NLO results with operator mixing for fully heavy tetraquarks in QCD sum rules

Abstract

We study the mass spectra of $\bar{Q}Q\bar{Q}Q(Q=c,b)$ systems in QCD sum rules with the complete next-to-leading order (NLO) contribution to the perturbative QCD part of the correlation functions. Instead of meson-meson or diquark-antidiquark currents, we use diagonalized currents under operator renormalization. We find that differing from conventional mesons $\bar{q}q$ and baryons $qqq$, a unique feature of the multiquark systems like $\bar{Q}Q\bar{Q}Q$ is the operator mixing or color configuration mixing induced by NLO corrections, which is crucial to understand the color structure of the states. Our numerical results show that the NLO corrections are very important for the $\bar{Q}Q\bar{Q}Q$ system, because they not only give significant contributions but also reduce the scheme and scale dependence and make Borel platform more distinct, especially for the $\bar{b}b\bar{b}b$ in the $\overline{\mathrm{MS}}$ scheme. We use currents that have good perturbation convergence in our phenomenological analysis. With the $\overline{\mathrm{MS}}$ scheme, we get three $J^{PC}=0^{++}$ states, with masses $6.35_{-0.17}^{+0.20}$ GeV, $6.56_{-0.20}^{+0.18}$ GeV and $6.95_{-0.31}^{+0.21}$ GeV, respectively. The first two seem to agree with the broad structure around $6.2\sim 6.8$ GeV measured by the LHCb collaboration in the $J/\psi J/\psi$ spectrum, and the third seems to agree with the narrow resonance $X(6900)$. For the $2^{++}$ states we find one with mass $7.03_{-0.26}^{+0.22}$ GeV, which is also close to that of $X(6900)$, and another one around $7.25_{-0.35}^{+0.21}$ GeV, which has good scale dependence but slightly large scheme dependence.

60 pages, 53 figures, nonrelativistic (NR) reductions of some operators are illustrated

References in corpus (26)

• Pentaquark and Tetraquark states
• Observation of structure in the $J/\psi$-pair mass spectrum
• $QQ\bar{Q}\bar{Q}$ states: masses, production, and decays
• Masses of fully heavy tetraquarks $QQ\bar{Q}\bar{Q}$ in an extended relativized quark model
• Heavy tetraquarks in the relativistic quark model
• Full-heavy tetraquarks in constituent quark models
• Doubly-hidden scalar heavy molecules and tetraquarks states from QCD at NLO
• Fully-heavy tetraquark spectra and production at hadron colliders
• Scalar Fully-heavy Tetraquark States $Q{Q}^{\prime }\bar{Q}\overline{Q^{\prime }}$ in QCD Sum Rules
• Gluonic Tetracharm Configuration of $X(6900)$
• $0^{+}$ fully-charmed tetraquark states
• Tetraquark state $X(6900)$ and the interaction between diquark and antidiquark
• Tetraquark candidates in the LHCb's di-$J/\psi$ mass spectrum
• Insights into the inner structures of the fully charmed tetraquark state $X(6900)$
• Nonrelativistic model of tetraquarks and predictions for their masses from fits to charmed and bottom meson data
• Spectrum of the Hidden-Bottom and the Hidden-Charm/Strange Exotics in the Dynamical Diquark Model
• Study of charmonium-like and fully-charm tetraquark spectroscopy
• Mass spectra and wave functions of $T_{QQ\bar{Q}\bar{Q}}$ tetraquarks
• Deciphering the recently discovered tetraquark candidates around 6.9 GeV
• Higher fully-charmed tetraquarks: Radial excitations and P-wave states
• Some remarks on $X(6900)$
• SVZ sum rules : 30 + 1 years later
• Pair structure of heavy tetraquark systems
• NLO effects for ${\Omega }_{QQQ}$ Baryons in QCD Sum Rules
• Heavy baryon properties with NLO accuracy in perturbative QCD
• Next-to-Leading Order perturbative QCD corrections to baryon correlators in matter

Cited by in corpus (15)

• An updated review of the new hadron states
• Fully-heavy tetraquark spectroscopy in the relativistic quark model
• Going in quest of potential tetraquark interpretations for the newly observed $T_{\psi \psi }$ states in light of the diquark-antidiquark scenarios
• Decay behaviors of the fully-bottom and fully-charm tetraquark states
• Hadronic molecules with four charm or beauty quarks
• P-wave fully charm and fully bottom tetraquark states
• The $X(6900)$ peak could be a molecular state
• Predictions of the hybrid mesons with exotic quantum numbers $J^{PC}=2^{+-}$
• $Z_c$ and $Z_{cs}$ systems with operator mixing at NLO in QCD sum rules
• Fully-heavy tetraquarks in the vacuum and in a hot environment
• Discovering an Unquenched Dynamics Mechanism for Charmonium Scattering
• Possible bound states in the triple-${\eta }_c$ and triple-$J/\psi$ systems
• Baryons and baryoniums in the perspective of QCD sum rules
• Strange pentaquark molecules in QCD sum rules
• Study of the ${\Omega }_{ccc}{\Omega }_{ccc}$ and ${\Omega }_{bbb}{\Omega }_{bbb}$ dibaryons in QCD Sum Rules