Decay Behaviors of Possible Λcc¯ States in Hadronic Molecule Pictures
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PHYSICAL REVIEW D 100, 056006 (2019) Decay behaviors of possible Λcc¯ states in hadronic molecule pictures † ‡ Chao-Wei Shen ,1,* Jia-Jun Wu,1, and Bing-Song Zou1,2,3, 1University of Chinese Academy of Sciences (UCAS), Beijing 100049, China 2Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China 3School of Physics, Central South University, Changsha 410083, China (Received 12 June 2019; published 11 September 2019) ΛÃ ¼ −1 Ã In 2010, cc¯ states were predicted as the strange number S partners of Ncc¯ , which are well known now as the Pc states and observed experimentally by the LHCb Collaboration. We analyze the decay behaviors of Λcc¯ as S-wave hadronic molecules within the effective Lagrangian framework by a similar method, which has been applied on Pc states successfully. With partial widths of possible decay channels calculated, we find that Λcc¯ ð4213Þ and Λcc¯ ð4403Þ, which are formed as pseudoscalar meson baryon molecules, mainly decay to the ηcΛ channel. For the two vector meson baryon molecule states, our results P 1− P 3− show that the total decay width with J ¼ 2 is by one order of magnitude larger than that with J ¼ 2 . Ã− þ ¯ Ã The decay patterns and relative decay ratios are very different for Λcc¯ ð4370Þ being a Ds Λc or D Ξc ¯ ðÞ ð;0Þ molecule state. The main decay channels of Λcc¯ ð4550Þ are D Ξc because of the pseudoscalar meson ¯ Ã exchange mechanism. In addition, D Ξc is the dominant decay channel of Λcc¯ ð4490Þ, which is assumed as ¯ ΞÃ ΛÃ a D c bound state. These decay patterns of the cc¯ states would provide guidance for future experimental searches and help us to understand their internal structures. DOI: 10.1103/PhysRevD.100.056006 I. INTRODUCTION invariant spectrum. Only their masses and total widths can be extracted. The quantum numbers and the internal In Ref. [1], within the hidden local symmetry, not only structures of these states are still unknown. Many models Ncc¯ states but also Λcc¯ states are predicted. The predicted ¯ ¯ Ã have been applied to study them, and various explanations N ¯ states are DΣ or D Σ S-wave bound states which cc c c have been proposed [4,5]. Roughly speaking, there are locate around 4.3 GeV. They are found to be consistent with the observed three peak structures by the LHCb three different views of these peaks. First, they are Collaboration in 2019 [2]. In the LHCb earlier paper recognized as meson baryon molecular states, which can [3], they named such states as P , whose flavor quanta be divided in anticharmed meson charmed baryon states c – number is the same as NÃ but definitely have cc¯ compo- [1,6 34], baryocharmonium states [35,36], or a mixture of nents. However, the newest results with higher statistic data them [37,38]. Second, they are considered in the constitu- – from the LHCb group have not been partial wave analyzed; ent quark model [39 42], diquark-diquark-antiquark pic- – thus, the spin and parity of these states are still unknown. ture [43 47], and diquark-triquark picture [48]. Third, the narrow peak of P ð4450Þ might result from the triangle The Pc states have attracted much attention since the first c proposal in 2010 [1] and became a very hot topic once singularity (TS) effect [49–51], which is a purely kinematic the signals of them were first seen in 2015 by LHCb [3]. effect, although for some quantum numbers of the Pc state − þ The main reason is that they are the first exotic baryons preferred in Ref. [3], such as 3=2 or 5=2 , the TS cannot discovered experimentally. But until now the only exper- explain the peak as shown in Ref. [52]. Recently, the new imental information of these states comes from the J=ψp updated results by the LHCb Collaboration [2] clearly show that the three narrow states are all just below the corre- sponding anticharmed meson charmed baryon thresholds, *[email protected] † which strongly suggests a hadronic molecule nature for [email protected] ‡ – [email protected] them. There are several new theoretical papers [53 62] triggered by the new LHCb results that support the meson Published by the American Physical Society under the terms of baryon state description, mainly from D¯ ðÞΣðÞ, although the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to they have different views in detail. Only Ref. [63] argues the author(s) and the published article’s title, journal citation, that the internal structures still