K}^{\pm}$ , p and $\overline{\rm p}$ multiplicities are measured with precisions from $\pm4$ % to $\pm6$ %. For the ${\rm Z}^0 \rightarrow q\overline{q}$ , and ${\rm Z}^0 \rightarrow b\overline{b}$ , event samples, these improve on previous measurements. The $\pi^{\pm}$ , ${\rm K}^{\pm}$ , p and $\overline{\rm p}$ multiplicities for ${\rm Z}^0 \rightarrow u\overlineu$ , $d\overline{d}$ , $s\overline{s}$ are presented for the first time.

Perturbative universality in soft particle production b

The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (“fan invariance”). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in e+e− annihilation and di-jet production events in γp, γγ and \(p\bar p\) collisions. They are based upon the difference in the intensity of the soft radiation from primary \(q\bar q\) and gg antennae.

Erratum: Parton-hadron duality in QCD sum rules: Quantum-mechanical examples [Phys. Rev. D57, 2676 (1998)

Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use the simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in two-point sum rules works fine, the duality in three-point sum rules may be 100%- violated, leading to completely unreliable predictions for the matrix elements in question. The implications for three-point QCD sum rules are discussed. A new estimate for the parameter $\lambda_1$ of HQET is given.

Low and high energy limits of particle spectra in QCD jets

Charged particle energy spectra in e+e- annihilation are compared with the analytical predictions from the QCD evolution equation in the Modified Leading Log Approximation. With the nonperturbative initial condition shifted down to threshold as suggested by the Local Parton Hadron Duality picture a good description of the data from the lowest up to highest available energies results. The two essential parameters in this approach are determined from a moment analysis. The sensitivity of the fit to the running of alpha_s and to the number of active flavours (including a light gluino) is demonstrated. For very high energies the theory predicts a scaling behaviour in certain rescaled variables (``zeta-scaling''). The data show an approximate behaviour of this type in the present energy range and come close to the predicted asymptotic scaling function for the small particle energies.

Exclusive ${f_2}$ leptoproduction via the odderon exchange

Cross sections of high energy semielastic $\gamma^*p\to f_2p$ leptoproduction of $f_2(1270)$ or $\eta(548)$ mesons as well as the $\gamma p\to f_2+M^2_D$ photoproduction at large $t$ are estimated in the framework of perturbative QCD using the hypothesis of parton-hadron duality.

Parton-hadron duality in QCD sum rules: Quantum-mechanical examples

Motivated by recent work on three-point QCD sum rules in heavy quark physics, we use simple quantum mechanical models to study the basic issue of duality in three-point sum rules. We show that while in all of these models the duality in two-point sum rules works fine, the duality in three-point sum rules may be 100% violated, leading to completely unreliable predictions for the matrix elements in question. The implications for three-point QCD sum rules are discussed. A new estimate for the parameter ${\mathrm{\ensuremath{\lambda}}}_{1}$ of HQET is given.

Perturbative universality in soft particle production b

The spectrum of partons in a QCD jet becomes independent of the primary energy in the low momentum limit. This follows within the perturbative QCD from the colour coherence in soft gluon branching. Remarkably, the hadrons follow such behaviour closely, suggesting the parton hadron duality picture to be appropriate also for the low momentum particles. More generally, this scaling property holds for particles of low transverse and arbitrary longitudinal momentum, which explains an old experimental observation (``fan invariance''). Further tests of the perturbatively based picture for soft particle production are proposed for three-jet events in e+e- annihilation and di-jet production events in gamma p, gamma-gamma and p\bar p collisions. They are based upon the difference in the intensity of the soft radiation from primary q\bar q and gg antennae.

Diffractive electroproduction ofρmeson excitations

We use perturbative QCD and parton-hadron duality to estimate the cross sections for the diffractive electroproduction of rhoprime(1-) and rho(3-) resonances which occur in the 1.3-1.8 GeV mass interval. We present the cross sections and the ratios sigma_L/sigma_T as a function of Q^2. We compare the predictions with those for the diffractive electroproduction of rho mesons. We show how such diffractive electroproduction measurements at HERA can probe features of the perturbative QCD 'Pomeron'.

Perturbative-QCD Approach to Multiparticle Production

In this review we discuss the analytical perturbative approach, based on perturbative QCD and local parton hadron duality (LPHD), and its application to multiparticle production in jets in the semisoft region. Analytical formulae are presented for various observables within the accuracy of the modified leading logarithmic approximation (MLLA), i.e. with terms of relative order [Formula: see text] taken into account systematically, and in some cases with even higher accuracy. These predictions are confronted with existing experimental data. Many details of the perturbative approach to multiple hadroproduction have been consolidated in recent years, and the overall picture is remarkably healthy. The prospects of future studies of the semisoft jet physics are also discussed.

QCD description of diffractiveρmeson electroproduction

We critically review the QCD predictions for the cross sections sigma_L and sigma_T for diffractive rho meson electroproduction in longitudinally and transversely polarised states in the HERA energy region. We show that both perturbative and non-perturbative approaches which involve convolution with the rho meson wave function predict values of sigma_T which fall-off too quickly with increasing Q^2, in comparison with the data. We present a perturbative QCD model based on the open production of light qqbar pairs and parton-hadron duality, which describes all features of the data for rho electroproduction at high Q^2 and, in particular, predicts a satisfactory Q^2 behaviour of sigma_L/sigma_T. We find that precise measurements of the latter can give valuable information on the Q^2 behaviour of the gluon distribution at small x.

Perturbative description of inclusive energy spectra

The recent LEP-1.5 data on charged particle inclusive energy spectra are analyzed within the analytical QCD approach based on Modified Leading Log Approximation plus Local Parton Hadron Duality. The shape, the position of the maximum and the cumulants moments of the inclusive energy spectrum are well described within this model. The sensitivity of the results to the running of the coupling is pointed out. A scaling law for the one-particle invariant density $E dn/d^3p$ at small momenta is observed, consistently with the predictions of colour coherence in soft gluon bremsstrahlung.