17,146 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 $(m,\Gamma{})$ 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 $\sim 1.5 GeV$. The slope $k_s$ 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
$k_s$ 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 $1^+$ 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) $0^{++}$ 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 $2000MeV$ (excluding
$\sigma(600)$) and one with the mass $2200\div2400MeV$ belong to two
multiplets: the nonet $(a_0(980), K_0(1430), f_0(980), f_0(1710))$ and the
decuplet $(a_0(1450), K_0(1950), f_0(1370), f_0(1500), f_0(2200)/f_0(2330))$.
It is shown that the famed anomalies of the $f_0(980)$ and $a_0(980)$ 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 $q\bar{q}$ structure of them. A unitary singlet state (glueball)
is included into the higher lying multiplet (decuplet) and is divided among the
$f_0(1370)$ and $f_0(1500)$ mesons. The glueball contents of these particles
are totally determined by the masses of decuplet particles. Mass ordering rules
indicate that the meson $\sigma(600)$ 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

### Sum rules for total hadronic widths of mesons

Mass sum rules for meson multiplets derived from exotic commutators may be
written for complex masses. Then the real parts give the well known mass
formulae (GM-O, Schwinger, Ideal) and the imaginary ones give the corresponding
sum rules for total hadronic widths. The masses and widths of the meson nonets
submit to a definite orders. It thus follows that tables of the meson nonets
should include information about masses, widths and the orders as well as the
mixing angle. The width sum rule for the nonet complying with Schwinger mass
formula may be depicted as a straight line in the $(m,\Gamma)$ plane. It is
easily verifiable and satisfied better for high mass nonets.Comment: LaTeX, 4pp, 1 figure. To appear in Proceedings of "Hadron 2001

### Sample path large deviations for multiclass feedforward queueing networks in critical loading

We consider multiclass feedforward queueing networks with first in first out
and priority service disciplines at the nodes, and class dependent
deterministic routing between nodes. The random behavior of the network is
constructed from cumulative arrival and service time processes which are
assumed to satisfy an appropriate sample path large deviation principle. We
establish logarithmic asymptotics of large deviations for waiting time, idle
time, queue length, departure and sojourn-time processes in critical loading.
This transfers similar results from Puhalskii about single class queueing
networks with feedback to multiclass feedforward queueing networks, and
complements diffusion approximation results from Peterson. An example with
renewal inter arrival and service time processes yields the rate function of a
reflected Brownian motion. The model directly captures stationary situations.Comment: Published at http://dx.doi.org/10.1214/105051606000000439 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org

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