The decay is an ideal process in which to study flavor-conserving and violation beyond the Standard Model. We deduce the - and -odd quark operators that contribute to originating from the mass-dimension 6 Standard Model effective field theory. The corresponding hadron-level operators that generate a non-vanishing amplitude at order in the chiral effective theory are presented for the first time, in addition to the leading order operatorsascribed to the final state. By fitting the KLOE-2 and the most recent BESIII experimental data, we determine the coefficients of the lowest order and amplitudes and estimate the potential new physics energy scale. We also perform an impact study of the future experiments.

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