As in previous decades, a comprehensive understanding of the intricate internal configuration of hadrons continues to be a central objective within both experimental and theoretical hadron physics. This pursuit plays a pivotal role in advancing our knowledge of quantum chromodynamics (QCD) and critically evaluating the robustness and accuracy of the theoretical models developed to date. Furthermore, deciphering the underlying mechanisms of exotic states, both those currently observed and those anticipated in future experiments, remains a pressing and unresolved challenge. Motivated by this, in the present study, we investigate the electromagnetic properties of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2420</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">(</mo><mn>2400</mn><mo stretchy="false">)</mo></math> molecular tetraquark states with quantum numbers <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mrow><mi>P</mi><mi>C</mi></mrow></msup><mo>=</mo><msup><mn>1</mn><mrow><mo>−</mo><mo>−</mo></mrow></msup></math>, using the QCD light-cone sum rule method. These states are analyzed within a hadronic molecular framework, where their magnetic and quadrupole moments are computed to probe internal structure and geometric deformation. Our results reveal distinct electromagnetic signatures, with the magnetic moments primarily dominated by light-quark contributions, and the quadrupole moments suggesting an oblate charge distribution. The findings are compared with prior studies assuming compact tetraquark configurations, emphasizing the sensitivity of electromagnetic observables to the underlying hadronic structure. This analysis provides critical insights into the nature of exotic hadrons and contributes to the broader understanding of QCD dynamics in the nonperturbative regime.

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<math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mi>D</mi><msub><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mn>1</mn></msub><mo stretchy="false">(</mo><mn>2420</mn><mo stretchy="false">)</mo></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>D</mi><mo>*</mo></msup><msup><mover accent="true"><mi>D</mi><mo stretchy="false">¯</mo></mover><mo>*</mo></msup><mo stretchy="false">(</mo><mn>2400</mn><mo stretchy="false">)</mo></math> molecular states: Probing their electromagnetic fingerprints

In this work, the electromagnetic structure of the hidden-charm pentaquark $$P_c(4337)$$ is investigated within the diquark–diquark–antiquark model using the QCD light-cone sum rule approach. The magnetic moments of the $$ P_c(4337) $$ state are calculated for the spin-parity assignments $$ J^P = \frac{1}{2}^- $$ and $$\frac{3}{2}^-.$$ The results are found to be $$ \mu _{P_c} = 1.76 \pm 0.44~\mu _N $$ for the $$ \frac{1}{2}^- $$ case and $$ \mu _{P_c} = -1.38 \pm 0.35~\mu _N $$ for the $$ \frac{3}{2}^- $$ scenario. These findings offer important insights into the internal quark-gluon structure and electromagnetic features of this multiquark system. Beyond their theoretical relevance, the results serve as essential benchmarks for future experimental studies aimed at determining the quantum numbers and underlying configuration of the $$ P_c(4337) .$$ Additionally, the electric quadrupole and magnetic octupole moments of the spin- $$\frac{3}{2}$$ state are extracted, indicating a non-spherical charge distribution for this exotic pentaquark.

Probing the electromagnetic structure of the $$P_c(4337)^+$$ pentaquark: insights from a diquark–diquark–antiquark picture for $$J^P = \frac{1}{2}^-$$ and $$\frac{3}{2}^-$$ states

To shed light on the properties of states whose nature, internal structure, and spin-parity quantum numbers are not fully elucidated, we systematically study their electromagnetic properties. In light of this concept, we present a comprehensive analysis of the magnetic dipole moment of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow></math> pentaquark within the context of QCD light cone sum rules, utilizing three distinct interpolating currents in the form of diquark-diquark-antiquark configurations that are likely to couple this pentaquark with <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msup><mi>J</mi><mi>P</mi></msup><mo>=</mo><msup><mfrac><mn>3</mn><mn>2</mn></mfrac><mo>−</mo></msup></math> quantum numbers. The numerical analysis yielded the following results: <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>μ</mi></mrow><mrow><msubsup><mrow><mi>J</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mn>1</mn></mrow></msubsup></mrow></msub><mo>=</mo><mo>−</mo><mn>0.60</mn><mo>±</mo><mn>0.15</mn><msub><mrow><mi>μ</mi></mrow><mrow><mi>N</mi></mrow></msub></mrow></math>, <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><msubsup><mi>J</mi><mi>μ</mi><mn>2</mn></msubsup></msub><mo>=</mo><mn>1.60</mn><mo>±</mo><mn>0.30</mn><msub><mi>μ</mi><mi>N</mi></msub></math>, and <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>μ</mi><msubsup><mi>J</mi><mi>μ</mi><mn>3</mn></msubsup></msub><mo>=</mo><mn>0.99</mn><mo>±</mo><mn>0.20</mn><msub><mi>μ</mi><mi>N</mi></msub></math>. The numerical results obtained have led to the conclusion that the magnetic dipole moments of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math> state are capable of projecting its inner structure. As is seen, the different diquark-diquark-antiquark configurations of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow></math> pentaquark state contain important information about its internal structure. Thus, this study will provide prominent data to investigate the inner structure of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math> pentaquark state. We compared our results with other theoretical predictions that could be a useful complementary tool for interpreting the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><msub><mi>P</mi><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></math> state. A thorough examination reveals that the results obtained by employing disparate theoretical approaches and different internal structure models are not consistent with each other. It is recommended that further studies be conducted using alternative nonperturbative techniques to gain a more comprehensive understanding of the observed results.

