Revisiting $C$ and $CP$ violation in $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ decay

Journal Article · 26 September 2024 · Physical Review. D.

DOI: https://doi.org/10.1103/PhysRevD.110.055039 · OSTI ID:2448125

Shi, Jun ; Liang, Jian ; Gardner, Susan

The decay $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ 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 $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ 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 $p^6$ 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 $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ experiments. Published by the American Physical Society 2024

• Research Organization: Univ. of Kentucky, Lexington, KY (United States)
• Sponsoring Organization: USDOE Office of Science (SC); USDOE Office of Science (SC), Nuclear Physics (NP)
• Grant/Contract Number: FG02-96ER40989
• OSTI ID: 2448125
• Journal Information: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 5 Vol. 110; ISSN PRVDAQ; ISSN 2470-0010
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English