Analysis of the isospin eigenstate $$\bar{D} \Sigma _c$$, $$\bar{D}^{*} \Sigma _c$$, and $$\bar{D} \Sigma _c^{*}$$ pentaquarks by their electromagnetic properties
U. Özdem
Abstract
Abstract To shed light on the nature of the controversial and not yet fully understood exotic states, we are carrying out a systematic study of their electromagnetic properties. The magnetic moment of a hadron state is as fundamental a dynamical quantity as its mass and contains valuable information on the deep underlying structure. In this study, we use the QCD light-cone sum rule to extract the magnetic moments of the $$\mathrm {P_{c}(4312)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4312</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , $$\mathrm {P_{c}(4380)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4380</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> , and $$\mathrm {P_{c}(4440)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>P</mml:mi> <mml:mi>c</mml:mi> </mml:msub> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>4440</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> pentaquarks by considering them as the molecular picture with spin-parity $$\mathrm {J^P= \frac{1}{2}^-}$$ <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:mfrac> <mml:mn>1</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> , $$\mathrm {J^P= \frac{3}{2}^-}$$ <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:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> , and $$\mathrm {J^P= \frac{3}{2}^-}$$ <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:mfrac> <mml:mn>3</mml:mn> <mml:mn>2</mml:mn> </mml:mfrac> <mml:mo>-</mml:mo> </mml:msup> </mml:mrow> </mml:math> , respectively. We define the isospin of the interpolating currents of these states, which is the key to solving the puzzle of the hidden-charm pentaquark states, to make these analyses more precise and reliable. We have compared our results with other theoretical predictions that could be a useful complementary tool for the interpretation of the hidden-charm pentaquark sector, and we observe that they are not in mutual agreement with each other. We have also calculated higher multipole moments for spin-3/2 $$\bar{D}^{*} \Sigma _c$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:msup> <mml:msub> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> and $$\bar{D} \Sigma _c^{*}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>D</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mmultiscripts> <mml:mi>Σ</mml:mi> <mml:mi>c</mml:mi> <mml:mrow> <mml:mrow/> <mml:mo>∗</mml:mo> </mml:mrow> </mml:mmultiscripts> </mml:mrow> </mml:math> pentaquarks, indicating a non-spherical charge distribution.