Axial-vector Tetraquark Research Articles

Newly observed exotic doubly charmed meson [formula omitted

In this work, we treat the newly observed doubly charmed four-quark state Tcc+ as an axial-vector tetraquark with content ccu‾d‾, and calculate its spectroscopic parameters and width. The mass and current coupling of the tetraquark Tcc+ are found by means of the QCD two-point sum rule method by taking into account quark, gluon and mixed condensates up to dimension 10. The width of the Tcc+ is evaluated using partial widths of decay processes Tcc+→T˜π0 and Tcc+→Tcc;u‾u‾0π+, where T˜=ccu‾d‾ and Tcc;u‾u‾0 are scalar tetraquarks. To compute the partial width of the first process, we apply the QCD three-point sum rule approach and exact numerical value of the strong coupling g that corresponds to the vertex Tcc+T˜π0. The width of the second decay is estimated using isospin symmetry and the prediction obtained for the first channel. Our results for the mass m=(3868±124)MeV and width Γ=(489±92)keV of the tetraquark Tcc+ are in a nice agreement with recent measurements of the LHCb collaboration.

Analysis of Zcs (3985) as the axialvector tetraquark state * *Supported by National Natural Science Foundation of China (11775079)

In this study, we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states in the framework of the QCD sum rules. The predicted tetraquark mass is in excellent agreement with the experimental value from the BESIII collaboration, which supports identifying as the cousin of with quantum numbers . We take into account the light flavor mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

Semileptonic and nonleptonic decays of the axial-vector tetraquark $$T_{bb;\overline{u} \overline{d}}^{-}$$

The semileptonic and nonleptonic decays of the double-beauty axial-vector tetraquark $T_{bb;\overline{u} \overline{d}}^{-}$ to a state $\widetilde{T}_{bc; \overline{u}\overline{d}}^{0}$ (hereafter $T_{bb}^{-}$ and $\widetilde{T} _{bc}^{0}$, respectively) are investigated in the context of the QCD sum rule method. The final-state tetraquark $\widetilde{T}_{bc}^{0}$ is treated as an axial-vector particle built of a heavy axial-vector diquark $ b^{T}\gamma _{\mu }Cc$ and light scalar antidiquark $\overline{u}C\gamma_{5} \overline{d}^{T}$. Its spectroscopic parameters are calculated using the two-points sum rules by taking into account contributions of quark, gluon and mixed condensates up to dimension $10$. We study the dominant semileptonic $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}l\overline{\nu }_{l}$ and nonleptonic decays $T_{bb}^{-} \to \widetilde{T}_{bc}^{0}M$, where $M$ is one of the pseudoscalar mesons $\pi^{-}, K^{-}, D^{-}$ and $D_s^{-}$. The partial widths of these processes are computed in terms of weak form factors $G_{i}(q^2),\ i=1,2,3,4$, extracted by employing the QCD three-point sum rule approach. Predictions obtained for partial widths of considered decays are used to improve accuracy of theoretical predictions for full width and lifetime of the tetraquark $T_{bb}^{-}$, which are important for experimental exploration of this exotic meson.

A family of double-beauty tetraquarks: Axial-vector state * *The work of K. A, B. B., and H. S was Supported in part by the TUBITAK (119F050)

The spectroscopic parameters and decay channels of the axial-vector tetraquark (in what follows, ) are explored using the quantum chromodynamics (QCD) sum rule method. The mass and coupling of this state are calculated using two-point sum rules by taking into account various vacuum condensates, up to 10 dimensions. Our prediction for the mass of this state confirms that it is stable with respect to strong and electromagnetic decays and can dissociate to conventional mesons only via weak transformations. We investigate the dominant semileptonic and nonleptonic decays of . In these processes, is a scalar tetraquark built of a color-triplet diquark and an antidiquark, whereas M is one of the vector mesons , , , and . To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors ( ), which govern these processes. The full width and the mean lifetime of the tetraquark are computed using the aforementioned weak decays. The obtained information about the parameters of and is useful for experimental investigations of these double-heavy exotic mesons.

