Resonant $$a_0(980)$$ state in triangle rescattering $$D_s^+\rightarrow \pi ^+\pi ^0\eta $$ decays

Abstract

We study the $$D_s^+\rightarrow \pi ^+(a_0(980)^0\rightarrow )\pi ^0\eta $$ D s + → π + ( a 0 ( 980 ) 0 → ) π 0 η , $$\pi ^0(a_0(980)^+\rightarrow )\pi ^+\eta $$ π 0 ( a 0 ( 980 ) + → ) π + η decays, which have been recently measured by the BESIII collaboration. We propose that $$D_s^+\rightarrow \pi ^{+(0)}(a_0(980)^{0(+)}\rightarrow )\pi ^{0(+)}\eta $$ D s + → π + ( 0 ) ( a 0 ( 980 ) 0 ( + ) → ) π 0 ( + ) η receives the contributions from the triangle rescattering processes, where $$M^0$$ M 0 and $$\rho ^+$$ ρ + in $$D_s^+\rightarrow M^0 \rho ^+$$ D s + → M 0 ρ + , by exchanging $$\pi ^{0(+)}$$ π 0 ( + ) , are formed as $$a_0(980)^{0(+)}$$ a 0 ( 980 ) 0 ( + ) and $$\pi ^{+(0)}$$ π + ( 0 ) , respectively, with $$M^0=(\eta ,\eta ')$$ M 0 = ( η , η ′ ) . Accordingly, we calculate that $$\mathcal{B}(D_s^+\rightarrow a_0(980)^{0(+)}\pi ^{+(0)})= (1.7\pm 0.2\pm 0.1)\times 10^{-2}$$ B ( D s + → a 0 ( 980 ) 0 ( + ) π + ( 0 ) ) = ( 1.7 ± 0.2 ± 0.1 ) × 10 - 2 and $$\mathcal{B}(D_s^+\rightarrow \pi ^{+(0)}(a_0(980)^{0(+)}\rightarrow )\pi ^{0(+)}\eta ) =(1.4\pm 0.1\pm 0.1)\times 10^{-2}$$ B ( D s + → π + ( 0 ) ( a 0 ( 980 ) 0 ( + ) → ) π 0 ( + ) η ) = ( 1.4 ± 0.1 ± 0.1 ) × 10 - 2 , being consistent with the data.

Amplitude analysis and branching fraction measurement of the decay $$ {D}_s^{+} $$ → π+π0π0

“…Furthermore, hadronic D + s decays can be used to probe the interplay of short-distance weak-decay matrix elements and long-distance QCD interactions, and the measured BFs provide valuable information concerning the amplitudes and phases that induce in decay processes [10][11][12][13][14].…”

Study of the $$D_s^+\rightarrow a_0(980) \rho $$ and $$a_0(980) \omega $$ decays

“…It is hence considered to receive the long-distance annihilation contribution [1,3]. The D + s → S P, SV decays can help to investigate the short and long-distance annihilation mechanisms [8][9][10], where S stands for a non-strange scalar meson. For example, the WA process for D + s → a 0(+) 0 π +(0) violates Gparity [9,11], such that its branching fraction is expected as small as B(D [7,12].…”

“…The D + s → S P, SV decays can help to investigate the short and long-distance annihilation mechanisms [8][9][10], where S stands for a non-strange scalar meson. For example, the WA process for D + s → a 0(+) 0 π +(0) violates Gparity [9,11], such that its branching fraction is expected as small as B(D [7,12]. Clearly, it indicates the main contribution from the long-distance annihilation process [9].…”

“…For example, the WA process for D + s → a 0(+) 0 π +(0) violates Gparity [9,11], such that its branching fraction is expected as small as B(D [7,12]. Clearly, it indicates the main contribution from the long-distance annihilation process [9]. Explicitly, the longdistance annihilation process for D + s → a 0(+) 0 π +(0) starts with the D + s → η ( ) ρ + weak decay, followed by the η ( ) and ρ + rescattering.…”

Subprocesses $ρ(770,1450)\to K\bar{K}$ for the three-body hadronic $D$ meson decays

“…These decays are proceeded predominantly through the quasi-twobody processes [1][2][3]. Due to their small nonresonant components and abundant intermediate states, threebody D decays as well as their subprocesses were widely employed to study the properties and substructures of various resonant states [4][5][6][7][8][9][10][11][12][13][14][15][16][17], to analyses hadron-hadron interactions [18][19][20][21][22][23][24], and to extract information on the ππ, Kπ, and KK S-wave amplitude in the low energy region [25][26][27][28][29][30][31][32][33][34][35]. In the experimental analyses for relevant decay amplitudes [26,[36][37][38][39][40][41][42], Dalitz plot technique [43] was widely adopted in recent years.…”