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Register a new userSystematics of fully heavy tetraquarks
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In this work, we systematically study the mass spectrum of the fully heavy tetraquark in an extended chromomagnetic model, which includes both color and chromomagnetic interactions. Numerical results indicate that the energy level is mainly determined by the color interaction, which favors the color-sextet $ket{(QQ)^{6_{c}}(bar{Q}bar{Q})^{bar{6}_{c}}}$ configuration over the color-triplet $ket{(QQ)^{bar{3}_{c}}(bar{Q}bar{Q})^{3_{c}}}$ one. The chromomagnetic interaction mixes the two color configurations and gives small splitting. The ground state is always dominated by the color-sextet configuration. We find no stable state below the lowest heavy quarkonium pair thresholds. Most states may be wide since they have at least one $S$-wave decay channel into two $S$-wave mesons. One possible narrow state is the $1^{+}$ $bbbar{b}bar{c}$ state with a mass $15719.1~text{MeV}$. It is just above the $eta_{b}bar{B}_{c}$ threshold. But this channel is forbidden because of the conservation of the angular momentum and parity.
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We perform a SU(3) analysis for both semi-leptonic and non-leptonic heavy meson weak decays into a pseudoscalar meson and a fully-light tetraquark in 10 or 27 representation. A reduction of the SU(3) representation tensor for the fully-light tetraquarks is produced and all the flavor components for each representation tensor are listed. The decay channels we analysis include $B/D to U/T~P~l u$, $B/D to U/T~P $ and $B_c to U/T~P/D$, with $U/T$ represents a fully-light tetraquark in 10 or 27 representation and $P$ is a pseudoscalar meson. Finally, among these results we list all the golden decay channels which are expected to have more possibilities to be observed in experiments.
In this work we study the mass spectra of the fully-heavy tetraquark systems, i.e. $ccbar{c}bar{c}$, $bbbar{b}bar{b}$, $bbbar{c}bar{c}/ccbar{b}bar{b}$, $bcbar{c}bar{c}/ccbar{b}bar{c}$, $bcbar{b}bar{b}/bbbar{b}bar{c}$, and $bcbar{b}bar{c}$, within a potential model by including the linear confining potential, Coulomb potential, and spin-spin interactions. It shows that the linear confining potential has important contributions to the masses and is crucial for our understanding of the mass spectra of the fully-heavy tetraquark systems. For the fully-heavy tetraquarks $Q_1Q_2bar{Q}_3bar{Q}_4$ our explicit calculations suggest that no bound states can be formed below the thresholds of any meson pairs $(Q_1bar{Q}_3)$-$(Q_2bar{Q}_4)$ or $(Q_1bar{Q}_4)$-$(Q_2bar{Q}_3)$. Thus, we do not expect narrow fully-heavy tetraquark states to be existing in experiments.
Alerted by the recent LHCb discovery of exotic hadrons in the range (6.2 -- 6.9) GeV, we present new results for the doubly-hidden scalar heavy $(bar QQ) (Qbar Q)$ charm and beauty molecules using the inverse Laplace transform sum rule (LSR) within stability criteria and including the Next-to-Leading Order (NLO) factorized perturbative and $langle G^3rangle$ gluon condensate corrections. We also critically revisit and improve existing Lowest Order (LO) QCD spectral sum rules (QSSR) estimates of the $({ bar Q bar Q})(QQ)$ tetraquarks analogous states. In the example of the anti-scalar-scalar molecule, we separate explicitly the contributions of the factorized and non-factorized contributions to LO of perturbative QCD and to the $langlealpha_sG^2rangle$ gluon condensate contributions in order to disprove some criticisms on the (mis)uses of the sum rules for four-quark currents. We also re-emphasize the importance to include PT radiative corrections for heavy quark sum rules in order to justify the (ad hoc) definition and value of the heavy quark mass used frequently at LO in the literature. Our LSR results for tetraquark masses summarized in Table II are compared with the ones from ratio of moments (MOM) at NLO and results from LSR and ratios of MOM at LO (Table IV). The LHCb broad structure around (6.2 --6.7) GeV can be described by the $overline{eta}_{c}{eta}_{c}$, $overline{J/psi}{J/psi}$ and $overline{chi}_{c1}{chi}_{c1}$ molecules or/and their analogue tetraquark scalar-scalar, axial-axial and vector-vector lowest mass ground states. The peak at (6.8--6.9) GeV can be likely due to a $overline{chi}_{c0}{chi}_{c0}$ molecule or/and a pseudoscalar-pseudoscalar tetraquark state. Similar analysis is done for the scalar beauty states whose masses are found to be above the $overlineeta_beta_b$ and $overlineUpsilon(1S)Upsilon(1S)$ thresholds.
We use a diffusion Monte Carlo method to solve the many-body Schrodinger equation describing fully-heavy tetraquark systems. This approach allows to reduce the uncertainty of the numerical calculation at the percent level, accounts for multi-particle correlations in the physical observables, and avoids the usual quark-clustering assumed in other theoretical techniques applied to the same problem. The interaction between particles was modeled by the most general and accepted potential, i.e. a pairwise interaction including Coulomb, linear-confining and hyperfine spin-spin terms. This means that, in principle, our analysis should provide some rigorous statements about the mass location of the all-heavy tetraquark ground states, which is particularly timely due to the very recent observation made by the LHCb collaboration of some enhancements in the invariant mass spectra of $J/psi$-pairs. Our main results are: (i) the $ccbar cbar c$, $ccbar bbar b$ ($bbbar cbar c$) and $bbbar b bar b$ lowest-lying states are located well above their corresponding meson-meson thresholds; (ii) the $J^{PC}=0^{++}$ $ccbar cbar c$ ground state with preferred quark-antiquark pair configurations is compatible with the enhancement(s) observed by the LHCb collaboration; (iii) our results for the $ccbar cbar b$ and $bbbar cbar b$ sectors seem to indicate that the $0^+$ and $1^+$ ground states are almost degenerate with the $2^+$ located around $100,text{MeV}$ above them; (iv) smaller mass splittings for the $cbbar cbar b$ system are predicted, with absolute mass values in reasonable agreement with other theoretical works; (v) the $1^{++}$ $cbbar cbar b$ tetraquark ground state lies at its lowest $S$-wave meson-meson threshold and it is compatible with a molecular configuration.
We study strong decays of the possible fully-charm tetraquarks recently observed by LHCb, and calculate their relative branching ratios through the Fierz rearrangement. Together with our previous QCD sum rule study [Phys. Lett. B 773, 247 (2017)], our results suggest that the broad structure around $6.2$-$6.8$ GeV can be interpreted as an $S$-wave $ccbar c bar c$ tetraquark state with $J^{PC} = 0^{++}$ or $2^{++}$, and the narrow structure around 6.9 GeV can be interpreted as a $P$-wave one with $J^{PC} = 0^{-+}$ or $1^{-+}$. These structures were observed in the di-$J/psi$ invariant mass spectrum, and we propose to confirm them in the di-$eta_c$, $J/psi h_c$, $eta_c chi_{c0}$, and $eta_c chi_{c1}$ channels. We also propose to search for their partner states having the negative charge-conjugation parity in the $J/psi eta_c$, $J/psi chi_{c0}$, $J/psi chi_{c1}$, and $eta_c h_c$ channels.
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