Resonant $$a_0(980)$$ a 0 ( 980
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Regular Article - Theoretical Physics
Resonant a0 (980) state in triangle rescattering Ds+ → π + π 0 η decays Yu-Kuo Hsiao1,a , Yao Yu2,b , Bai-Cian Ke1,c 1 2
School of Physics and Information Engineering, Shanxi Normal University, Linfen 041004, China Chongqing University of Posts and Telecommunications, Chongqing 400065, China
Received: 4 March 2020 / Accepted: 12 September 2020 © The Author(s) 2020
Abstract We study the Ds+ → π + (a0 (980)0 →)π 0 η, π 0 (a0 (980)+ →)π + η decays, which have been recently measured by the BESIII collaboration. We propose that Ds+ → π +(0) (a0 (980)0(+) →)π 0(+) η receives the contributions from the triangle rescattering processes, where M 0 and ρ + in Ds+ → M 0 ρ + , by exchanging π 0(+) , are formed as a0 (980)0(+) and π +(0) , respectively, with M 0 = (η, η ). Accordingly, we calculate that B(Ds+ → a0 (980)0(+) π +(0) ) = (1.7±0.2±0.1)×10−2 and B(Ds+ → π +(0) (a0 (980)0(+) →)π 0(+) η) = (1.4 ± 0.1 ± 0.1) × 10−2 , being consistent with the data.
1 Introduction Recently, the BESIII collaboration has measured the branching fraction of the Ds+ decay that involves one of the scalar mesons below 1 GeV, a0 ≡ a0 (980), which still has a controversial identification [1–6]. Explicitly, the branching fractions are observed as [7] B(Ds+ → π +(0) (a0
0(+)
→)π 0(+) η)
= (1.46 ± 0.15 ± 0.23) × 10−2 ,
(1)
where the Ds+ → a0+ π 0 , a00 π + decays are claimed as the W-annihilation (WA) dominant processes observed for the first time, as depicted in Fig. 1. Nonetheless, if Ds+ → a0 π proceeds through the WA c¯s → W + → u d¯ decay, the Gparities of u d¯ and a0 π are odd and even, respectively [8,9], such that a0 π formed from u d¯ violates G-parity conservation, indicating the suppressed WA process for Ds+ → a0 π . The same WA processes can also be applied to the D + section, being barely allowed by the current data. With a e-mail:
[email protected] (corresponding author)
b e-mail:
[email protected]
c e-mail:
[email protected]
0123456789().: V,-vol
BWA (η() ) ≡ B(D + → π +(0) (a0 obtain that
0(+)
BWA (η)
fD f Ds
2
|Vcd | |Vcs |
2
τD τ Ds
× B(Ds+ → π +(0) (a0
0(+)
= (1.2 ± 0.2) × 10−3 ,
m Ds mD
→)π 0(+) η() ), we 3
→)π 0(+) η) (2)
where f D(s) ,τ D(s) , m D(s) , and Vcq (q = d, s) represent + meson, and the decay constant, lifetime, mass for the D(s) the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements, respectively. It has been measured that B(η, η ) ≡ B(D + → π + π 0 η, π + π 0 η ) = (1.4 ± 0.4, 1.6 ± 0.5) × 10−3 [10]. The fact of B(η) B(η ) indicates that D + → π + π 0 η, π + π 0 η have the same topologies except for the difference from the η − η mixing. With Bρ (η() ) ≡ B(D + → η() (ρ + → )π + π 0 ) and BWA (η() ) that mainly contribute to B(η() ), that is, B(η() ) = Bρ (η() ) + BWA (η() ), one should have Bρ,WA (η) Bρ,WA (η ). Nonetheless, due to B(a0 → π η ) 0, caused by B(a0 → π η + K K¯ ) 100% [10], 0(+) it is estimated that BWA (η ) = B(D + → π +(0) a0 ) × 0(+) → π 0(+) η ) 0. This leads to BWA (η) B(a0 BWA (η )
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