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# Couplings of light I=0 scalar mesons to simple operators in the complex plane

Abstract : The flavour and glue structure of the light scalar mesons in QCD are probed by studying the couplings of the I=0 mesons $\sigma(600)$ and $f_0(980)$ to the operators $\bar{q}q$, $\alpha_s G^2$ and to two photons. The Roy dispersive representation for the $\pi\pi$ amplitude $t_0^0(s)$ is used to determine the pole positions as well as the residues in the complex plane. On the real axis, $t_0^0$ is constrained to solve the Roy equation together with elastic unitarity up to the $K\Kbar$ threshold leading to an improved description of the $f_0(980)$. The problem of using a two-particle threshold as a matching point is discussed. A simple relation is established between the coupling of a scalar meson to an operator $j_S$ and the value of the related pion form-factor computed at the resonance pole. Pion scalar form-factors as well as two-photon partial-wave amplitudes are expressed as coupled-channel Omnés dispersive representations. Subtraction constants are constrained by chiral symmetry and experimental data. Comparison of our results for the $\bar{q}q$ couplings with earlier determinations of the analogous couplings of the lightest I=1 and $I=1/2$ scalar mesons are compatible with an assignment of the $\sigma$, $\kappa$, $a_0(980)$, $f_0(980)$ into a nonet. Concerning the gluonic operator $\alpha_s G^2$ we find a significant coupling to both the $\sigma$ and the $f_0(980)$.
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http://hal.in2p3.fr/in2p3-00638841
Contributor : Sophie Heurteau <>
Submitted on : Monday, November 7, 2011 - 2:44:26 PM
Last modification on : Wednesday, September 16, 2020 - 4:08:10 PM

### Citation

B. Moussallam. Couplings of light I=0 scalar mesons to simple operators in the complex plane. European Physical Journal C: Particles and Fields, Springer Verlag (Germany), 2011, 71 (12), pp.1814. ⟨10.1140/epjc/s10052-011-1814-z⟩. ⟨in2p3-00638841⟩

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