Journal ArticleRevisiting <math display='inline'><mrow><mi>C</mi></mrow></math> and <math display='inline'><mi>C</mi><mi>P</mi></math> violation in <math display='inline'><mrow><mi>η</mi><mo stretchy='false'>→</mo><msup><mrow><mi>π</mi></mrow><mrow><mo>+</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mrow><mo>−</mo></mrow></msup><msup><mrow><mi>π</mi></mrow><mn>0</mn></msup></mrow></math> decayShi, Jun; Liang, Jian; Gardner, Susan<p>The decay<math display='inline'><mi>η</mi><mo stretchy='false'>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>is an ideal process in which to study flavor-conserving<math display='inline'><mi>C</mi></math>and<math display='inline'><mi>C</mi><mi>P</mi></math>violation beyond the Standard Model. We deduce the<math display='inline'><mi>C</mi></math>- and<math display='inline'><mi>C</mi><mi>P</mi></math>-odd quark operators that contribute to<math display='inline'><mi>η</mi><mo stretchy='false'>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>originating from the mass-dimension-six Standard Model effective field theory. The corresponding hadron-level operators that generate a nonvanishing<math display='inline'><mi>I</mi><mo>=</mo><mn>0</mn></math>amplitude at order<math display='inline'><msup><mi>p</mi><mn>6</mn></msup></math>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<math display='inline'><mi>I</mi><mo>=</mo><mn>2</mn></math>final state. By fitting the KLOE-2 and the most recent BESIII experimental data, we determine the coefficients of the lowest-order<math display='inline'><mi>I</mi><mo>=</mo><mn>0</mn></math>and<math display='inline'><mi>I</mi><mo>=</mo><mn>2</mn></math>amplitudes and estimate the potential new physics energy scale. We also perform an impact study of the future<math display='inline'><mi>η</mi><mo stretchy='false'>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup><msup><mi>π</mi><mn>0</mn></msup></math>experiments.</p> <sec><supplementary-material><permissions><copyright-statement>Published by the American Physical Society</copyright-statement><copyright-year>2024</copyright-year></permissions></supplementary-material></sec>APS2024-09-0110609092Physical Review D11052470-0010https://doi.org/10.1103/PhysRevD.110.0550392020275National Science Foundation