| Experiment | Measurement [10-6] | $\Delta\chi^2$ | Reference | Comments |
|---|---|---|---|---|
| Average | $4.04 \pm0.64$ | 7.49 | $p=0.59$ (ndf=9) | |
| LHCb | $4.04 \pm0.08 \pm0.64$ using ${\cal{B}}(B^+ \to \pi^+ \pi^+ \pi^-)$ | 0.00 | Phys.Rev.Lett. 124,031801 (2020) | LHCb accounts the $S$-wave component using a model that comprises the coherent sum of a $\sigma$ pole. See Ref.~\cite{LHCb:2019jta} for details. Multiple systematic uncertainties are added in quadrature. |
| Source | Parameter | Correlation [%] | Value | $\Delta\chi^2$ |
|---|---|---|---|---|
| fit | ${\cal B}(B^+ \to \rho^0(770) \pi^+)$ | 7.7 | $8.76 \pm0.46 \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to f_2(1270) \pi^+) \times {\cal B}(f_2(1270) \to \pi^+ \pi^-)$ | 5.1 | $1.27 \pm0.19 \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to f_2(1270) \pi^+)$ | 4.1 | $2.26 \pm0.37 \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \omega(782) \pi^+)$ | 2.6 | $6.60\,^{+0.46}_{-0.45} \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \rho(1450)^0 \pi^+) \times {\cal B}(\rho(1450)^0 \to \pi^+ \pi^-)$ | 1.7 | $1.14\,^{+0.59}_{-0.67} \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \rho_3(1690)^0 \pi^+) \times {\cal B}(\rho_3(1690)^0 \to \pi^+ \pi^-)$ | 0.3 | $8 \pm16 \times 10^{-8}$ | |
| fit | ${\cal B}(B^+ \to \rho_3(1690)^0 \pi^+)$ | -0.1 | $5 \pm10 \times 10^{-7}$ | |
| external | ${\cal{B}}(B^+ \to \pi^+ \pi^+ \pi^-)$ | 17.4 | $1.590 \pm0.045 \times 10^{-5}$ | 0.00 |
| external | ${\cal B}(\omega(782) \to \pi^+ \pi^-)$ | 3.1 | $1.44\,^{+0.12}_{-0.11} \times 10^{-2}$ | 0.55 |
| external | ${\cal B}(f_2(1270) \to \pi \pi)$ | -1.8 | $0.843\,^{+0.031}_{-0.010}$ | 0.00 |
| external | ${\cal B}(\rho_3(1690)^0 \to \pi \pi)$ | 0.0 | $0.236 \pm0.013$ | 0.00 |