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Identifying Hidden Charm Pentaquark Signal from Non-Resonant Background in Electron–Proton Scattering*

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Identifying Hidden Charm Pentaquark Signal from Non-Resonant Background in Electron–Proton Scattering* Chinese Physics C Vol. 44, No. 8 (2020) 084102 Identifying hidden charm pentaquark signal from non-resonant background in electron–proton scattering* 1,2;1) 1,2;2) 1,2;3) 3;4) Zhi Yang(杨智) Xu Cao(曹须) Yu-Tie Liang(梁羽铁) Jia-Jun Wu(吴佳俊) 1Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China 2University of Chinese Academy of Sciences, Beijing 100049, China 3School of Physical Sciences, University of Chinese Academy of Sciences (UCAS), Beijing 100049, China Abstract: In this study, we analyze the electroproduction of the LHCb pentaquark states with the assumption that they are resonant states. Our main concern is to investigate the final state distribution in the phase space to extract a feeble pentaquark signal from a large non-resonant background. The results indicate that the signal to background ra- tio will increase significantly with a proper kinematic cut, which will be beneficial for future experimental analysis. Keywords: pentaquark, electroproduction, Pomeron, electron-ion collider DOI: 10.1088/1674-1137/44/8/084102 1 Introduction diquark–diquark–antiquark states [11, 19-21], etc. A data- driven analysis of Pc(4312) found it to be a virtual state [22]. In contrast, several recent works found that the spin In the last few decades, numerous possible candid- parity assignments for Pc (4440) and Pc (4457) are sensit- ates for exotic Hadrons have been experimentally estab- ive to the details of the one-pion exchange potential [3, lished. Specifically, in 2015, the LHCb Collaboration an- 15, 23, 24]. The fits of the measured J= p -invariant nounced the observation of two pentaquark states, one mass distributions indeed point to different quantum = narrow Pc(4450), and one broad Pc(4380), in the J p - numbers for P (4440) and P (4457) [3]. Notably, a hid- Λ0 ! = − c c invariant mass distribution in the b J K p decay den charm pentaquark was predicted [25, 26] before it [1]. In 2019, the LHCb Collaboration updated know- was observed by the LHCb. Moreover, other possible ledge of the pentaquarks, with multiple collected data pentaquarks in a strange and bottom sector were sugges- samples of the same decay [2]. A new narrow pentaquark ted [27-30]; however, they have not yet been observed candidate, Pc(4312) , was observed, whereas the old experimentally. For more details, refer to the compre- Pc(4450) peak was found to be resolved into two narrow- hensive reviews in [31-39]. er structures, Pc(4440) and Pc(4457) , owing to the larger However, since its discovery, it has been noted that statistics. In a coupled-channel approach, it is argued that the narrow peaks of the pentaquarks could be caused by the existence of a narrow Pc(4380) is required by heavy triangle singularities [40, 41], and it was recently sugges- quark spin symmetry [3]. After their discovery, numer- ted to distinguish them in isospin breaking decays [39, ous discussions in association with their properties were 42]. Furthermore, their decay and production properties triggered, and various interpretations have been proposed are extensively studied in various scenarios [43-50]. To for their internal structure. Because their masses are close discriminate their nature, the production of pentaquarks (∗) to the ΣcD¯ thresholds, many studies assigned them as has been proposed in photo-induced [51-55] and pion-in- (∗) ΣcD¯ molecular states [3-17]. Alternative explanations duced reactions [56-59], because a triangle singularity include hadro-charmonium states [18], compact cannot be present in the two-body final states of the pro- Received 18 March 2020, Published online 16 June 2020 * Supported in part by the National Natural Science Foundation of China (11405222, 11975278), the Pioneer Hundred Talents Program of Chinese Academy of Sci- ences (CAS) and the Key Research Program of CAS (XDPB09) 1) E-mail: [email protected] 2) E-mail: [email protected], Corresponding author 3) E-mail: [email protected] 4) E-mail: [email protected] Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must main- tain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by 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 Pub- lishing Ltd 084102-1 Chinese Physics C Vol. 44, No. 8 (2020) 084102 duction process. Thus, if they are observed in the J= p or as follows. In Sec. 2, we will briefly describe the analytic open charm production [52], they should be genuine formalism in our computation, following which the res- states other than kinematic effects. Subsequently, an ex- ults and discussions will be introduced in Sec. 