Stability of the Zagreb realization of the Carnegie-Mellon-Berkeley coupled-channels unitary model

In Had$\check{\mathrm{z}}$imehmedović et al. [Phys. Rev. C 84, 035204 (2011)] we have used the Zagreb realization of Carnegie-Melon-Berkeley coupled-channel, unitary model as a tool for extracting pole positions from the world collection of partial-wave data, with the aim of eliminating model dependence in pole-search procedures. In order that the method is sensible, we in this paper discuss the stability of the method with respect to the strong variation of different model ingredients. We show that the Zagreb CMB procedure is very stable with strong variation of the model assumptions and that it can reliably predict the pole positions of the fitted partial-wave amplitudes.

Figure 1

Parameterization of channel-intermediate particle vertex in the CMB model.

Figure 2

Pietarinen expansion for the $S_{11}$ partial wave.

Figure 3

The principle of numerically finding the pole positions using Eq. (12) with the Pietarinen expansion of the channel propagator.

Figure 4

The input data sets together with our fit to them with the standard model for the S${}_{11}$, $P_{11}$, and $D_{13}$ partial waves $T$ matrices.

Figure 5

Real and imaginary parts of channel propagator. Several values of parameter $f_0$ are used: $0.4$, $0.7$, and $0.9$.

Figure 6

Real and imaginary parts of the $S_{11}$, $P_{11}$, and $D_{13}$ elastic channel propagator. We change the intermediate part of the channel propagator.

Figure 7

The extracted $S_{11}$, $P_{11}$, and $D_{13}$ partial-wave $T$-matrix poles using different solutions of the channel propagator. We change the intermediate part of the channel propagator and the modification is the same for all three used channels. Red arrows indicate the position of standard solution poles.

Figure 8

Real and imaginary parts of the $S_{11}$, $P_{11}$, and $D_{13}$ elastic channel propagator. Threshold behavior: Sol th1, $\mathrm{Im}{\Phi }_{\text{corr}}=\mathrm{Im}\Phi ·\sqrt{q}(a+c{s}^2)$; Sol th2, $\mathrm{Im}{\Phi }_{\text{corr}}=\mathrm{Im}\Phi ·\sqrt{q}(a+0.5s+c{s}^2)$; Sol th3, $\mathrm{Im}{\Phi }_{\text{corr}}=\mathrm{Im}\Phi ·\left(\frac{1}{\sqrt{q}}\right)(a+c{s}^2)$; Sol th4, $\mathrm{Im}{\Phi }_{\text{corr}}=\mathrm{Im}\Phi ·\left(\frac{1}{\sqrt{q}}\right)(a-0.5s+c{s}^2)$.

Figure 9

The extracted $S_{11}$, $P_{11}$, and $D_{13}$ partial-wave $T$-matrix poles using different solutions of the channel propagator. We change the threshold behavior of the channel propagator and the modification is the same for all three used channels. Red arrows indicate the position of standard solution poles.

Figure 10

Real part of the S${}_{11}$, $P_{11}$, and $D_{13}$ elastic channel propagator. We change the dispersion integral subtraction constant.

Figure 11

The extracted S${}_{11}$, $P_{11}$, and D${}_{13}$ partial-wave $T$-matrix poles using different solutions of the channel propagator. We change the dispersion integral subtraction constant for all three used channels. Red arrows indicate the positions of standard solution poles.

Figure 12

Real part of the S${}_{11}$, $P_{11}$, and $D_{13}$ elastic channel propagator. We change the dispersion integral subtraction point value.

Figure 13

The extracted $S_{11}$, $P_{11}$, and $D_{13}$ partial-waves $T$-matrix poles. Additional background poles below and above the physical region are added. Red arrows indicate the position of the standard solution poles.

Figure 14

Real and imaginary parts of the $S_{11}$, $P_{11}$, and $D_{13}$ effective channel propagator.

Figure 15

The extracted $S_{11}$, $P_{11}$, and $D_{13}$ partial-wave $T$-matrix poles using different masses of the effective channel.