Study of a00(980) -f0(980) mixing from a0(1450) → a00(980)f0(500) → π+π-f0(500)

The a(0)(0)(980) - f(0)(980) mixing is one of the most promising potential tools to learn about the nature of a(0)(0)(980) and f(0)(980). Using the f(0)(980) - a(0)(0)(980) mixing intensity xi(af) measured recently at the BESIII experiment, we calculate the branching ratio of the isospin violation decay J/psi -> gamma eta(c) -> gamma pi(0)a(0)(0)(1450) -> gamma pi(0)a(0)(0)(980)f(0)(500) -> gamma pi(0)f(0)(980)f(0)(500) -> gamma pi(0)pi(+)pi(-)pi(+)pi(-). The value of the branching ratio is found to be O(10(-6)), which can be observed with 10(10) J/psi events collected at the BESIII experiment. The narrow peak from the f(0)(980) - a(0)(0)(980) mixing in the pi(+)pi(-) mass square spectrum can also be observed. In addition, we study the nonresonant decay a(0)(0)(1450) -> f(0)(980)pi(+)pi(-)(nonresonant), which is dominated by the a(0)(0)(980) - f(0)(980) mixing. We find that the nonresonant decay a(0)(0)(1450) -> f(0)(980)pi(+)pi(-) and the decay a(0)(0)(1450) -> f(0)(980)f(0)(500) can be combined to measure the mixing intensity xi(af) in experiment. These decays are the perfect complement to the decay chi(c1) -> f(0)(980)pi(0) -> pi(+)pi(-)pi(0), which had been observed at the BESIII experiment, the observations of which will make the measurement of the mixing intensity xi(af) more precisely.