| Experiment | Measurement [10-6] | $\Delta\chi^2$ | Reference | Comments |
|---|---|---|---|---|
| Average | $1.27 \pm0.19$ | 7.49 | $p=0.59$ (ndf=9) | |
| LHCb | $1.43 \pm0.05 \pm0.27$ using ${\cal{B}}(B^+ \to \pi^+ \pi^+ \pi^-)$ | 0.36 | Phys.Rev.Lett. 124,031801 (2020) | Result extracted from Dalitz-plot analysis of $B^+ \to \pi^+ \pi^+ \pi^-$ decays. This analysis uses three different approaches: isobar, $K$-matrix and quasi-model-independent, to describe the $S$-wave component. The results are taken from the isobar model with an additional error accounting for the different S-wave methods as reported in Appendix D of Ref.~\cite{LHCb:2019sus}. Multiple systematic uncertainties are added in quadrature. |
| BaBar | $0.9 \pm0.2\,^{+0.3}_{-0.1}$ | 0.98 | Phys.Rev.D 79,072006 (2009) | Result extracted from Dalitz-plot analysis of $B^+ \to \pi^+ \pi^+ \pi^-$ decays. Multiple systematic uncertainties are added in quadrature. |
| Source | Parameter | Correlation [%] | Value | $\Delta\chi^2$ |
|---|---|---|---|---|
| fit | ${\cal B}(B^+ \to \rho^0(770) \pi^+)$ | 14.4 | $8.76 \pm0.46 \times 10^{-6}$ | |
| fit | ${\cal{B}}(B^+ \to \pi^+ \pi^+ \pi^-)~S\rm{-wave}$ | 5.1 | $4.04 \pm0.64 \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \omega(782) \pi^+)$ | -4.5 | $6.60\,^{+0.46}_{-0.45} \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \rho(1450)^0 \pi^+) \times {\cal B}(\rho(1450)^0 \to \pi^+ \pi^-)$ | 1.9 | $1.14\,^{+0.59}_{-0.67} \times 10^{-6}$ | |
| fit | ${\cal B}(B^+ \to \rho_3(1690)^0 \pi^+)$ | 1.0 | $5 \pm10 \times 10^{-7}$ | |
| fit | ${\cal B}(B^+ \to \rho_3(1690)^0 \pi^+) \times {\cal B}(\rho_3(1690)^0 \to \pi^+ \pi^-)$ | 0.4 | $8 \pm16 \times 10^{-8}$ | |
| fit | ${\cal B}(B^+ \to f_2(1270) \pi^+)$ | -0.1 | $2.26 \pm0.37 \times 10^{-6}$ | |
| external | ${\cal{B}}(B^+ \to \pi^+ \pi^+ \pi^-)$ | 22.1 | $1.590 \pm0.045 \times 10^{-5}$ | 0.00 |
| external | ${\cal B}(f_2(1270) \to \pi \pi)$ | -1.9 | $0.843\,^{+0.031}_{-0.010}$ | 0.00 |
| external | ${\cal B}(\omega(782) \to \pi^+ \pi^-)$ | 0.0 | $1.44\,^{+0.12}_{-0.11} \times 10^{-2}$ | 0.55 |
| external | ${\cal B}(\rho_3(1690)^0 \to \pi \pi)$ | -0.0 | $0.236 \pm0.013$ | 0.00 |