Striking regularity in meson and baryon production rates in e+e− annihilations

Abstract

It is shown that e + e data on the production rates of all particles (apart from pions) belonging to the SU(3) nonets of the pseudoscalar and vector mesons and, to the octet and decuplet of the baryons are determined only by particle spins, isospins and their masses. Contrary to a general belief and popular models, such as the Jetset model, the 2J + 1 spin counting factor works perfectly. The meson and baryon production rates at Z 0 pole at LEP as a function of particle mass squared lie on the one universal curve described by a simple formula < N ( particle) > = 2J+1 2Im+1 a exp( bM 2 ) with parameters a = 1 1 : 28 0:31 and b = 3 : 872 0:027 (GeV/c 2 ) 2 and 2 =N D F = 15/10, where I m is isospin for baryons or modied isospin I m for mesons introduced in this paper. Similar universal dependence with the same value of the slope b is observed at PETRA and PEP energies.To be submitted to Phys. Lett. B 1 Hadron production in Z 0 decays proceeds through two main steps: parton shower development from the primary q q pair produced from the Z 0 , followed by fragmentation of the coloured partons into colorless hadrons. The rst is well described by QCD, the theory of strong interactions. However, perturbative QCD is not applicable to the soft processes of hadronization. The formation of hadrons, mesons and baryons, out of quarks and gluons has been studied in many experiments in an attempt to understand the hadronization process better and to test phenomenological models of parton fragmentation. The most successful of these models are the string [1] and the cluster fragmentation [2] models implemented in the widely used Monte Carlo programs Jetset 7.4 PS [3] and Herwig 5.8 [4] respectively. H o w ever, the number of parameters in these models is quite large. Thus in the Jetset model many parameters control production of pseudoscalar and vector mesons. The most important are the suppression of s quark pair production compared with u or d pair production, the probability that a light meson (containing u and d quarks) has spin 1 and the probability that a strange meson has spin 1.The treatment of baryon production in e + e annihilations by the existing hadronization models is based on the experimental observations at PETRA and PEP energies that the dierential momentum spectra of mesons and baryons are rather similar. This justies the diquark model in which the fragmentation functions for baryons and mesons are assumed to be almost the same, quark-antiquark and diquark-antidiquark pairs are produced from the sea and a diquark combines with a quark to form a baryon. The relative production rates of the dierent octet and decuplet baryons are again controlled by free parameters tuned to the experimental data. The number of such parameters is also large. Thus in the Jetset model, the parameters relevant to octet and decuplet baryon production include the diquark to quark ratio (qq=q), the strange to non-strange quark ratio ((s=d), the same as used for the mesons), the strange diquark suppression factor (us=ud) (d=s), t...

Measurement of Δ++(1232) production in hadronic Z decays

“…On the other hand, the value (8) agrees within errors with the estimate < N ( ++ (1232) + (1232)) > = 0 : 064 0:002 obtained in [19] from the exponential dependence on their mass squared of the spin/isospin weighted particle production rates in e + e annihilations. The production rates of particles for one isospin projection (and with antibaryons not included) weighted with the factor (2I m + 1 ) = (2J + 1), where J is the particle spin and I the isospin (or modied isospin I m for mesons, see [19]) are shown as a function of their masses squared in g. 6.…”

“…The production rates of particles for one isospin projection (and with antibaryons not included) weighted with the factor (2I m + 1 ) = (2J + 1), where J is the particle spin and I the isospin (or modied isospin I m for mesons, see [19]) are shown as a function of their masses squared in g. 6. The plot is taken from ref.…”

“…The plot is taken from ref. [19], but with the additional ++ (1232) data point included. A t of the form a exp ( bM 2 ) to all the data except the pion (the straight line in g. 6) yields a = 1 1 : 28 0:31 and b = 3 : 872 0:027 (GeV/c 2 ) 2 (as was also found 8 in [19]), with P( 2 ) = 13%.…”

“…The ++ (1232) average multiplicity and its dierential cross section are presented and compared with the expectations of the JETSET 7.4 PS [14,15], HERWIG 5.8 [16,17] and UCLA 7.44 [18] models and with the regularities in particle yields observed in ref. [19].…”

Mass suppression in octet baryon production

“…A specific regularity in baryon production rates in e + e − annihilation has been recently noticed by Chliapnikov and Uvarov [6]. However, to our knowledge, there has not been a detailed investigation on the relation among the octet baryon fragmentation functions.…”