arXiv subjects
Publications and source records attributed to Sergio Lupia.
Scenarios for particle production in the GeV and TeV regions are reviewed. The expected increase with c.m. energy of the average number of clans for the soft component and the decrease for the semihard one indicate possible classical and quantum behaviour of gluons, respectively. Clan thermodynamics, discussed in the paper, appears as the natural framework to deal with such phenomena.
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.
The complete QCD evolution equation for factorial moments in quark and gluon jets is numerically solved with initial conditions at threshold by fully taking into account the energy-momentum conservation law. Within the picture of Local Parton Hadron Duality, the perturbative QCD predictions can successfully describe the available experimental data.
It is shown that the gluons produced with small transverse momenta $k_\perp$ inside a jet ($k_\perp <k_\perp^{cut}$, $k_\perp^{cut} \to 0$) are independently emitted from the primary parton, as QCD coherence suppresses their showering. Consequently, the low $k_{\perp}$ gluons follow a Poisson distribution, very much like the soft photons radiated by a charged particle in QED. On the contrary, the distribution of gluons with limited absolute momenta $|\vec{k} | <k^{cut}$ remains non-Poissonian even for small $k^{cut}$. It will be interesting to find out to what extent this perturbative prediction for partons survives the hadronization process.
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.
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 alpha_s.
Recently exact numerical results from the evolution equation for parton multiplicities in QCD jets have been obtained. A comparison with various approximate results is presented. A good description is obtained not only of the jet multiplicities measured at LEP-1 but also of the hadron multiplicities for $cms$ energies above 1.6 GeV in \epem annihilation. The solution suggests that a final state hadron can be represented by a jet in the limit of small (nonperturbative) $k_\perp$ cut-off $Q_0$. In this description using as adjustable parameters only the QCD scale $Λ$ and the cut-off $Q_0$, the coupling $α_s$ can be seen to rise towards large values above unity at low energies.
The evolution equation for parton multiplicities in quark and gluon jets which takes into account the soft gluon interference is solved numerically using the initial conditions at threshold. If the k_T-cutoff Q_c is lowered towards the hadronic scale Q_0 of a few hundred MeV, the jets are fully resolved into hadrons. Both hadron and jet multiplicities in e+e- annihilation are well described with a common normalization. Evidence is presented within this perturbative approach that the coupling α_s(k_T) rises by an order of magnitude when approaching the low energy region. The ratio of hadron multiplicities in gluon and quark jets is found smaller than in previous approximate solutions of the evolution equation.
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.
We show, via a simple parametrization of the multiplicity distribution of charged particles in e(+)e(-) annihilation at the Z0 peak in terms of the weighted superposition of two negative binomial distributions, that both the shoulder structure in the intermediate multiplicity range and the oscillation in sign of the ratio of factorial cumulants over factorial moments of increasing order are related to hard gluon radiation.
We show that both the multiplicity distribution and the ratio of factorial cumulants over factorial moments for 2-jet events in e+e- annihilation at the Z^0 peak can be well reproduced by the weighted superposition of two negative binomial distributions, associated to the contribution of $b\bar b$ and light flavoured events respectively. The negative binomial distribution is then suggested to describe the multiplicity distribution of 2-jet events with fixed flavour.
The shoulder structure of charged particles multiplicity distributions (MD's) in full phase space in $e^+e^-$ annihilation at the $Z_0$ peak and the quasi-oscillatory behavior of the ratio of factorial cumulants over factorial moments, $H_q$, as a function of the order $q$, are quantitatively reproduced within a simple parametrization of the MD in terms of a weighted superposition of two Negative Binomial Distributions, associated to two- and multi-jet production, i.e., to hard gluons radiation.
Single particle inclusive energy spectra in $e^+e^-$ annihilation are analyzed in terms of moments. By assuming Local Parton Hadron Duality (LPHD), experimental data in a wide c.m. energy range from 3 GeV up to LEP energy are compared to the theoretical predictions of Modified Leading Log Approximation (MLLA) of QCD with and without taking into account the running of $α_s$. MLLA with running coupling (Limiting Spectrum) is found to reproduce experimental results very well, while the model with fixed coupling is inconsistent with data. Rescaled cumulants are shown to be sensitive to the running of $α_s$ in the asymptotic regime, while the Lorentz-invariant distribution, $E dn/d^3p$, points out this effect at very small energy $E$ of few hundreds MeV. These results give a direct evidence of the running of the QCD coupling in inclusive energy spectra and lend further support to the LPHD picture.
The spectra of charged particles in the energy variable $ξ= \log 1/x$ (``the hump backed plateau'') are analyzed in terms of moments in order to investigate the sensitivity to the running of $α_s$ in particular towards small scales, and to further test thereby the local parton hadron duality picture. The modified leading log approximation (MLLA) of QCD provides a very satisfying description of the $e^+e^-$ data in the full range of c.m. energies from about 1 up to 91 GeV. The same calculation but with fixed coupling $α_s$ yields moments which are inconsistent with the data already close to threshold. In particular the soft particles ($E\le 1$~GeV) reflect directly the running of $α_s$.