PHYSICAL REVIEW D 102, 116014 (2020) Discovery potential for the LHCb fully charm tetraquark Xð6900Þ state via pp¯ annihilation reaction † ‡ Xiao-Yun Wang,1,* Qing-Yong Lin,2, Hao Xu,3 Ya-Ping Xie,4 Yin Huang,5 and Xurong Chen4,6,7, 1Department of physics, Lanzhou University of Technology, Lanzhou 730050, China 2Department of Physics, Jimei University, Xiamen 361021, China 3Department of Applied Physics, School of Science, Northwestern Polytechnical University, Xi’an 710129, China 4Institute of Modern Physics, Chinese Academy of Sciences, Lanzhou 730000, China 5School of Physical Science and Technology, Southwest Jiaotong University, Chendu 610031, China 6University of Chinese Academy of Sciences, Beijing 100049, China 7Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China (Received 2 August 2020; accepted 16 November 2020; published 18 December 2020) Inspired by the observation of the fully-charm tetraquark Xð6900Þ state at LHCb, the production of Xð6900Þ in pp¯ → J=ψJ=ψ reaction is studied within an effective Lagrangian approach and Breit-Wigner formula. The numerical results show that the cross section of Xð6900Þ at the c.m. energy of 6.9 GeV is much larger than that from the background contribution. Moreover, we estimate dozens of signal events can be detected by the D0 experiment, which indicates that searching for the Xð6900Þ via antiproton-proton scattering may be a very important and promising way. Therefore, related experiments are suggested to be carried out. DOI: 10.1103/PhysRevD.102.116014 I. INTRODUCTION Γ ¼ 168 Æ 33 Æ 69 MeV; ð2Þ In recent decades, more and more exotic hadron states have been observed [1]. These exotic hadron states are not respectively. Actually, based on various theoretical models, only conducive to the development of the hadron spectrum a lot of studies have been conducted on fully-heavy but also provide an important opportunity for us to better tetraquark states [5–32], which are important to reveal the understand the multiquark states and strong interactions structure and properties of the fully-heavy tetraquark states. [2,3]. In the past years, the experimental explorations focus After its observation, Xð6900Þ has inspired extensive studies on the multiquark states composed of light and heavy on its underlying properties, where it is interpreted as a P- quarks, while studies for the states composed entirely of wave tetraquark state in a nonrelativistic quark model [27], heavy quarks are still very limited [1–3]. the first radial excitation of ccc¯ c¯ in an extended relativized Very recently, the LHCb experiment reported a narrow quark model [28]. Besides, in the QCD sum rule framework, structure, named Xð6900Þ, in the J=ψ pair invariant mass the narrow structure Xð6900Þ can be interpreted as a second spectrum with a significance level of more than 5σ [4]. radial excited S-wave tetraquark state [29] with JPC ¼ 0−þ Based on the simple model with interference, the mass and or a P-wave state [30] with 1−þ, respectively. In width of the Xð6900Þ resonance are measured to be Refs. [31,32], the theoretical results indicate that there may exist the resonance states, with masses ranging between M ¼ 6886 Æ 11 Æ 11 MeV; ð1Þ 6.3 to 7.4 GeV, and the quantum numbers JP ¼ 0þ; 1þ, and 2þ. In Ref. [33], the spin parity of the state formed by the * two-vector system was discussed, and a possible method for Corresponding author. – [email protected] determining its quantum number was given. In Refs. [34 † [email protected] 36], the spectrum or mass of fully-heavy tetraquarks was ‡ [email protected] discussed in diquark model with different approaches. In addition to the study of the mass spectrum and the Published by the American Physical Society under the terms of decay behavior of Xð6900Þ, studying the production of the Creative Commons Attribution 4.0 International license. ð6900Þ Further distribution of this work must maintain attribution to X through different scattering reactions is also very the author(s) and the published article’s title, journal citation, important and will help us to understand its nature as and DOI. Funded by SCOAP3. genuine states. For example, in Ref. [37], the production of 2470-0010=2020=102(11)=116014(5) 116014-1 Published by the American Physical Society WANG, LIN, XU, XIE, HUANG, and CHEN PHYS. REV. D 102, 116014 (2020) the ground ccc¯ c¯ with JPC ¼ 0þþ; 2þþ in pp collisions was The production cross section of Xð6900Þ structure calculated, and the upper limit of the cross section