Molecular pentaquarks with hidden charm and double strangeness

Abstract

We analyze theoretically the coupled-channel meson-baryon interaction with global flavor <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mover accent="true"><a:mi>c</a:mi><a:mo stretchy="false">¯</a:mo></a:mover><a:mi>c</a:mi><a:mi>s</a:mi><a:mi>s</a:mi><a:mi>n</a:mi></a:math> and <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mover accent="true"><e:mi>c</e:mi><e:mo stretchy="false">¯</e:mo></e:mover><e:mi>c</e:mi><e:mi>s</e:mi><e:mi>s</e:mi><e:mi>s</e:mi></e:math>, where mesons are pseudoscalars or vectors, and baryons have <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:msup><i:mi>J</i:mi><i:mi>P</i:mi></i:msup><i:mo>=</i:mo><i:mn>1</i:mn><i:mo>/</i:mo><i:msup><i:mn>2</i:mn><i:mo>+</i:mo></i:msup></i:math> or <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mn>3</k:mn><k:mo>/</k:mo><k:msup><k:mn>2</k:mn><k:mo>+</k:mo></k:msup></k:math>. The aim is to explore whether the nonlinear dynamics inherent in the unitarization process within coupled channels can dynamically generate double- and triple-strange pentaquark-type states (<m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:msub><m:mi>P</m:mi><m:mrow><m:mi>c</m:mi><m:mi>s</m:mi><m:mi>s</m:mi></m:mrow></m:msub></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:msub><o:mi>P</o:mi><o:mrow><o:mi>c</o:mi><o:mi>s</o:mi><o:mi>s</o:mi><o:mi>s</o:mi></o:mrow></o:msub></o:math>, respectively), for which there is no experimental evidence to date. We evaluate the s-wave scattering matrix by implementing unitarity in coupled channels, using potential kernels obtained from t-channel vector meson exchange. The required <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mi>P</q:mi><q:mi>P</q:mi><q:mi>V</q:mi></q:math> and <s:math xmlns:s="http://www.w3.org/1998/Math/MathML" display="inline"><s:mi>V</s:mi><s:mi>V</s:mi><s:mi>V</s:mi></s:math> vertices are obtained from Lagrangians derived through appropriate extensions of the local hidden gauge symmetry approach to the charm sector, while capitalizing on the symmetry of the spin and flavor wave function to evaluate the <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"><u:mi>B</u:mi><u:mi>B</u:mi><u:mi>V</u:mi></u:math> vertex. We find four different poles in the double strange sector, some of them degenerate in spin. For the triple-strange channel, we find the meson-baryon interaction insufficient to generate a bound or resonance state through the unitary coupled-channel dynamics. Published by the American Physical Society 2024

Topics & Concepts