Abstract
The present notes prepare the countin of 'oscillatory modes of N _fl = 3 light quarks', - u, d, s -, using the [??] broken symmetry classification, extended to the harmonic oscillator symmetry of 3 pairedoscillator modes. [??] stands for the space rotation group generated by the sum of the 3 individual angular momenta of quarks in their c.m. system . The motivation arises from modeling the yields of hadrons in heavy ion collisions at RHIC and LHC, necessitating at the respective highest c.m. energies per nucleon pairs an increase of heavy hadron resonances relative to e.g. SPS energies, whence the included hadrons are treated as a noninteracting gas.
Highlights
The comparison of hadron yields measured at RHIC and LHC with a noninteracting hadron resonance gas necessitates the counting of these resonances, which is not obvious
2 Here we focus on the cornerstones, which allow to count these oscillatory modes, as outlined in extenso in refs. 1 and 2, op.cit. , beginning with the classification of the representations of S 3 – the permutation group of the three quarks in configuration space – arising through the induced representation from the associated wave functions, in the subsequent sections
We hope that at the high energy frontier, despite the odds looking unfavorable, exploiting the increased production cross sections of hitherto unobserved resonances , the art of resonance spectroscopy – even of low energy resonances – can witness a new frontier
Summary
The comparison of hadron yields measured at RHIC and LHC with a noninteracting hadron resonance gas necessitates the counting of these resonances , which is not obvious Let us turn towards the title of this subsection and counterpose the hypothesis that there exists an essentially unique consistent local field theory in the limiting case of uncurved d = 3 + 1 space time – called QCD today – with the following properties : a) describes strong hadronic interactions b) admits perturbative as well as nonperturbative renormalizability in the ultraviolet limit as appropriate for uncurved space-time c) accounts for the composite nature of hadrons as composed of at least several flavors of q q fields for ordinary mesons and qqqqqq fields for associated baryons ( anti-baryons ) respectively.
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