The factorization-assisted topological-amplitude approach and its applications

doi:10.1007/s11467-023-1321-3

Frontiers of Physics

2023, Vol. 18

Issue (6): 64602 https://doi.org/10.1007/s11467-023-1321-3

本期目录

The factorization-assisted topological-amplitude approach and its applications

Qin Qin¹(

), Chao Wang²(

), Di Wang³(

), Si-Hong Zhou⁴(

)

¹. School of Physics, Huazhong University of Science and Technology, Wuhan 430074, China
². Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223001, China
³. Department of Physics, Hunan Normal University, Changsha 410081, China
⁴. School of Physical Science and Technology, Inner Mongolia University, Hohhot 010021, China

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Abstract：

Heavy meson decays provide an important platform for studies of both QCD and electroweak dynamics, which may contain some portals to understanding of nonperturbative QCD and physics beyond the Standard Model. The factorization-assisted topological-amplitude approach was proposed to study two-body non-leptonic D meson decays, where a promising QCD inspired approach from first principles is still missing. It was also applied to B meson decays whose subleading power contributions are difficult to calculate. By factorizing topological amplitudes into short distance Wilson coefficients and long distance hadronic matrix elements either to be calculated or to be parameterized, it provides an effective framework to extract information of nonperturbative dynamics involved. With important flavor SU(3) breaking effects taken into account, the data of the decay branching ratios (and also CP asymmetries in B decays) can be fitted well. The extracted amplitudes were further applied to make predictions for other observables, such as CP asymmetries in D decays, mixing parameters in the $D 0 − D ¯ 0$ system. By this review, we will describe the formulation of the factorization-assisted topological-amplitude approach and summarize its applications in D and B meson decays and highlight some of its achievements.

Key words： heavy meson decay factorization-assisted topological-amplitude approach SU(3) breaking

收稿日期: 2023-02-23 出版日期: 2023-11-29

Corresponding Author(s): Qin Qin,Chao Wang,Di Wang,Si-Hong Zhou

引用本文:

. [J]. Frontiers of Physics, 2023, 18(6): 64602.
Qin Qin, Chao Wang, Di Wang, Si-Hong Zhou. The factorization-assisted topological-amplitude approach and its applications. Front. Phys. , 2023, 18(6): 64602.

链接本文:

https://academic.hep.com.cn/fop/CN/10.1007/s11467-023-1321-3
https://academic.hep.com.cn/fop/CN/Y2023/V18/I6/64602

Fig.1

Channel	FAT	Data	Channel	FAT	Data

$D 0 → K S 0 K S 0$	$0.15 ± 0.04$ [33]	$0.141 ± 0.005$	$D 0 → π 0 η$	$0.74 ± 0.03$ [33]	$0.63 ± 0.06$
$D 0 → π 0 η ′$	$1.08 ± 0.05$ [33]	$0.92 ± 0.10$	$D 0 → η η$	$1.86 ± 0.06$ [33]	$2.11 ± 0.19$
$D 0 → η η ′$	$1.05 ± 0.08$ [33]	$1.01 ± 0.19$	$D 0 → π + π ?$	$1.44 ± 0.02$ [33]	$1.454 ± 0.024$
$D 0 → K + K ?$	$4.05 ± 0.07$ [33]	$4.08 ± 0.06$	$D 0 → K ? π +$	$39.3 ± 0.4$ [33]	$39.47 ± 0.30$
$D 0 → K S 0 π 0$	$12.1 ± 0.4$ [33]	$12.40 ± 0.22$	$D 0 → K S 0 η$	$4.8 ± 0.3$ [33]	$5.13 ± 0.14$ [34]
$D 0 → K S 0 η ′$	$9.8 ± 0.5$ [33]	$9.49 ± 0.41$ [34]	$D + → π + π 0$	0.89 [24]	$1.247 ± 0.033$
$D + → K + π 0$	0.197 [24]	$0.208 ± 0.021$	$D + → π + η$	3.39 [24]	$3.77 ± 0.09$
$D + → K + η$	0.066 [24]	$0.125 ± 0.016$	$D + → π + η ′$	4.58 [24]	$4.97 ± 0.19$
$D + → K + η ′$	0.114 [24]	$0.185 ± 0.020$	$D + → π + K S 0$	16.2 [24]	$15.62 ± 0.31$
$D + → K + K S 0$	2.98 [24]	$3.04 ± 0.09$	$D s + → π + π 0$	0 [24]	$0.037 ± 0.059$ [35]
$D s + → π 0 K +$	0.67 [24]	$0.74 ± 0.05$	$D s + → π + K S 0$	1.105 [24]	$1.10 ± 0.05$
$D s + → K + K S 0$	15.03 [24]	$14.53 ± 0.35$	$D s + → π + η$	16.5 [24]	$16.8 ± 0.9$
$D s + → K + η$	1.0 [24]	$1.73 ± 0.08$	$D s + → π + η ′$	34.4 [24]	$39.4 ± 2.5$
$D s + → K + η ′$	1.92 [24]	$2.64 ± 0.24$

