Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
2000-10-18
Phys.Rev. D63 (2001) 074003
Physics
High Energy Physics
High Energy Physics - Phenomenology
11 pages, 3 figures
Scientific paper
10.1103/PhysRevD.63.074003
The experimental isoscalar $\pi\pi\to\pi\pi$ S-wave amplitude squared below 1.75 GeV is characterized by a very broad structure $f_0(400-1200)$ with two narrow dips due to its destructive interference with the $f_0(980)$ and $f_0(1500)$. The $f_0(1370)$ and $f_0(1710)$ do not show up clearly in the $\pi\pi\to\pi\pi$ S-wave amplitude due to their weak coupling to $\pi\pi$. This paper is about the controversial nature of the broad $f_0(400-1200)$. We decompose it into two parts, i.e., t-channel $\rho$ meson exchange plus an additional s-channel resonance $f_0(X)$. With the t-channel $\rho$ meson exchange fixed by the isotensor $\pi\pi\to\pi\pi$ S-wave scattering, we re-fit the CERN-Munich (CM) data on $\pi\pi$ scattering to get parameters for the $f_0(X)$. We find that the $f_0(X)$ is very broad with a nearby pole at (1.67-0.26i) GeV, while the t-channel $\rho$ meson exchange part produces a pole at (0.36-0.53i) GeV. The implication of our results for the study of $\sigma$ and glueball is discussed.
Li Guang-lie
Li Long
Zou Bing-Song
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