is about relative to that of all J=ψ pair, times the branching fraction 40 fb for the four muons channel. In addition to pp BrðX → ψψÞ, R, is determined as ½2.6 Æ 0.6 ðstatÞ collisions, determining the tetraquark states via the annihi- 0.8 ðsystÞ% by the LHCb experiment [4]. Therefore, in lation of positive and negative protons is usually an this work, we roughly take the value of the branching important and effective way [38–44]. In this work, the ratio BrðX → ψψÞ ≃ 2%. discovery potential for the tetraquark state Xð6900Þ via pp¯ Having fixed the branch ratio BrðX → ψψÞ, we turn to annihilation reaction will be investigated. One will estimate the value of BrðX → pp¯ Þ, which is indispensable in Eq. (3). the cross section of Xð6900Þ production via pp¯ → J=ψJ=ψ However, it has never been determined in experiments. reaction and analyze the corresponding background con- Meanwhile, we notice in Refs. [39,40] that the branching tribution. The theoretical results obtained will be an impor- fractions of BrðYð4260Þ → pp¯ Þ and Brðψð4040Þ → pp¯ Þ tant theoretical basis for the pp¯ annihilation experiment. were estimated using the branching ratio of J=ψ state, This paper is organized as follows. After the Introd- multiplying by the ratio of the width of the Yð4260Þ or uction, we present the formalism for the production of ψð4040Þ to the width of J=ψ. Thus, in this work, we will Xð6900Þ in Sec. II. The numerical results of the Xð6900Þ adopt the same method as in Refs. [39,40] to naively production follow in Sec. III. Finally, the paper ends with a determine the branching ratio of X decaying into pp¯ .Due brief summary. to the lack of deep understanding of the fully-charm tetraquark Xð6900Þ, its inner structure and quantum num- bers are still unknown. Different JPC assignments were II. FORMALISM assumed to evaluate the mass of a full-charm tetraquark, as A. Xð6900Þ production in pp¯ annihilation discussed in Sec. I. To carry out the estimation of the cross section of the s channel, we assume that the quantum The Feynman diagram of the pp¯ → J=ψJ=ψ reaction via number JPC of Xð6900Þ is 0þþ or 2þþ, the same as the the s channel Xð6900Þ exchange is depicted in Fig. 1(a). assumption in Ref. [37]. In the known charmonium family, For convenience, Xð6900Þ and J=ψ will be abbreviated as þþ þþ the spin parities of χ 0 and χ 2 are 0 and 2 , X and ψ, respectively. c c respectively. Therefore, we plan to simply replace J=ψ For the production of the resonance Xð6900Þ in the s with χ 0 and χ 2 to estimate the branching ratio of X → pp¯ , channel of pp¯ → ψψ reaction, the cross section can be c c namely, calculated by the standard Breit-Wigner formula [1] Γ χc0 BrðX → pp¯ Þ ≃ Brðχc0 → pp¯ Þ × ; 2J þ1 4π Γ2 BrðX → pp¯ ÞBrðX → ψψÞ Γ σ ¼ ; X X ð2 þ1Þð2 þ1Þ 2 4 ð − Þ2 þΓ2 4 PC ¼ 0þþ ð Þ S1 S2 kin W W0 = for X with J 4 ð Þ 3 and Γχ where W is the c.m. energy, J is the spin of the resonance ð → ¯ Þ ≃ ðχ → ¯ Þ c2 Br X pp Br c2 pp × Γ ; Xð6900Þ, and S1 and S2 are the spins of the initial X PC þþ antiproton and proton, respectively. Moreover, kin is the for X with J ¼ 2 ; ð5Þ c.m. momentum in the initial state, W0 is the c.m. energy Γχ ¼ 10 8 Γχ ¼ 1 97 Γ ¼ corresponding to the mass threshold of Xð6900Þ, and Γ is where c0 . MeV, c2 . MeV, and X 168 χ χ ð6900Þ the full width of Xð6900Þ. MeV are the total width of c0, c2, and X states, respectively. By taking the branching ratio −4 Brðχc0 → pp¯ Þ¼2.24 × 10 and Brðχc2 → pp¯ Þ¼ 7.33 × 10−5, one gets BrðX → pp¯ Þ¼1.44 × 10−5 for X with JPC ¼ 0þþ and BrðX → pp¯ Þ¼8.6 × 10−7 for X with JPC ¼ 2þþ. Here, it must be noted that if we use the (a) branching ratio of J=ψ for estimation BrðX → pp¯ Þ¼ 1.17 × 10−6 is obtained, which is just between the value estimated by the branching ratio of χc0 and χc2. B. Background analysis ¯ → ψψ (b) (c) Figures 1(b) and 1(c) present the pp reaction with the t and u channels by exchanging a nucleon, which FIG. 1. Feynman diagrams for the reaction pp¯ →Xð6900Þ→ can be considered as the main background contributions for ψψ. the production of Xð6900Þ. By employing the effective 116014-2 DISCOVERY POTENTIAL FOR THE LHCB FULLY-CHARM … PHYS. REV. D 102, 116014 (2020) Lagrangian approach, the cross section of the pp¯ → ψψ III. NUMERICAL RESULTS reaction can be calculated. After the above preparations, we calculated the total The Lagrangian density for the vertex of ψNN is written cross section for the reaction pp¯ → ψψ from threshold to as [41] 12 GeV of the center of mass energy, as depicted in Fig.