Particle Spectra

A striking prediction of the perturbative approach to QCD jet physics is the depletion of soft particle production and the resulting approximately Gaussian shape of the inclusive distribution in the variable $\xi=\log E_{jet}/E$ for particles with energy E in a jet of energy E_jet--the famous ``hump-back plateau'' [2]. Due to the intrajet coherence of gluon radiation, not the softest partons but those with intermediate energies ($E\propto E_{jet}^{0.3-0.4}$)multiply most effectively in QCD cascades.

The shapes of the measured particle energy spectra in e⁺e^- annihilation turn out to be surprisingly close, over the whole momentum range down to momenta of a few hundred MeV, to the perturbative predictions based on the Modified Leading Log Approximation (MLLA) [3]. These observations can be taken as evidence that the perturbative phase of the cascade development indeed leaves its imprint on the final state hadrons. This, in turn, suggests that the conversion of partons into hadrons occurs at a low virtuality scale (of the order of the hadron masses), independent of the scale of the primary process, and involves only low-momentum transfers. This Local Parton-Hadron Duality (LPHD) may be connected to pre-confinement properties of QCD which ensure that colour charges are compensated locally [13]. LPHD remains, however, a strong hypothesis that is supposed to be valid only in an inclusive and average sense. With LPHD, only two essential parameters are involved in the perturbative description: the effective QCD scale $\Lambda$ and a (transverse momentum) cut-off parameter Q₀, resulting in a highly constrained theoretical framework; non-perturbative effects are essentially reduced to normalisation constants.

New data on charged particle spectra were presented at this workshop by H1 [14], ZEUS [15] and CDF [16]. The HERA experiments concentrate on the current fragmentation region in DIS and perform the analysis in the Breit frame, where the exchanged boson is completely spacelike. The new data confirm with much increased statistical significance the features observed in e⁺e^-: approximately Gaussian shape of the $\xi$ spectra with peak-position and width increasing with Q as predicted in MLLA. Moreover, for sufficiently large Q, they demonstrate the expected equivalence of the current region with one hemisphere of an e⁺e^- event. With increasing luminosity being accumulated at HERA, this work should be extended to include moment and cumulant analyses of the spectra for which detailed predictions exist [3].

Beautiful confirmation of the MLLA+LPHD approach has been presented by CDF [16]. This experiment studies charged particle momentum distributions in subsamples of dijet events. For fixed dijet masses (hence fixed jet energy) in the range $83<M_{\rm JJ}< 625$ GeV, the $\xi$ distribution of tracks, within cones of various opening angle $\Theta$ (with respect to the jet axis), is studied (see Fig. 1(a)). As dijet mass $\times$ jet opening angle increases, the peak of the spectrum, $\xi_o$,shifts towards larger values of $\xi$ in perfect agreement with MLLA predictions and e⁺e^- data, as shown in Fig. 1(b). Similar analyses should be possible in DIS and photoproduction at HERA but have not yet been attempted.

  

Figure: Comparison of preliminary CDF inclusive momentum distributions with MLLA predictions and e⁺e^- annihilation data.

Although present data on charged particles appear to confirm strikingly the perturbative approach to soft hadronisation, the situation is less clear-cut when spectra of identified particles/resonances are examined. At LEP, the conclusion is unambiguous: the peak positions do not agree with the naively expected mass dependence. Here also, data on spectra of different hadron species and from different jets at the Tevatron and HERA would be most helpful.