Study of $X(6900)$ with unitarized coupled channel scattering amplitudes

Abstract

In this paper, we study the resonant state X(6900). The scattering amplitudes of coupled channels, J/ψJ/ψ-J/ψψ(2S)-J/ψψ(3770), are constructed with the interaction of four vector mesons described by effective Lagrangians. The amplitudes are calculated up to one loop, decomposed by partial wave projection, and unitarized by Padé approximation. These amplitudes are fitted to the latest experimental data sets of di-J/ψ and J/ψψ(2S) invariant mass spectra of LHCb, CMS, and ATLAS. High-quality solutions are obtained. With these partial wave amplitudes, we extract the pole parameters of the X(6900). Its quantum number is likely to be 0 ++ . According to the pole counting rule as well as analysis of the phase shifts of the partial waves, it supports our previous conclusion that the X(6900) prefers to be a compact tetra-quark. I. INTRODUCTIONSince the 1960s, quark model [1-3] has turned out to be a successful classification scheme for hadrons, that is, a meson is composed of a pair of quark and anti-quark, and a baryon/anti-baryon is composed of three quarks/antiquarks. Hundreds of hadrons listed in the particle data group (PDG) [4] can be formed as such inner structure. However, until now, there is no fundamental principle to rule out other inner structures of hadrons, such as hadronic molecules, quark-gluon hybrids, glueballs, and multi-quark states. Searching for exotic states remains a keen interest of the physics community. In 2003, a tetraquark candidate, X(3872), was discovered by Belle [5] and other collaborations [6][7][8]. In 2013, BESIII and Belle discovered the Z + c (3900) [9,10] in the J/ψπ + invariant mass spectrum, implying the cc du component. In 2015, LHCb discovered two P c states [11] and later they are found to be 'splitted' into three such states [12], P + c (4312), P + c (4440), P + c (4457), with about nine more times decay events collected. The P c s are observed in the J/ψp invariant mass spectra, and hence they should contain at least five quarks, ccuud. In 2021, LHCb discovered the T + cc in D 0 D 0 π + invariant mass spectrum [13,14]. This further grasps the attention of theorists as it is very likely to be evidence for multi-quark states, ccū d. All these exotic hadrons observed so far contain at most two heavy (charm or bottom) quarks/anti-quarks, but as many models predicted, there should also be multi-quark states composed of three or more heavy quarks/anti-quarks [15][16][17][18][19]. This is confirmed by the very recent experiment of LHCb collaboration [20]. With the datasets of proton-proton collision in the center-of-mass energies √ s = 7, 8 and 13 TeV collected by the LHCb detector, the invariant mass spectrum of J/ψJ/ψ was measured in the energy range of [6.2-7.4] Gev/c 2 , and a narrow structure was found near 6.9Gev/c 2 , labeled as X(6900), with the signal statistical significance being larger than 5 σ. Its mass and width are given in two ways: On the one hand, they assume that the non-resonant single-parton scattering (NRSPS) continuum is not disturbed, and Breit-Wigner forms fi...

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“…To date, the mass spectra of fully-heavy tetraquarks have been extensively studied using various models and techniques in the literature , most of which assume the di-J/ψ resonances as fully-charm compact tetraquark states. However, the identities of the observed resonances are still under debate; many works have been dedicated to the interpretation of them [61][62][63][64][65][66][67][68][69][70][71][72][73], most considering these resonances as effects of two charmonia produced simultaneously. We call such effects, regardless of whether the two charmonia are bound, a molecule-like state.…”