Fig. 1 | The European Physical Journal A

Fig. 1

From: Thermal study of a coupled-channel system: a brief review

Fig. 1

Landscape of S-matrix phase \(\ln \mathrm{det} \, S(\sqrt{s})\) of the \(\pi \pi , K {\bar{K}}\) coupled-channel system on the energy sheets (left) I and II and (right) IV and III. See Table 1 for the definition of Riemann sheets. Color signifies the value of the phase angle and contour lines specify magnitudes of \( \ln \, \vert \mathrm{det} \, S \vert \). Poles (roots) are characterized by the clockwise (anti-clockwise) rotation of the color phase and by a large, positive (negative) values of \( \ln \, \vert \mathrm{det} \, S \vert \) reflected in the contour lines. The physical line is identified with the real line in sheet I (\(\mathrm{Re} \,(\sqrt{s}) + i \, 0^+\)). The continuity of the phase across the Riemann sheets (see text): between sheet I and II (I and III) below (above) the \(K {\bar{K}}\) threshold, is clearly visible as the continuity of color across the real line. Five resonances can be identified in this model: 3 on sheet II (left, bottom half) and 2 on sheet III (right, bottom half)

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