Electromagnetic properties of the P c (4312) pentaquark state Ulaş Özdem † Health Services Vocational School of Higher Education, Istanbul Aydin University, Sefakoy-Kucukcekmece, 34295 Istanbul, Turkey P c (4312) ¯ DΣ c J P = 1 2 − P c (4312) P c (4312) Abstract: Using the light-cone QCD sum rules, we evaluate the magnetic moment of the pentaquark state by considering both the molecular and diquark-diquark-antiquark state, with quantum numbers . In the calculations, we use the diquark-diquark-antiquark and molecular form of the interpolating currents for the pentaquark and the distribution amplitudes of the photon. The numerical results for the magnetic moment obtained using the two different pictures are quite different from each other, which can be used to pin down the underlying structure of . Any experimental measurement of the magnetic moment in the near future will provide an un- derstanding of the internal structure of this pentaquark state. Keywords: pentaquarks, magnetic moment, molecular picture, diquark-diquark-antiquark picture DOI: 10.1088/1674-1137/abd01c I. MOTIVATION P + c (4380) P + c (4450) J/ψ p Λ 0 b → J/ψ K − p P + c (4380) 4380 ± 8 ± 29 205 ± 18± 86 P + c (4450) 4449.8± 1.7 ± 2.5 39 ± 5 ± 19 3/2 5/2 Research into exotic hadrons that are composed of multi-quark states is among the current subjects of in- terest in particle physics. Experimental information col- lected through various collaborations, and theoretical pro- gress obtained using different theoretical models, consti- tutes the rapidly growing field of exotic studies [1-10]. In 2015, the LHCb Collaboration reported two pentaquark states, and , in the invariant mass spectrum of in the decay [11]. From the LHCb measurements the has a mass of MeV and a width of MeV, while the has a mass of MeV and a width of MeV. The quantum numbers of these states were determined by partial wave analysis and the spins reported as and with opposite parities. In 2019, the LHCb Collaboration updated their analysis and reported three new narrow pentaquark states [12]. The measured masses and decay widths are: P c (4312) : M = 4311.9 ± 0.7 +6.8 −0.6 , Γ= 9.80 ± 2.7 +3.7 −4.5 , P c (4440) : M = 4440.3 ± 1.3 +4.1 −4.7 , Γ= 20.6 ± 4.9 +8.7 −10.1 , P c (4457) : M = 4457.3 ± 0.6 +4.1 −1.7 , Γ= 6.40 ± 2.0 +5.7 −1.9 . All values are given in units of MeV. From the updated P c (4450) P c (4440) P c (4457) P c (4312) P c (4380) P c (4312) Σ c ¯ D P c (4440) P c (4457) Σ c ¯ D ∗ J/ψ p measurements, we observe that the previous peak of is now split into two narrower structures, and , and a fluctuation observed in the old spectrum is now a new narrow resonance, . The broad resonance is now less clear and its existence needs to be verified in a complete amplitude analysis. One can see that the is just below the threshold, while the masses of the and are slightly lower than the threshold. Since these states have only been observed in the invariant mass spectrum by the LHCb Collaboration, it is important to investigate some other decay mechanisms to better understand their internal structure. The experiment- al discovery stimulated extensive theoretical predictions on the nature of pentaquark states, their spectroscopic parameters, decays and production mechanisms, employ- ing different scenarios and frameworks [13-45]. The ma- jority of these studies are aimed at understanding the spectroscopy and decay properties of these particles, and the results obtained using different models are close to each other. To put it another way, the spectroscopic para- meters or decay properties alone cannot distinguish the substructure of the pentaquark states. Therefore, addition- al investigations of these pentaquark states are required to explain the situation with the pentaquark resonances. J/ψ The magnetic moment of hadrons is one of the most significant properties in the study of their electromagnet- ic structure, and can also give important knowledge of the QCD dynamics in the low energy region. It is also a key component in the computation of photo-production cross sections, which can ensure an independent investig- ation of the pentaquark states. In this work, we focus all Received 8 November 2020; Accepted 30 November 2020; Published online 4 January 2021 † E-mail: ulasozdem@aydin.edu.tr Chinese Physics C Vol. 45, No. 2 (2021) 023119 ©2021 Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Sciences and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd 023119-1