3. Finally, perimental study of pentaquarks through photoproduc- we will present a short summary. tion was proposed at the JLab [60]. The GlueX Collabor- ation searched for the pentaquark states through the near- 2 Formalism threshold J= exclusive photoproduction off proton [61]. No evidence for pentaquark photoproduction was determ- = ined, and model-dependent upper limits on their branch- As shown in Fig. 1, pJ in the final states of ep ! epJ= can be produced from a pentaquark decay (b) ing fraction B(Pc ! J= p) were set. The photoproduc- tion rate was investigated in model-dependent calcula- and non-resonant t-channel (a). Here, u-channel contribu- tion is from a Pc or p exchange, but both of them are tions [47, 62], where the coupling of the Pc radiative de- cay was evaluated by the vector meson dominance negligible because of the highly off-shell intermediate Pc = (VMD) model. Although the extracted branching ratio, state and the significantly small coupling between J p, respectively. Several phenomenological models were B(Pc ! J= p), is dependent on the details of the VMD, e.g., off-shell form factor, the photoproduction rate tends constructed to parameterize the t-channel diagram with a to not be high compared to the non-resonant contribution. gluon or Pomeron exchange. A detailed comparison of Υ Double polarization observables were proposed to be use- these models can be found in Ref. [64] for the photo- ful in the search of pentaquark photoproduction [45]. production. Here, we employ the soft dipole Pomeron However, the LHCb results indicate a model-independ- model, which can describe vector meson photoproduc- tion from low to high energies [65]. We use a covariant ent lower limit of B(Pc ! J= p) [62]; thus, it is expected to observe pentaquark eletro and photoproduction after orbital–spin (L–S) scheme to construct the Langrangians enough events are accumulated, if P is a real resonant of thePc couplings [66], which has been used widely for c ∗ ∗ state. Moreover, it is expected that the distributions of normal N and ∆ resonances [67-69]. = J from a pentaquark and Pomeron are different in large 2.1 Pomeron exchange angles of the differential cross-sections [47, 51], which could be helpful for identifying a pentaquark in cross-sec- The Pomeron exchange model [70-72] accounts for tions. the dominant contribution in the leptoproduction process. After the update of the JLab accelerator to 12 GeV, The Pomeron mediates the long-range interaction the search for pentaquark electroproduction at JLab12 between the nucleon and confined (anti-)quarks within a will continue. Recently, an electron-ion collider at China quarkonium. This is an effective and useful model to (EicC) was proposed, where Hadron physics is a main parameterize the diffractive process for the production of concern [63]. Its designed center of mass (c.m.) energy of neutral vector mesons in a high-energy region. By includ- 15 − 20 GeV covers charmonium electroproduction. In ing a double Regge pole with an intercept equal to one, this study, we investigate the electroproduction of the soft dipole Pomeron model does not violate the unit- pentaquark states in these machines. The main concern arity bounds and can describe nearly all the available here is on the final state distributions, from which a kin- cross-section data of the photo and electroproduction of ematic cut would isolate a feeble pentaquark signal from vector mesons, from light to heavy and near the threshold a large non-resonant background. This paper is organized to a high-energy region in a consistent manner [65]. Fig. 1. Diagrams for the electroproduction of heavy quarkonium J= . (a) Contribution of the t-channel Pomeron exchange. (b) Pentaquark P production in the s-channel, where V stands for all possible vector mesons. c 084102-2 Chinese Physics C Vol. 44, No. 8 (2020) 084102 µ 0 µ We start from the photoproduction of vector meson V where R1 is a sub-reaction, e ! eγ, M = ieu¯(k )γ u(k), R1 off proton in the soft dipole Pomeron model with the for- and R2 is a sub-reaction, γp ! V p. By neglecting the po- mula of the t-dependent cross-section [65], larization correlations between the two sub-reactions, we dσ obtain the amplitude square, = 4πjMP j2; (1) dt γp!V p X 2 1 µ ∗λ 2 ν λ 2 jMep!eV pj = jM ϵµ 1 j jM ϵν 2 j ; (6) where the amplitudes are defined as 2 2 R1 R2 3(q ) λ ,λ P 1 2 M = P(z;t; M2 ; Q2) + F (z;t; M2 ; Q2); (2) γp!V p V V where ϵ is the polarization vector of an intermediate photon with spin of z-direction λ ; . The amplitude for α − α − 1 2 P ; ; 2 ; 2 = − P(t) 1 + − − P(t) 1; (z t MV Q ) ig0( iz) ig1ln( iz)( iz) sub-reaction, R2 , can be determined from differential (3) cross-section dσ/dt by the dipole Pomeron model men- P α − jM j2 = F ; ; 2 ; 2 = − f (t) 1: tioned in Eq.
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