Shedding light on the nature of the <math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><msub><mrow><mi>P</mi></mrow><mrow><mi>c</mi><mi>s</mi></mrow></msub><mo stretchy="false">(</mo><mn>4459</mn><mo stretchy="false">)</mo></mrow></math> pentaquark state

Accessing a full picture of the internal structure of hadrons would be a key topic of hadron physics, with the main motivation to study the strong interaction binding the visible matter. Furthermore, the underlying structure of known exotic states remains an unresolved fundamental issue in hadron physics, which is currently being addressed by hadron physics community. It is well known that electromagnetic characteristics can serve as a distinguishing feature for states whose internal structures are complex and not yet fully understood. The aim of this study is to determine the magnetic moments of vector hidden-charm tetraquark states by making use of QCD light-cone sum rules. In order to achieve this objective, the states mentioned above are considered in terms of the diquark-antidiquark structure. Subsequently, a comprehensive examination is conducted, with four distinct interpolating currents being given particular consideration, as these have the potential to couple with the aforementioned states. It has been observed that there are considerable discrepancies between the magnetic moment results extracted employing different diquark-antidiquark structures. Such a prediction may be interpreted as the possibility of more than one tetraquark with the identical quantum numbers and similar quark constituents but with different magnetic moments. The numerical predictions yielded have led to the conclusion that the magnetic moments of the vector hidden-charm tetraquark states are capable of projecting the inner structure of these states, which may then be used to determine their quark-gluon structure and quantum numbers. In order to provide a comprehensive analysis, the individual quark contributions to the magnetic moments are also examined. As a byproduct, the quadrupole moments of these states are also extracted, and the obtained values differ from zero, which indicates that the charge distribution of these states is not spherical.

Investigating the underlying structure of vector hidden-charm tetraquark states via their electromagnetic characteristics

The magnetic moments of the $$B_c$$ mesons provide significant insights into their inner structure and geometric shape. Furthermore, a comprehensive understanding of the electromagnetic characteristics of $$B_c$$ mesons is essential for advancing our knowledge of confinement and heavy flavor effects. In light of this, we proceed to extract the magnetic moments of the ground-state vector and axial-vector $$B_c$$ mesons through the medium of the QCD light-cone sum rules. The magnetic moments of the axial-vector and vector $$B_c$$ mesons are found to be $$\mu _{B_c}= -0.47 \pm 0.07~\mu _N$$ , and $$\mu _{B_c}= 0.15 \pm 0.02~\mu _N$$ , respectively. A comparison of our results for the vector $$B_c$$ meson with other theoretical predictions has revealed discrepancies between the various predictions, which could prove useful as a complementary tool for interpreting the vector $$B_c$$ meson. The current experimental data set is limited to a small number of observed states of beauty-charm mesons. However, theoretical studies can play a valuable role in elucidating their nature and guiding future experimental investigations.

Exploring electromagnetic characteristics of the vector and axial-vector $$B_c$$ mesons

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 $$\mathrm {P_{c}(4312)}$$ <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4312</mn> <mo>)</mo> </mrow> </mrow> </math> , $$\mathrm {P_{c}(4380)}$$ <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4380</mn> <mo>)</mo> </mrow> </mrow> </math> , and $$\mathrm {P_{c}(4440)}$$ <math> <mrow> <msub> <mi>P</mi> <mi>c</mi> </msub> <mrow> <mo>(</mo> <mn>4440</mn> <mo>)</mo> </mrow> </mrow> </math> pentaquarks by considering them as the molecular picture with spin-parity $$\mathrm {J^P= \frac{1}{2}^-}$$ <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> </mrow> </math> , $$\mathrm {J^P= \frac{3}{2}^-}$$ <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> </mrow> </math> , and $$\mathrm {J^P= \frac{3}{2}^-}$$ <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> </mrow> </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 $$\bar{D}^{*} \Sigma _c$$ <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </mrow> </math> and $$\bar{D} \Sigma _c^{*}$$ <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mmultiscripts> <mi>Σ</mi> <mi>c</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math> pentaquarks, indicating a non-spherical charge distribution.

