<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> 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>4337</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 interfering <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:msup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> threshold cusps
Satoshi Nakamura, Atsushi Hosaka, Yasuhiro Yamaguchi
Abstract
The recent LHCb data on ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p\overline{p}$ revealed a new pentaquark-like ${P}_{c}(4337{)}^{+}$ structure, while finding no evidence for ${P}_{c}(4312{)}^{+}$ discovered earlier in ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$. Though puzzling, the data actually offer an important hint to understand the nature of the pentaquark candidates. We develop a model to analyze the ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p\overline{p}$ data. We find that a ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ one-loop mechanism causes a threshold cusp that fits well the ${P}_{c}(4337{)}^{+}$ peak. Also, the ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{D}}^{*}$ threshold cusps interfere with each other to reproduce an oscillating behavior in the proton helicity angle distribution. These results combined with our earlier analysis on ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$ indicate that ${P}_{c}(4312{)}^{+}$ and ${P}_{c}(4337{)}^{+}$ are created by different interference patterns between the ${\mathrm{\ensuremath{\Sigma}}}_{c}\overline{D}$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{D}}^{*}$ (anomalous) threshold cusps. The proposed scenario consistently explains why the ${P}_{c}(4312{)}^{+}$ and ${P}_{c}(4337{)}^{+}$ peaks appear in ${\mathrm{\ensuremath{\Lambda}}}_{b}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p{K}^{\ensuremath{-}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}J/\ensuremath{\psi}p\overline{p}$, respectively, but not vice versa or both.