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A coherent study of the production of $f_0^i$ ($i=1$, 2, 3 corresponding to$f_0(1710)$, $f_0(1500)$, and $f_0(1370)$) in $J/\psi\to V f_0 \to V PP$ isreported based on a previously proposed glueball and $Q\bar{Q}$ nonet mixingscheme, and a factorization for the decay of $J/\psi\to V f_0^i$, where $V$denotes the isoscalar vector mesons $\phi$ and $\omega$, and $P$ denotespseudoscalar mesons. The results show that the $J/\psi$ decays are verysensitive to the structure of those scalar mesons, and suggest a glueball inthe $1.5-1.7$ GeV region, in line with Lattice QCD. The presence of significantglueball mixings in the scalar wavefunctions produces peculiar patterns in thebranching ratios for $J/\psi\to V f_0^i\to VPP$, which are in good agreementwith the recently published experimental data from the BES collaboration.Comment: Version accepted by PRD; Numerical results in Tab IV and VI changed  due to correction of an error in quoting an experimental datum; Conclusion is  not change

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

Production of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1710</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>,<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>f</mml:mi><mml:mn>0</mml:mn></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>1500</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and<mml:math …

Production off0(1710),f0(1500), and