Analysis of the isospin eigenstate $$\bar{D} \Sigma _c$$ <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </mrow> </math> , $$\bar{D}^{*} \Sigma _c$$ <math> <mrow> <msup> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </msup> <msub> <mi>Σ</mi> <mi>c</mi> </msub> </mrow> </math> , and $$\bar{D} \Sigma _c^{*}$$ <math> <mrow> <mover> <mrow> <mi>D</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mmultiscripts> <mi>Σ</mi> <mi>c</mi> <mrow> <mrow></mrow> <mo>∗</mo> </mrow> </mmultiscripts> </mrow> </math> pentaquarks by their electromagnetic properties

We are systematically studying the electromagnetic characteristics of multiquark systems to shed light on their internal structure, whose nature and quantum numbers are controversial. In this study, we investigate the magnetic dipole, electric quadrupole, and magnetic octupole moments of the $$\Xi _c^*{\bar{K}}$$ <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> state within the context of the QCD light-cone sum rule. During this analysis, we posit that the $$\Xi _c^*{\bar{K}}$$ <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> state assumes a molecular structure with quantum numbers $$J^P = \frac{3}{2}^-$$ <math> <mrow> <msup> <mi>J</mi> <mi>P</mi> </msup> <mo>=</mo> <msup> <mfrac> <mn>3</mn> <mn>2</mn> </mfrac> <mo>-</mo> </msup> </mrow> </math> . The extracted outcomes are given as $$\mu _{\Xi _c^*{\bar{K}}} = 0.15^{+0.04}_{-0.03}\,\mu _N$$ <math> <mrow> <msub> <mi>μ</mi> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mo>=</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>15</mn> <mrow> <mo>-</mo> <mn>0.03</mn> </mrow> <mrow> <mo>+</mo> <mn>0.04</mn> </mrow> </msubsup> <mspace width="0.166667em"></mspace> <msub> <mi>μ</mi> <mi>N</mi> </msub> </mrow> </math> , $${\mathcal {Q}}_{\Xi _c^*{\bar{K}}} = (-0.93^{+0.22}_{-0.17})\times 10^{-3}\,\textrm{fm}^{\textrm{2}}$$ <math> <mrow> <msub> <mi>Q</mi> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mo>-</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>93</mn> <mrow> <mo>-</mo> <mn>0.17</mn> </mrow> <mrow> <mo>+</mo> <mn>0.22</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>3</mn> </mrow> </msup> <mspace width="0.166667em"></mspace> <msup> <mtext>fm</mtext> <mtext>2</mtext> </msup> </mrow> </math> , and $${\mathcal {O}}_{\Xi _c^*{\bar{K}}} = (-0.45^{+0.10}_{-0.09})\times 10^{-4}\,{\textrm{fm}}^{\textrm{3}}$$ <math> <mrow> <msub> <mi>O</mi> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mo>-</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>45</mn> <mrow> <mo>-</mo> <mn>0.09</mn> </mrow> <mrow> <mo>+</mo> <mn>0.10</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>4</mn> </mrow> </msup> <mspace width="0.166667em"></mspace> <msup> <mrow> <mtext>fm</mtext> </mrow> <mtext>3</mtext> </msup> </mrow> </math> . The findings of this study, when considered alongside other pertinent characteristics, may assist in elucidating the nature of this controversial phenomenon.

Analysis of the $$\Xi _c^* {\bar{K}}$$ <math> <mrow> <msubsup> <mi>Ξ</mi> <mi>c</mi> <mo>∗</mo> </msubsup> <mover> <mrow> <mi>K</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> </mrow> </math> molecular pentaquark state by its electromagnetic properties

The magnetic moment yields an excellent framework to explore the inner structure of particles determined by the quark-gluon dynamics of QCD, as it is the leading-order response of a bound system to a weak external magnetic field. Motivated by this, in this study, the magnetic moments of possible axial-vector <math> <msub> <mi>T</mi> <mrow> <mi>bc</mi> <mover> <mi>u</mi> <mo>¯</mo> </mover> <mover> <mi>u</mi> <mo>¯</mo> </mover> </mrow> </msub> </math> $$ {T}_{bc\overline{u}\overline{u}} $$ , <math> <msub> <mi>T</mi> <mrow> <mi>bc</mi> <mover> <mi>d</mi> <mo>¯</mo> </mover> <mover> <mi>d</mi> <mo>¯</mo> </mover> </mrow> </msub> </math> $$ {T}_{bc\overline{d}\overline{d}} $$ , and <math> <msub> <mi>T</mi> <mrow> <mi>bc</mi> <mover> <mi>u</mi> <mo>¯</mo> </mover> <mover> <mi>d</mi> <mo>¯</mo> </mover> </mrow> </msub> </math> $$ {T}_{bc\overline{u}\overline{d}} $$ tetraquarks are obtained with the help of light-cone QCD sum rules. For this purpose, we assume that these states are represented as a diquark-antidiquark picture with different structures and interpolating currents. The magnetic moment results derived using different diquark-antidiquark configurations differ substantially from each other. This can be translated into more than one tetraquark state with the same quantum number and quark content yet possessing different magnetic moments. From the numerical results obtained, we have concluded that the magnetic moments of the T bc states can project their inner structure, which can be used for their quantum numbers and quark-gluon organization. The contribution of individual quarks to the magnetic moments is also analyzed for completeness. We hope that our predictions of the magnetic moments of the T bc tetraquarks, together with the results of other theoretical investigations of the spectroscopic parameters and decay widths of these interesting tetraquarks, may be valuable in the search for these states in future experiments and in unraveling the internal structure of these tetraquarks.