Tab.1

Channel	FAT	Data	Channel	FAT	Data

$D 0 → η ω$	$2.1 ± 0.1$ [33]	$1.98 ± 0.18$	$D 0 → η K ˉ ∗ 0$	$6.1 ± 1.0$ [33]	$13.4 ? 0.9 + 1.2$
$D 0 → π 0 ?$	$1.4 ± 0.1$ [33]	$1.34 ± 0.12$	$D 0 → η ?$	$0.18 ± 0.04$ [33]	$0.184 ± 0.012$
$D + → π + ?$	5.65(5.65) [25]	$5.70 ± 0.14$	$D + → K + ?$	0.001(0.002) [25]	$< 0.021$
$D + → K + ω$	0.09(0.07) [25]	$0.057 ? 0.021 + 0.025$	$D + → K S 0 K ∗ +$	5.5(5.5) [25]	$2.89 ± 0.30$
$D s + → η ′ ρ +$	17(16) [25]	$58 ± 15$	$D s + → π + ω$	3.0(2.6) [25]	$1.92 ± 0.30$
$D s + → K + ω$	0.6(0.07) [25]	$0.87 ± 0.25$

Tab.2

Fig.2

Fig.3

Channel	FAT	Data	Channel	FAT	Data

$D 0 → π + π ?$	$0.58$	$1.3 ± 1.4$	$D 0 → π 0 π 0$	$0.05$	$? 0 ± 6$
$D 0 → K S 0 K S 0$	$1.38$	$? 19 ± 10$	$D 0 → K + K ?$	$? 0.42$	$? 0.7 ± 1.1$
$D 0 → η ?$	$0.003$	$? 20 ± 40$	$D + → π + π 0$	$0$	$4 ± 13$
$D + → π + η$	$? 0.26$	$3 ± 8$	$D + → π + η ′$	$1.18$	$? 6 ± 7$
$D + → π + ?$	$? 0.0001$	$0.1 ± 0.9$	$D s + → K + π 0$	$0.39$	$20 ± 40$
$D s + → K + η$	$0.70$	$18 ± 19$	$D s + → K + η ′$	$? 1.60$	$60 ± 190$

Tab.3

Fig.4

Channel	FAT	Data	Channel	FAT	Data

$D 0 → K S, L 0 π 0$	$0.113 ± 0.001$	$0.108 ± 0.035$ [46]	$D + → K S, L 0 π +$	$0.025 ± 0.008$	$0.022 ± 0.024$ [46]
$D 0 → K S, L 0 η$	$0.113 ± 0.001$	$0.080 ± 0.022$ [47]	$D 0 → K S, L 0 η ′$	$0.113 ± 0.001$	$0.080 ± 0.023$ [47]
$D 0 → K S, L 0 ω$	$0.113 ± 0.001$	$? 0.024 ± 0.031$ [47]	$D 0 → K S, L 0 ?$	$0.113 ± 0.001$	$? 0.001 ± 0.047$ [47]

