Spectroscopy of $$\mathbf {B_c}$$ mesons and the possibility of finding exotic $$\mathbf {B_c}$$-like structures

Abstract

Abstract The bottom-charmed ( $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> ) mesons are more stable than their charmonium ( $$c{{\bar{c}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>c</mml:mi><mml:mover><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> ) and bottomium ( $$b{{\bar{b}}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi>b</mml:mi><mml:mover><mml:mrow><mml:mi>b</mml:mi></mml:mrow><mml:mrow><mml:mo>¯</mml:mo></mml:mrow></mml:mover></mml:mrow></mml:math> ) partners because they cannot annihilate into gluons. However, the low production cross-sections and signal-to-background ratios avoided until now their clear identification. The recent experimental results reported by CMS and LHCb at CERN open the possibility of having a $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> spectrum as complete as the ones of charmonium and bottomonium. Motivated by this expectation, we compute bottom-charmed meson masses in the region energies in which decay meson–meson thresholds are opened, looking for the analogs to the X (3872) in the $$B_c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>B</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> spectroscopy. We use a constituent quark model in which quark–antiquark degrees of freedom are complemented by four-body Fock states configurations. The model has been applied to a wide range of hadronic observables, in particular to the X (3872), and thus the model parameters are completely constrained. No extra states are found in the $$J^P=0^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mn>0</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> and $$J^P=1^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mn>1</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> sectors. However, in the $$J^P=2^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>J</mml:mi><mml:mi>P</mml:mi></mml:msup><mml:mo>=</mml:mo><mml:msup><mml:mn>2</mml:mn><mml:mo>+</mml:mo></mml:msup></mml:mrow></mml:math> sector we found an additional state very close to the $$D^*B^*$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:msup><mml:mi>D</mml:mi><mml:mo>∗</mml:mo></mml:msup><mml:msup><mml:mi>B</mml:mi><mml:mo>∗</mml:mo></mml:msup></mml:mrow></mml:math> threshold which could be experimentally detected.

Topics & Concepts