Figure 1

The upper plot shows the $K_{l3}$ form factor $f_0(q^2)$, with a 68% error band, obtained from a fit using a once-subtracted Omnès relation. Red points are the inputs from Table  and the blue square shows the result from [12] for $f_0(0)$ (not fitted). The lower plot shows the isospin-$1/2$ $K\pi$ $s$-wave phase shift with a 68% error band (gray). The phase-shift plot also shows experimental data points from [39] (blue), [40] (red), [41] (cyan), [42] (green), and [20] (orange).Reuse & Permissions

Figure 2

The upper plot shows the $K_{l3}$ form factor $f_0(q^2)$, with a 68% error band, obtained from a fit using a twice-subtracted Omnès relation. Red points are the inputs from Table  and the blue square shows the result from 12 for $f_0(0)$ (not fitted). The lower plot shows the isospin-$1/2$ $K\pi$ $s$-wave phase shift with a 68% error band (gray). The green dotted line shows the phase shift obtained with the inclusion of resonances (see text in paragraph preceding discussion of the $K\eta$ coupled channel). The dashed lines indicate the corresponding band obtained by artificially halving the error on the last four input form-factor points in Table . The phase-shift plot also shows experimental data points as in Fig. 1.Reuse & Permissions

Figure 3

The upper plot shows the $K_{l3}$ form factor $f_0(q^2)$, with a 68% error band, obtained from a fit using a twice-subtracted Omnès relation, implementing a linear relation between $f_0(0)$ and the scattering length as described in the text. Red points are the inputs from Table  and the blue square shows the result from 12 for $f_0(0)$ (not fitted). The lower plot shows the isospin-$1/2$ $K\pi$ $s$-wave phase shift with a 68% error band (gray). The phase-shift plot also shows experimental data points as in Fig. 1.Reuse & Permissions

Figure 4

$B\pi$ isospin-$1/2$ scalar form factor and phase shift, together with 68% confidence level bounds (gray bands). The points on the form-factor plot are the inputs given in Table . The dashed curves on the phase-shift plot show the effect on the statistical uncertainty of reducing the input errors to $1/4$ of their current value. The intercept of the phase shift with the horizontal line at 90° indicates the position of a resonance.Reuse & Permissions

Figure 5

$D\pi$ isospin-$1/2$ scalar form factor and phase shift, together with 68% confidence level bounds. The points on the form-factor plot are read off from Figure 3 of 34, but with error bars expanded to include a 10% systematic error, and are displayed to show the good agreement with our fit. The intercept of the phase shift with the horizontal line at 90° indicates the position of a resonance.Reuse & Permissions