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Sigma-Meson and Confinement Singularity | | A.V. Anisovich
; V.V. Anisovich
; M.A. Matveev
; K.V. Nikonov
; V.A. Nikonov
; J. Nyiri
; A.V. Sarantsev
; T.O. Vulfs
; | | Date: |
30 May 2011 | | Abstract: | We describe the meson-meson data for the ($IJ^{PC}=00^{++}$) wave at
$280leqsqrt sleq 1900$ MeV in two approaches: (i) the K-matrix approach and
(ii) the dispersion relation D-matrix method. With a good description of low
energy data (at $280leqsqrt sleq 900$ MeV) as well as the data of two-meson
transition amplitudes and antiproton-proton annihilation into three
pseudoscalar meson states (at $450leqsqrt sleq 1950$ MeV) we have found the
positions of the resonance poles: (i) for the $sigma$ meson pole: $M_sigma =
(390pm 35)-i(235pm 50)$ MeV; (ii) two poles for the $f_0(980)$, on the second
sheet (under the $pipi$ cut): $M_{I} = (1011pm 5)-i(35pm 5)$ MeV, and on
the third sheet (under the $pipi$ and $Kar K$ cuts), $M_{II} = (1035pm
50)-i(460pm 50)$ MeV; for the $f_0(1370)$ meson, $M= (1285pm 30)-i(160pm
20)$ MeV; for the $f_0(1500)$ meson, $M = (1488pm 4)-i(53pm 5)$ MeV; for the
$f_0(1790)$ meson, $M = (1775pm 25)-i(140pm 15)$ MeV and for the broad state
$f_0(1200-1600)$ $M=(1540pm 120)-i(550pm 70)$ MeV. Our estimation of the
scalar-isoscalar scattering length obtained under different parameterizations
and assumptions about the quality of low energy $pipi$ scattering data is
$a^0_0=(0.215pm 0.040)mu^{-1}_pi$. We also discuss the idea according to
which the $sigma$-meson could be a remnant of the confinement singularity,
$1/s^2$, in a white channel. | | Source: | arXiv, 1105.5923 | | Services: | Forum | Review | PDF | Favorites | |
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