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SU(3) Subalgebras of SU(6) and Mass Sum Rules for Hadrons With Charm, Beauty and Taste

  • Camiz, P.
  • Dattoli, G.
  • Mignani, R.
  • Prosperi, D.
Publication Date
Mar 01, 1979
DOI: 10.1007/BF02776482
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Motivated by the well-established experimental evidence for the new quark flavour «beauty», we discuss the problem of mass splitting for hadrons, under the hypothesis that their spectroscopy is grounded on six quark flavours. In order to derive mass sum rules involving both the light and charmed hadrons and the heavy («beautiful» and «tasty») ones, we do not consider them as belonging toSU6 representations, but use is made of a formalism based on the twentySU3 subsectors ofSU6, which are obtained by removing three of the six quarks in all possible ways. By generalizing toSU6 a procedure we followed forSU4 in dealing with the magnetic moments of charmed baryons, we divide the three-quark subsectors ofSU6 in four classes, according to the charges of the quarks constituting them. For any class of sectors, aSU3 algebra can be defined in a suitable way, by introducing generalized operators (like hypercharge and isospin) induced by theSU6 generators. By making suitable assumptions on theSU3 transformation properties of the mass operator, we get a modified Gell-Mann-Okubo (GMO) mass formula, which, in general, depends on five parameters. In any sector, the number of parameters surviving in the mass formula (i.e. the pattern of symmetry breaking) is determined by the quark content and the generalized operator assignement in the sector. By the modified GMO mass formula, we get mass sum rules for light and charmed vector mesons and for some of the heavy ones. However, in order to reconcile the results for the vector mesons in the sector built up by the quarks d, s and c with some quantum chromodynamics predictions, one has to add one more term to the mass formula. Numerical values of the masses of the vector mesons K*, D* and F*—as deduced by the mass relations—together with predictions on the masses of the new vector mesons \(u\bar b\), \(s\bar b\) and \(c\bar b\) are also given. A simple recipe is described to get, from the already exploited mass relations, sum rules for the other new vector mesons. A number of sum rules is also derived for light, charmed and heavy «beautiful» baryons, and a simple rule is given to extend the results in a straightforward way to «tasty» baryons. A new notation for the baryon states containing b- and t-quarks is proposed.

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