9,129 research outputs found
Sum rules for total hadronic widths of light mesons and rectilineal stitch of the masses on the complex plane
Mass formulae for light meson multiplets derived by means of exotic
commutator technique are written for complex masses and considered as complex
mass sum rules (CMSR). The real parts of the (CMSR) give the well known mass
formulae for real masses (Gell-Mann--Okubo, Schwinger and Ideal Mixing ones)
and the imaginary parts of CMSR give appropriate sum rules for the total
hadronic widths - width sum rules (WSR). Most of the observed meson nonets
satisfy the Schwinger mass formula (S nonets). The CMSR predict for S nonet
that the points form the rectilinear stitch (RS) on the complex
mass plane. For low-mass nonets WSR are strongly violated due to
``kinematical'' suppression of the particle decays, but the violation decreases
as the mass icreases and disappears above . The slope of
the RS is not predicted, but the data show that it is negative for all S nonets
and its numerical values are concentrated in the vicinity of the value -0.5. If
is known for a nonet, we can evaluate ``kinematical'' suppressions of its
individual particles. The masses and the widths of the S nonet mesons submit to
some rules of ordering which matter in understanding the properties of the
nonet. We give the table of the S nonets indicating masses, widths, mass and
width orderings. We show also mass-width diagrams for them. We suggest to
recognize a few multiplets as degenerate octets. In Appendix we analyze the
nonets of mesons.Comment: 20 pages, 3 figures; title and discussion expanded; additional text;
final version accepted for publication in EPJ
The multiplets of finite width 0++ mesons and encounters with exotics
Complex-mass (finite-width) nonet and decuplet are investigated by
means of exotic commutator method. The hypothesis of vanishing of the exotic
commutators leads to the system of master equations (ME). Solvability
conditions of these equations define relations between the complex masses of
the nonet and decuplet mesons which, in turn, determine relations between the
real masses (mass formulae), as well as between the masses and widths of the
mesons. Mass formulae are independent of the particle widths. The masses of the
nonet and decuplet particles obey simple ordering rules. The nonet mixing angle
and the mixing matrix of the isoscalar states of the decuplet are completely
determined by solution of ME; they are real and do not depend on the widths.
All known scalar mesons with the mass smaller than (excluding
) and one with the mass belong to two
multiplets: the nonet and the
decuplet .
It is shown that the famed anomalies of the and widths
arise from an extra "kinematical" mechanism, suppressing decay, which is not
conditioned by the flavor coupling constant. Therefore, they do not justify
rejecting the structure of them. A unitary singlet state (glueball)
is included into the higher lying multiplet (decuplet) and is divided among the
and mesons. The glueball contents of these particles
are totally determined by the masses of decuplet particles. Mass ordering rules
indicate that the meson does not mix with the nonet particles.Comment: 22 pp, 1 fig, a few changes in argumentation, conclusions unchanged.
Final version to appear in EPJ
Where is the pseudoscalar glueball ?
The pseudoscalar mesons with the masses higher than 1 GeV are assumed to
belong to the meson decuplet including the glueball as the basis state
supplementing the standard nonet of light states
. The decuplet is investigated by means of an algebraic approach based
on hypothesis of vanishing the exotic commutators of "charges" and
their time derivatives. These commutators result in a system of equations
determining contents of the isoscalar octet state in the physical isoscalar
mesons as well as the mass formula including all masses of the decuplet:
, K(1460), , and . The physical
isoscalar mesons , are expressed as superpositions of the "ideal"
states ( and ) and the glueball with the mixing
coefficient matrix following from the exotic commutator restrictions. Among
four one-parameter families of the calculated mixing matrix (numerous solutions
result from bad quality of data on the and K(1460) masses) there is
one family attributing the glueball-dominant composition to the
meson. Similarity between the pseudoscalar and scalar decuplets, analogy
between the whole spectra of the and mesons and affinity of
the glueball with excited states are also noticed.Comment: 18 pp., 2. figs., 2 tabs.; Published version. One of the authors
withdraws his nam
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