<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4312</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo></mml:msup></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4380</mml:mn><mml:msup><mml:mo stretchy="false">)</mml:mo><mml:mo>+</mml:mo></mml:msup></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4457</mml:mn><mml:msup><mml:mrow><mml:mo stretchy="false">)</mml:mo></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> as double triangle cusps
Satoshi Nakamura
Abstract
Understanding the nature of the hidden charm pentaquark(like) signals in the LHCb data for ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$ is a central problem of hadron spectroscopy. We propose a scenario completely different from previous ones such as hadron molecules and compact pentaquarks. We identify relevant double triangle mechanisms with leading or lower-order singularities. The associated anomalous threshold cusps at the ${\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}{\overline{D}}^{(*)}$ thresholds are significantly more singular than the ordinary ones. Then we demonstrate that the double triangle amplitudes reproduce the peak structures of ${P}_{c}(4312{)}^{+}$, ${P}_{c}(4380{)}^{+}$, and ${P}_{c}(4457{)}^{+}$ in the LHCb data, through an interference with other common mechanisms. Only the ${P}_{c}(4440{)}^{+}$ peak is due to a resonance with a width and strength significantly smaller than previously estimated. ${P}_{c}^{+}$ signals are expected in other processes, and the proposed model (partly) explains the current data, such as the GlueX $J/\ensuremath{\psi}$ photoproduction data with no ${P}_{c}^{+}$ signals and the LHCb ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{\ensuremath{\pi}}^{\ensuremath{-}}$ data with a possible signal only from ${P}_{c}(4440{)}^{+}$. In general, the double triangle singularity is now a possible option to interpret resonancelike structures near thresholds.