Revisiting C and CP violation in η →π⁺π^-π⁰ decay

The decay η→π+π-π0 is an ideal process in which to study flavor-conserving C and CP violation beyond the Standard Model. We deduce the C- and CP-odd quark operators that contribute to η→π+π-π0 originating from the mass-dimension-six Standard Model effective field theory. The corresponding hadron-level operators that generate a nonvanishing I=0 amplitude at order p6 in the chiral effective theory are presented for the first time, to the best of our knowledge, in addition to the leading-order operators ascribed to the I=2 final state. By fitting the KLOE-2 and the most recent BESIII experimental data, we determine the coefficients of the lowest-order I=0 and I=2 amplitudes and estimate the potential new physics energy scale. We also perform an impact study of the future η→π+π-π0 experiments.