First Observation of D⁺ → a₀(980)ρ and D⁺ → a₀(980)⁺ f₀(500) in D⁺ → π⁺π⁺π⁻η and D⁺ → π⁺π⁰π⁰η Decays

We perform the first amplitude analysis of the singly Cabibbo-suppressed decays D⁺ → π⁺π⁺⁽⁰⁾π⁻⁽⁰⁾η, using e⁺e⁻ collision data collected with the BESIII detector at a center-of-mass energy of 3.773 GeV, corresponding to an integrated luminosity of 20.3 fb⁻¹. The absolute branching fractions of the D⁺ → π⁺π⁺π⁻η and D⁺ → π⁺π⁰π⁰η decays are measured to be (3.20 ± 0.06_stat. ± 0.03_syst.) × 10⁻³ and (2.43 ± 0.11_stat. ± 0.04_syst.) × 10⁻³, respectively. The decay process D⁺ → a₀(980)⁺f₀(500) is observed for the first time with an unexpectedly large branching fraction. Moreover, we observe the decays D⁺ → a₀(980)⁺⁽⁰⁾ρ(770)⁰⁽⁺⁾ and measure for the first time the ratio r₊/₀ ≡ ℬ(D⁺ → a₀(980)⁺ρ(770)⁰) / ℬ(D⁺ → a₀(980)⁰ρ(770)⁺) to be 0.55 ± 0.08_stat. ± 0.05_syst. These results offer novel insight into our understanding of the nature of the a₀(980) and f₀(500) states. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.