Interference phenomena in the decay $D^+_s\toηπ^0π^+$ induced by the $a^0_0(980)-f_0(980)$ mixing

Abstract

Using the data on the decay D + s → f0(980)π + → K + K − π + , we estimate the amplitude of the process D + s → f0(980) → (K + K − + K 0 K0 ) → a 0 0 (980) π + → ηπ 0 π + , caused by the mixing of a 0 0 (980) and f0(980) resonances that breaks the isotopic invariance due to the K + and K 0 meson mass difference. Effects of the interference of this amplitude with the amplitudes of the main mechanisms responsible for the decay D + s → ηπ 0 π + are analyzed. As such mechanisms, we examine the transition D + s → ηρ + → ηπ 0 π + , which is observed in experiment, and the possible transition D + s → a 0 0 (980)π + + a + 0 (980)π 0 → ηπ 0 π + . It is shown that the rapidly varying phase of the a 0 0 (980) − f0(980) transition amplitude strongly influences the interference curves.

Manifestations of the $a^0_0(980)-f_0(980)$ mixing in $D^0\to K^0_Sπ^+π^-$ and $D^0\to K^0_Sηπ^0$ decays

“…Recently, we have examined the interference phenomena in the ηπ 0 mass spectrum in the D + s → ηπ 0 π + decay [1] caused by the isospin-breaking a 0 0 (980) − f 0 (980) mixing [2,3]. Their detection would help clarify the production and decay mechanisms of the light scalars f 0 (980) and a 0 0 (980) in weak three-body hadronic D + s decays.…”

“…In Ref. [1], it has been noted that the investigations of the a 0 0 (980) − f 0 (980) mixing in three-body decays of the D 0 meson, such as D 0 → K 0 S π + π − , D 0 → K 0 S ηπ 0 , D 0 → K0 K − K + , D 0 → K − K + π 0 , and D 0 → π + π − π 0 , are also promising and interesting. In the present work, we analyze a possible manifestation of the a 0 0 (980) − f 0 (980) mixing in the decays D 0 → K 0 S π + π − and D 0 → K 0 S ηπ 0 .…”

“…Formulas for the inverse propagators D f 0 (m) and D a 0 0 (m) of the f 0 (980) and a 0 0 (980) resonances and the amplitude Π a 0 0 f 0 (m) describing the a 0 0 (980) → (K + K − + K 0 K0 ) → f 0 (980) transition, together with the values of coupling constants g f 0 ab , ab = (π + π − , π 0 π 0 , K + K − , K 0 K0 , ηη), and g a 0 0 ab , ab = (ηπ 0 , K + K − , K 0 K0 , η ′ π 0 ), which we use here, have been written in detail in Refs. [1,4]. The values of C 1 = 0.047 GeV −1/2 and C 2 = 0.095 GeV −1/2 are fixed taking into account the CLEO Collaboration results [5,6], together with the Particle Data Group information [7], and the relations…”