Tab.4

Fig.5

Diagram	T	C	$P C$	P(PP)	$P E W$	E	A	$P A$ (PV)	$P E$

FAT	$a 1$	$χ C (′) e i ? C (′)$	$χ P C (′) e i ? P C (′)$	$a 4 (μ) + χ P e i ? P r χ$	$a 9 (μ)$	$χ E e i ? E$	$?$	$? i χ P A e i ? P A$	$?$
	$?$	$0.48 e ? 1.58 i$	$0.048 e 1.56 i$	$? 0.12 e ? 0.24 i$	?0.009	$0.057 e 2.71 i$		$0.0059 e ? 0.006 i$
QCDF	$α 1$	$α 2$	$α 3$	$α 4$	$α 3 EW$	$β 1$	$β 2$	$β 3$	$β 4$
	$?$	$0.22 e ? 0.53 i$	$0.011 e 2.23 i$	$? 0.089 e 0.11 i$	$? 0.009 e 0.04 i$	0.025	?0.011	?0.008	?0.003

Tab.5

Mode	$A e x p$	$A FAT$	$A Flavor diagram$	$S e x p$	$S FAT$	$S Flavor diagram$

$π + π ?$	$0.32 ± 0.04$	$0.31 ± 0.04$	$0.326 ± 0.081$	$? 0.65 ± 0.04$	$? 0.60 ± 0.03$	$? 0.717 ± 0.061$
$π 0 π 0$	$0.33 ± 0.22$	$0.57 ± 0.06$	$0.611 ± 0.113$		$0.58 ± 0.06$	$0.454 ± 0.112$
$π 0 η$		$? 0.16 ± 0.16$	$0.566 ± 0.114$		$? 0.98 ± 0.04$	$? 0.098 ± 0.338$
$π 0 η ′$		$0.39 ± 0.14$	$0.385 ± 0.114$		$? 0.90 ± 0.07$	$0.142 ± 0.234$
$η η$		$? 0.85 ± 0.06$	$? 0.405 ± 0.129$		$0.33 ± 0.12$	$? 0.796 ± 0.077$
$η η ′$		$? 0.97 ± 0.04$	$? 0.394 ± 0.117$		$? 0.20 ± 0.15$	$? 0.903 ± 0.049$
$η ′ η ′$		$? 0.87 ± 0.07$	$? 0.122 ± 0.136$		$? 0.46 ± 0.14$	$? 0.964 ± 0.037$
$π 0 K s$	$0.00 ± 0.13$	$? 0.14 ± 0.03$	$? 0.173 ± 0.019$	$0.58 ± 0.17$	$0.73 ± 0.01$	$0.754 ± 0.014$
$η K s$		$? 0.30 ± 0.10$	$? 0.301 ± 0.041$		$0.68 ± 0.04$	$0.592 ± 0.035$
$η ′ K s$	$0.06 ± 0.04$	$0.030 ± 0.004$	$0.022 ± 0.006$	$0.63 ± 0.06$	$0.69 ± 0.00$	$0.685 ± 0.004$
$K 0 K 0 ˉ$		$? 0.057 ± 0.002$	$0.017 ± 0.041$	$0.8 ± 0.5$	$0.099 ± 0.002$	0
$π ? π 0$	$0.03 ± 0.04$	$? 0.026 ± 0.003$	$0.069 ± 0.027$
$π ? η$	$? 0.14 ± 0.07$	$? 0.14 ± 0.07$	$? 0.081 ± 0.074$
$π ? η ′$	$0.06 ± 0.16$	$0.37 ± 0.07$	$0.374 ± 0.087$
$π ? K 0 ˉ$	$? 0.017 ± 0.016$	$0.0027 ± 0.0001$	0
$π 0 K ?$	$0.037 ± 0.021$	$0.065 ± 0.024$	$0.047 ± 0.025$
$η K ?$	$? 0.37 ± 0.08$	$? 0.22 ± 0.08$	$? 0.426 ± 0.043$
$η ′ K ?$	$0.04 ± 0.011$	$? 0.021 ± 0.007$	$? 0.027 ± 0.008$
$K ? K 0$	$? 0.21 ± 0.14$	$? 0.057 ± 0.002$	0
$π + K ?$	$? 0.083 ± 0.004$	$? 0.081 ± 0.005$	$? 0.080 ± 0.011$

Tab.6

Mode	$B (10 ? 6)$	$f L$ (%)	$f ⊥$ (%)	$? / /$ (rad)	$? ⊥$ (rad)