Scalar or Vector Tetraquark State Candidate: Zc(4100)**supported by National Natural Science Foundation under Grant No. 11775079.

In this article, we separate the vector and axialvector components of the tensor diquark operators explicitly, construct the axialvector-axialvector type and vector-vector type scalar tetraquark currents and scalar-tensor type tensor tetraquark current to study the scalar, vector and axialvector tetraquark states with the QCD sum rules in a consistent way. The present calculations do not favor assigning the Zc(4100) to be a scalar or vector tetraquark state. If the Zc(4100) is a scalar tetraquark state without mixing effects, it should have a mass about 3.9 GeV or 4.0 GeV rather than 4.1 GeV; on the other hand, if the Zc(4100) is a vector tetraquark state, it should have a mass about 4.2 GeV rather than 4.1 GeV. However, if we introduce mixing, a mixing scalar tetraquark state can have a mass about 4.1 GeV. As a byproduct, we obtain an axialvector tetraquark candidate for the Zc(4020).

Light axial-vector and vector resonances X(2100) and X(2239)

We study features of the resonances X(2100) and X(2239) by treating them as the axial-vector and vector tetraquarks with the quark content sss‾s‾, respectively. The spectroscopic parameters of these exotic mesons are calculated in the framework of the QCD two-point sum rule method. Obtained prediction for the mass m=(2067±84)MeV of the axial-vector state is in excellent agreement with the mass of the structure X(2100) recently observed by the BESIII Collaboration in the decay J/ψ→ϕηη′ as the resonance in the ϕη′ mass spectrum. We also explore the decays X(2100)→ϕη′ and X(2100)→ϕη using QCD light-cone sum rule approach and technical methods of the soft-meson approximation. The width of the axial-vector tetraquark, Γ=(130.2±30.1)MeV, saturated by these two processes is comparable with the measured full width of the resonance X(2100). Our prediction for the vector sss‾s‾ tetraquark's mass m˜=(2283±114)MeV is consistent with the experimental result (2239.2±7.1±11.3)MeV of the BESIII Collaboration for the mass of the resonance X(2239).

Weak decays of the axial-vector tetraquark Tbb;u¯d¯−

The weak decays of the axial-vector tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$ to the scalar state $Z_{bc;\bar{u} \bar{d}}^{0}$ are investigated using the QCD three-point sum rule approach. In order to explore the process $T_{bb; \bar{u} \bar{d}}^{-} \to Z_{bc;\bar{u} \bar{d}}^{0}l \bar{\nu_l}$, we recalculate the spectroscopic parameters of the tetraquark $T_{bb;\bar{u} \bar{d}}^{-}$ and find the mass and coupling of the scalar four-quark system $Z_{bc;\bar{u} \bar{d}}^{0}$, which are important ingredients of calculations. The spectroscopic parameters of these tetraquarks are computed in the framework of the QCD two-point sum rule method by taking into account various condensates up to dimension ten. The mass of the $T_{bb;\bar{u} \bar{ d}}^{-}$ state is found to be $m=(10035~\pm 260)~\mathrm{MeV}$, which demonstrates that it is stable against the strong and electromagnetic decays. The full width $\Gamma$ and mean lifetime $\tau$ of $T_{bb;\bar{u} \bar{d} }^{-}$ are evaluated using its semileptonic decay channels $T_{bb; \bar{u} \bar{d}}^{-} \to Z_{bc;\bar{u} \bar{d}}^{0}l \bar{\nu_l}$, $l=e,\mu$ and $\tau$. The obtained results, $\Gamma=(7.17\pm 1.23)\times 10^{-8\ \ } \mathrm{MeV}$ and $\tau =9.18_{-1.34}^{+1.90}~\mathrm{fs}$, can be useful for experimental investigations of the doubly-heavy tetraquarks.

