$S=-1$ meson-baryon interaction and the role of isospin filtering processes

A study of the meson-baryon interaction in the $S=-1$ sector is performed, employing a chiral SU(3) Lagrangian up to next-to-leading order (NLO) and implementing unitarization in coupled channels. The model is constrained by a large set of experimental data, paying special attention to processes that are sensitive to the NLO contributions, such as the $K^{-}p\to K^{+}{\mathrm{\Xi }}^{-},K^0{\mathrm{\Xi }}^0$ reactions. The consideration of additional cross sections in single isospin channels, $K^{-}p\to \eta \mathrm{\Lambda },\eta \mathrm{\Sigma }$, has been found to provide NLO low-energy constants of rather similar size. The stability of these constants has also been tested by the inclusion of explicit resonant terms. Predictions for new isospin filtering processes, like the $I=1K_L^{0}p\to K^{+}{\mathrm{\Xi }}^0$ reaction that could be measured at the proposed secondary $K_L^0$ beam at Jlab, or the weak decay of the ${\mathrm{\Lambda }}_b$ into a $J/\mathrm{\Psi }$ and different meson-baryon pairs in $I=0$, available at LHCb, are presented. The measurement of such reactions would put valuable constraints on the chiral models describing the $S=-1$ meson-baryon interaction.

Figure 1

Feynman diagrams for the meson-baryon interaction: Weinberg-Tomozawa term (i), direct and crossed Born terms (ii) and (iii), and NLO terms (iv). Dashed (solid) lines represent the pseudoscalar octet mesons (octet baryons).

Figure 2

Diagram describing the weak decay of the ${\mathrm{\Lambda }}_b$ into the $J/\psi$ and a meson-baryon pair formed through a hadronization mechanism.

Figure 3

Diagrammatic representation of the decay amplitude for ${\mathrm{\Lambda }}_b\to J/\psi {\varphi }_j{B}_j$: (a) tree level and (b) the ${\varphi }_j{M}_j=\eta \mathrm{\Lambda },K^{+}{\mathrm{\Xi }}^{-}$ production through the coupled channel interaction of the initially produced ${\varphi }_i{M}_i=\eta \mathrm{\Lambda },\overline{K}N$ meson-baryon pairs.

Figure 4

$S$-type diagram describing the resonant amplitude, where the intermediate hyperon $[Y=\mathrm{\Lambda }(1890)$, $\mathrm{\Sigma }\left(2030\right)$, $\mathrm{\Sigma }\left(2250\right)]$ has mass $M_J$ and decay width ${\mathrm{\Gamma }}_J$.

Figure 5

Total cross sections of the $K^{-}p\to K^{-}p,{\overline{K}}^{0}n,{\pi }^{-}{\mathrm{\Sigma }}^{+},{\pi }^{+}{\mathrm{\Sigma }}^{-},{\pi }^0{\mathrm{\Sigma }}^0,{\pi }^0\mathrm{\Lambda },\eta \mathrm{\Lambda },\eta {\mathrm{\Sigma }}^0,K^{+}{\mathrm{\Xi }}^{-},K^0{\mathrm{\Xi }}^0$ reactions obtained for the WT+Born+NLO fit (solid line), with the corresponding estimation of the error bands (grey area), and for the WT+Born+NLO+RES fit (dashed line). Experimental data have been taken from [33, 34, 35, 36, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70]. See text for a detailed description of the models. The inset in the fourth panel of the left column shows the $K^{-}p\to \eta \mathrm{\Lambda }$ cross section in a reduced energy range close to threshold.

Figure 6

Pole positions of the $\mathrm{\Lambda }\left(1405\right)$ for the approaches included in Table 3, where we have also included the results from [27]. The colored areas indicate the possible pole positions by varying the fitting parameters within their corresponding error bars in our WT+NLO+Born model.

Figure 7

Squared $I=0$ amplitudes for transitions from initial $\overline{K}N$ and $\pi \mathrm{\Sigma }$ channels to final $\pi \mathrm{\Sigma }$, weighted by the three-momentum of the final particles in the c.m.

Figure 8

Total cross sections of the $K_L^{0}p\to K^{+}{\mathrm{\Xi }}^0$ reactions for the models described in the present work (WT+Born+NLO and WT+Born+NLO+RES) and for the models of our previous studies [30, 32]. A more detailed explanation can be found in the text. The grey area corresponds to the error band related to the WT+Born+NLO fit and the experimental points of the $I=1K^{-}n\to K^0{\mathrm{\Xi }}^{-}$ reaction, taken from [46, 47] and divided by 2; see Sec. 2b1 for more details.

Figure 9

The total cross section data of the $K^{-}p\to K^0{\mathrm{\Xi }}^0$ reaction is represented in the top panels, where the left figure corresponds to the WT+NLO model [30] and the right one corresponds to the WT+Born+NLO model. The same distribution for the bottom panels where the $K^{-}p\to K^{+}{\mathrm{\Xi }}^{-}$ cross section data are represented. The figure shows the complete results by means of solid lines, the results where only isospin $I=1$ component (dashed lines) or the $I=0$ one (dot-dashed line) have been retained.

Figure 10

Invariant mass distributions, in arbitrary units, of $K^{+}{\mathrm{\Xi }}^{-}$ states (upper panel) and $\eta \mathrm{\Lambda }$ states (lower panel) obtained for the two models discussed in this section: WT+NLO [30] (dash-dotted lines) and WT+Born+NLO (solid lines). The pure phase-space (PS) distributions (dotted and dashed lines) are normalized to the corresponding invariant mass distribution; see more details in the text. The invariant mass distribution of $K^{+}{\mathrm{\Xi }}^{-}$ state and the corresponding phase-space distribution for WT+Born+NLO are multiplied by a factor 10 to aid its visualization.