$B ? → ρ ? ρ 0$	$21.7 ± 5.1$	$95.5 ± 1.5$	$2.22 ± 0.64$	$? 0.09 ± 0.05$	$? 0.09 ± 0.05$
Expt.	$24.0 ± 1.9$	$95 ± 1.6$
$B ˉ 0 → ρ + ρ ?$	$29.5 ± 6.5$	$92.6 ± 1.6$	$3.65 ± 0.91$	$? 0.27 ± 0.08$	$? 0.27 ± 0.08$
Expt.	$27.7 ± 1.9$	$99.0 ? 1.9 + 2.1$
$B ˉ 0 → ρ 0 ρ 0$	$0.94 ± 0.49$	$81.7 ± 10.8$	$9.21 ± 5.50$	$? 0.04 ± 0.44$	$? 0.03 ± 0.44$
Expt.	$0.96 ± 0.15$	$71 ? 9 + 8$

	$A C P$ (%)	$A C P 0$ (%)	$A C P ⊥$ (%)	$Δ ? / /$ (rad)	$Δ ? ⊥$ (rad)
$B ? → ? K ∗ ?$	$0$	$0$	$0$	$0$	$0$
Expt.	$? 5 ± 5$
$B ˉ 0 → ? K ˉ ∗ 0$	$? 8.10 ± 2.94$	$1.30 ± 0.54$	$? 16.3 ± 8.2$	$? 0.41 ± 0.05$	$? 0.41 ± 0.05$
$B ˉ s 0 → ? ?$	$49.7 ± 13.4$	$10.5 ± 9.6$	$? 46.9 ± 13.9$	$1.89 ± 0.19$	$1.89 ± 0.19$

Tab.7

Mode	$B (10 ? 6)$	$f L$ (%)	$f ⊥$ (%)	$? / /$ (rad)	$? ⊥$ (rad)

$B ? → ? K ∗ ?$	$9.31 ± 2.81$	$48.0 ± 16.0$	$25.9 ± 8.6$	$2.47 ± 0.27$	$2.47 ± 0.27$
Expt.	$10 ± 2$	$50 ± 5$	$20 ± 5$	$2.34 ± 0.18$	$2.58 ± 0.17$
$B ˉ 0 → ? K ˉ ∗ 0$	$8.64 ± 2.61$	$48.0 ± 16.0$	$26.0 ± 8.6$	$2.47 ± 0.27$	$2.47 ± 0.27$
Expt.	$10.0 ± 0.5$	$49.7 ± 1.7$	$22.4 ± 1.5$	$2.43 ± 0.11$	$2.53 ± 0.09$
$B ˉ s 0 → ? ?$	$26.4 ± 7.6$	$39.7 ± 16.0$	$31.2 ± 8.9$	$2.53 ± 0.28$	$2.56 ± 0.27$
Expt.	$18.7 ± 1.5$	$37.8 ± 1.3$	$29.2 ± 0.9$	$2.56 ± 0.06$	$2.818 ± 0.192$

	$A C P$ (%)	$A C P 0$ (%)	$A C P ⊥$ (%)	$Δ ? / /$ (rad)	$Δ ? ⊥$ (rad)
$B ? → ? K ∗ ?$	$1.00 ± 0.27$	$1.26 ± 0.71$	$? 1.16 ± 0.30$	$? 0.02 ± 0.00$	$? 0.02 ± 0.00$
Expt.	$? 1 ± 8$	$17 ± 11$	$22 ± 25$	$0.07 ± 0.21$	$0.19 ± 0.21$
$B ˉ 0 → ? K ˉ ∗ 0$	$1.00 ± 0.27$	$1.26 ± 0.71$	$? 1.16 ± 0.30$	$? 0.02 ± 0.00$	$? 0.02 ± 0.00$
Expt.	$0 ± 4$	$? 0.7 ± 3.0$	$? 2 ± 6$	$0.05 ± 0.05$	$0.08 ± 0.05$
$B ˉ s 0 → ? ?$	$0.83 ± 0.28$	$1.55 ± 0.85$	$? 1.02 ± 0.29$	$? 0.01 ± 0.00$	$? 0.01 ± 0.00$

Tab.8

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