Revisit the \(X\)(4274) as the Axialvector Tetraquark State

In this article, we construct the $[sc]_A[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_A$ type tensor current to study the mass and width of the $X(4274)$ with the QCD sum rules in details. The predicted mass $M_{X}=(4.27\pm0.09) \, \rm{GeV}$ for the $J^{PC}=1^{++}$ tetraquark state is in excellent agreement with the experimental data $4273.3 \pm 8.3 ^{+17.2}_{-3.6} \mbox MeV}$ from the LHCb collaboration. The central value of the width $\Gamma(X(4274)\to J/\psi \phi)=47.9\,{\rm{MeV}}$ is in excellent agreement with the experimental data $56 \pm 11 ^{+8}_{-11} \mbox MeV}}$ from the LHCb collaboration. The present work supports assigning the $X(4274)$ to be the $J^{PC}=1^{++}$ $[sc]_A[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_A$ tetraquark state with a relative P-wave between the diquark and antidiquark constituents. Furthermore, we obtain the mass of the $[sc]_A[\bar{s}\bar{c}]_V-[sc]_V[\bar{s}\bar{c}]_A$ type tetraquark state with $J^{PC}=1^{-+}$ as a byproduct.

Tbbb: A three B-meson bound state

By solving exactly the Faddeev equations for the bound-state problem of three mesons, we demonstrate that current theoretical predictions pointing to the existence of a deeply-bound doubly bottom axial vector tetraquark lead to the existence of a unique bound state of three B mesons. We find that the BB⁎B⁎−B⁎B⁎B⁎ state with quantum numbers (I)JP=(1/2)2−, Tbbb, is about 90 MeV below any possible three B-meson threshold for the reported binding of the doubly bottom axial vector tetraquark, Tbb.

Probing an axial-vector tetraquark Zs via its semileptonic decay Zs $ \rightarrow$ → X(4274) $ \overline{{l}}$ l ¯ $ \nu_{l}^{}$ ν l

The semileptonic decays of the open charm-bottom axial-vector tetraquark $ Z_{s}=[cs][\overline{b}\overline{s}]$ to $X(4274)\overline{l} \nu_l$, $l=e, \mu, \tau $ are explored by means of the QCD three-point sum rule method. Both $Z_{s}$ and $X(4274)=[cs][\overline{c}\overline{s}]$ are treated as color sextet diquark-antidiquark states. The full width of the decays $Z_s \to X(4274)\overline{l} \nu_l$ is found. Obtained predictions for $ \Gamma(Z_s \to X(4274)\overline{l} \nu_l)$ demonstrate that, as in the case of the conventional hadrons, the semileptonic transitions form a very small part of its full width.

Tetraquark state candidates: Y(4260), Y(4360), Y(4660), and $$Z_c(4020/4025)$$ Z c ( 4020 / 4025 )

In this article, we construct the axialvector-diquark-axialvector-antidiquark type tensor current to interpolate both the vector and axialvector tetraquark states, then calculate the contributions of the vacuum condensates up to dimension-10 in the operator product expansion, and obtain the QCD sum rules for both the vector and axialvector tetraquark states. The numerical results support assigning the $Z_c(4020/4025)$ to be the $J^{PC}=1^{+-}$ diquark-antidiquark type tetraquark state, and assigning the $Y(4660)$ to be the $J^{PC}=1^{--}$ diquark-antidiquark type tetraquark state. Furthermore, we take the $Y(4260)$ and $Y(4360)$ as the mixed charmonium-tetraquark states, and construct the two-quark-tetraquark type tensor currents to study the masses and pole residues. The numerical results support assigning the $Y(4260)$ and $Y(4360)$ to be the mixed charmonium-tetraquark states.

Analysis of the Z(4430) as the First Radial Excitation of the Zc (3900)* *Supported by National Natural Science Foundation under Grant No. 11375063, and Natural Science Foundation of Hebei Province under Grant No. A2014502017

In this article, we take the Zc(3900) and Z(4430) as the ground state and the first radial excited state of the axial-vector tetraquark states with JPC = 1+−, respectively, and study their masses and pole residues with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension-10 in a consistent way in the operator product expansion. The numerical result favors assigning the Zc(3900) and Z(4430) as the ground state and first radial excited state of the axial-vector tetraquark states, respectively.