rely on the parities of these and DOI. Funded by SCOAP3. states. Here, we want to emphasize that the mass and total 2470-0010=2019=100(5)=056006(12) 056006-1 Published by the American Physical Society CHAO-WEI SHEN, JIA-JUN WU, and BING-SONG ZOU PHYS. REV. D 100, 056006 (2019) width are maybe not enough to distinguish among various studies show that there would be rather stable signals models. Definitely more information, such as the spin and of the hidden-charm strange states. And the partial parity, and partial decay widths of these states are needed widths are all consistent with the predictions in from new measurements in experiments. Correspondingly, Ref. [1], where only the contribution of vector meson it is worthy to make the prediction of the partial widths of exchange is considered. these states from the theoretical side to help experimen- Among the predicted states in Ref. [1], there are six Λcc¯ talists to find new reactions to search these states. states. Two of them are from the pseudoscalar meson ¯ þ In previous papers [17,21,23,30], the decay patterns of baryon (PB) channel. Λcc¯ ð4213Þ is coupled to both DsΛc ¯ Pc based on different assumptions of their internal struc- and DΞc channels, while Λcc¯ ð4403Þ couples only to the þð4380Þ P ¼ 3− ¯ 0 tures were studied. It is found that if Pc is a J 2 DΞc channel. The other four states are from the vector ¯ Ã D Σc molecular state, its width will be around 50 MeV, meson baryon (VB) channel, two of which are around ¯ Ã þ ¯ Ã which is much smaller than that analyzed from the 4370 MeV and couple to both Ds Λc and D Ξc channels, ¯ Ã 0 experimental data. However, the width would be around and the other two Λcc¯ states couple only to the D Ξc þ P 3− ¯ Ã 150 MeV if Pc ð4380Þ is assumed as a J ¼ 2 DΣc channel, with masses around 4550 MeV. Note that in molecular state. This implies that it has more possibilities to Ref. [1] for each VB case its bound states always appear ¯ Ã P 3− P − − be a DΣc molecular state with J ¼ 2 . On the other hand, as a degenerate pair of spin parity J ¼ 1=2 and 3=2 , þ ¯ Ã Pc ð4450Þ is more likely to be a D Σc molecule with respectively, due to an approximation of neglecting the P 5þ þ small spin-dependent force. We consider Λ ¯ ð4213=4370Þ J ¼ 2 . In the updated results from Ref. [2], Pc ð4380Þ is cc ¯ ðÞ þ ¯ ðÞ not mentioned, but this broad structure still exists in the fit, as either a Ds Λc or a D Ξc S-wave bound state and þð4450Þ þð4440Þ ¯ ðÞ 0 and Pc splits into two states, Pc and Λcc¯ ð4403=4550Þ as a D Ξc S-wave molecule. An addi- þð4457Þ ¯ Ã Pc , with both their spin and parity not yet decided. tional DΞc S-wave bound state is also taken into con- þð4440Þ The width of Pc is around 20 MeV, which is still sideration assuming to be Λcc¯ ð4490Þ with spin parity comparable with the calculations from Refs. [17,21,23,30]. 3=2− and a binding energy of about 23 MeV. In the work, ð4312Þ Also, another new state Pc is more likely to be a we make an estimation of the partial decay widths of ¯ Σ D c molecular state and is missing in the earlier meas- these seven Λcc¯ states to possible two-body decay urement. Correspondingly, in the previous relevant channels, which is expected to help figure out the nature ð4312Þ references, Pc has not yet been studied. In the of these Λcc¯ states. present work, we consider the decay behaviors of the This article is organized as follows. In Sec. II, we present predicted Λcc¯ states similarly, which should be quite the theoretical framework of our calculation. In Sec. III, the useful for understanding their nature with the help of numerical decay widths of the Λcc¯ states and relevant forthcoming experiments. discussions about these results are presented; then a brief Λ −1 The cc¯ , which are partners of Pc with strangeness summary in Sec. IV of this work follows, and an Appendix states, have already been investigated by several groups. is presented last. The strange hidden-charm state is considered in the quark model, and both the color octet type and color singlet type II. THEORETICAL FRAMEWORK are studied [64], which is different from this work, where Λ the cc¯ is assumed as a molecule with two color singlet The decays of these Λcc¯ states proceed through triangular Λ parts. It is found that the cc¯ below 4400 MeV are all diagrams as shown in Fig. 1. The possible molecular formed as two color octet parts, color octet uds and cc¯ assumptions, their decay modes, and corresponding − − parts, and the spin and parity can be 1=2 and 3=2 .