Unveiling the underlying structure of axial-vector bottom-charm tetraquarks in the light of their magnetic moments

To improve our understanding of the quark–gluon dynamics underlying multiquark states, we systematically study their electromagnetic properties. In this study, the magnetic and quadrupole moments of the theoretically predicted singly-charmed state with the quantum numbers $$\textrm{J}^\textrm{P} = 1^{+}$$ <math> <mrow> <msup> <mtext>J</mtext> <mtext>P</mtext> </msup> <mo>=</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </math> is investigated within the framework of the QCD light-cone sum rules method by considering the diquark–antidiquark configuration of this state with quark contents $$[ud][\bar{c}\bar{s}]$$ <math> <mrow> <mo>[</mo> <mi>u</mi> <mi>d</mi> <mo>]</mo> <mo>[</mo> <mover> <mrow> <mi>c</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mover> <mrow> <mi>s</mi> </mrow> <mrow> <mo>¯</mo> </mrow> </mover> <mo>]</mo> </mrow> </math> . The predicted results for the magnetic and quadrupole moments are as $$\mu _{\mathrm {X_{AV}}}=-0.89 ^{+0.14}_{-0.12}~\mu _N $$ <math> <mrow> <msub> <mi>μ</mi> <msub> <mi>X</mi> <mi>AV</mi> </msub> </msub> <mo>=</mo> <mo>-</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>89</mn> <mrow> <mo>-</mo> <mn>0.12</mn> </mrow> <mrow> <mo>+</mo> <mn>0.14</mn> </mrow> </msubsup> <mspace width="3.33333pt"></mspace> <msub> <mi>μ</mi> <mi>N</mi> </msub> </mrow> </math> and $$\mathcal {D}_{\mathrm {X_{AV}}} = (-0.46 ^{+0.07}_{-0.06})\times 10^{-2} ~\text{ fm}^2$$ <math> <mrow> <msub> <mi>D</mi> <msub> <mi>X</mi> <mi>AV</mi> </msub> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mo>-</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>46</mn> <mrow> <mo>-</mo> <mn>0.06</mn> </mrow> <mrow> <mo>+</mo> <mn>0.07</mn> </mrow> </msubsup> <mo>)</mo> </mrow> <mo>×</mo> <msup> <mn>10</mn> <mrow> <mo>-</mo> <mn>2</mn> </mrow> </msup> <mspace width="3.33333pt"></mspace> <mspace width="0.333333em"></mspace> <msup> <mtext>fm</mtext> <mn>2</mn> </msup> </mrow> </math> . The results obtained can be useful in determining the exact nature of this state. This work will hopefully stimulate experimental interest in the study of the electromagnetic properties of multiquark systems.

Analysis of the $$\mathrm {X_{AV}}$$ <math> <msub> <mi>X</mi> <mi>AV</mi> </msub> </math> state through its electromagnetic properties

We perform a systematic study of the electromagnetic properties of exotic states to shed light on their nature, which is still controversial and not fully understood. The magnetic dipole and higher multipole moments of a hadronic state are as fundamental a dynamical quantity as its mass, and they contain valuable information about the deep structure underlying it. In the present work, we have explored the magnetic dipole and higher multipole moments of the hidden-charm pentaquarks with quantum number <math><msup><mrow><mi>J</mi></mrow><mrow><mi>P</mi></mrow></msup><mo>=</mo><mn>3</mn><mo>/</mo><msup><mrow><mn>2</mn></mrow><mrow><mo>−</mo></mrow></msup></math> using the QCD light-cone sum rule method and different interpolating currents. The obtained results show that different interpolating currents employed to probe pentaquarks with the same quark content produce varying results for their magnetic dipole and higher multipole moments at all. This can be interpreted to mean that there is more than one hidden-charm pentaquark with identical quark content but with different magnetic dipole and higher multipole moments. The nature, internal structure, and quark-gluon configurations of these states can be better understood by studying their electromagnetic properties.