Hidden-charm tetraquarks and chargedZcstates

Experimentally several charged axial-vector hidden-charm states were reported. Within the framework of the color-magnetic interaction, we have systematically considered the mass spectrum of the hidden-charm and hidden-bottom tetraquark states. It is impossible to accommodate all of the three charged states ${Z}_{c}(3900)$, ${Z}_{c}(4025)$, and ${Z}_{c}(4200)$ within the axial-vector tetraquark spectrum simultaneously. Not all of these three states are tetraquark candidates. Moreover, the eigenvector of the chromomagnetic interaction contains valuable information of the decay pattern of the tetraquark states. The dominant decay mode of the lowest axial-vector tetraquark state is $J/\ensuremath{\psi}\ensuremath{\pi}$ while its ${D}^{*}\overline{D}$ and ${\overline{D}}^{*}{D}^{*}$ modes are strongly suppressed, which is in contrast with the fact that the dominant decay mode of ${Z}_{c}(3900)$ and ${Z}_{c}(4025)$ is $\overline{D}{D}^{*}$ and ${\overline{D}}^{*}{D}^{*}$, respectively. We emphasize that all the available experimental information indicates that ${Z}_{c}(4200)$ is a very promising candidate of the lowest axial-vector hidden-charm tetraquark state.

Exotic open-flavorbcq¯q¯,bcs¯s¯andqcq¯b¯,scs¯b¯tetraquark states

We study the exotic $bc\bar{q}\bar{q}$, $bc\bar{s}\bar{s}$ and $qc\bar{q}\bar{b}$, $sc\bar{s}\bar{b}$ systems by constructing the corresponding tetraquark currents with $J^P=0^+$ and $1^+$. After investigating the two-point correlation functions and the spectral densities, we perform QCD sum rule analysis and extract the masses of these open-flavor tetraquark states. Our results indicate that the masses of both the scalar and axial vector tetraquark states are about $7.1-7.2$ GeV for the $bc\bar{q}\bar{q}$ system and $7.2-7.3$ GeV for the $bc\bar{s}\bar{s}$ system. For the $qc\bar{q}\bar{b}$ tetraquark states with $J^P=0^+$ and $1^+$, their masses are extracted to be around $7.1$ GeV. The masses for the scalar and axial vector $sc\bar{s}\bar{b}$ states are $7.1$ GeV and $6.9-7.1$ GeV, respectively. The tetraquark states $qc\bar{q}\bar{b}$ and $sc\bar{s}\bar{b}$ lie below the thresholds of $D^{(\ast)}B^{(\ast)}$ and $D_s^{(\ast)}B_s^{(\ast)}$ respectively, but they can decay into $B_c$ plus a light meson. However, the tetraquark states $bc\bar{q}\bar{q}$ and $bc\bar{s}\bar{s}$ lie below the $D^{(\ast)}\bar B^{(\ast)}$ and $D_s^{(\ast)}\bar B_s^{(\ast)}$ thresholds, suggesting dominantly weak decay mechanisms.

Chiral structure of vector and axial-vector tetraquark currents

We investigate the chiral structure of local vector and axial-vector tetraquark currents, and study their chiral transformation properties. We consider the charge-conjugation parity and classify all the isovector vector and axial-vector local tetraquark currents of quantum numbers I(G)J(PC)=1(-)1(-+), I(G)J(PC)=1(+)1(--), I(G)J(PC)=1(-)1(++) and I(G)J(PC)=1(+)1(+-). We find that there is a one to one correspondence among them. Using these currents, we perform QCD sum rule analyses. Our results suggest that there is a missing b1 state having I(G)J(PC)=1(+)1(+-) and a mass around 1.47-1.66 GeV.