Analysis of Scalar Doubly Heavy Tetraquark States with QCD Sum Rules

In this article, we perform a detailed study of the mass spectrum of the scalar doubly charmed and doubly bottom tetraquark states using the QCD sum rules.

Search for Tetraquarks in Relativistic Heavy-Ion Collisions

Tetraquarks can be produced in relativistic heavy-ion collision. The yield of this kind of tetraquarks can increase significantly soon as the formation of QGP after the collision. If there is no phase transition after collision, the upper bound of the production of this four-quark states can be estimated from the free hadronlc gas model for nuclear matter. The relative yield ratio of tetraquark cs^-s^-s to Ω is less than 0.0164.

0^(--) hidden-heavy tetraquark states via QCD sum rules

In this study,we evaluated the mass spectra of the prospective 0^(--) hidden-charm and hidden-bottom tetraquark states in molecular configuration via QCD sum rules.In our calculation,the nonperturbative condensate contributions are considered up to dimension eight in operator product expansion.It is found that there could exist 4possible 0^(--) hidden-charm tetraquark states with masses(4.68±0.07),(4.22±0.09),(4.53±0.09),and(4.26±0.13) GeV.Their corresponding hidden-bottom partners are found lying at(11.04±0.10),(10.71±0.12),(11.09±0.10),and(11.82±0.14) GeV,respectively.The possible tetraquark decay modes were analyzed,which are expected to be measured in BESⅢ,BELLEⅡ,and LHCb experiments.

Fully-light vector tetraquark states with explicit P-wave via QCD sum rules

In this study,we apply the QCD sum rules to investigate the vector fully-light tetraquark states with an explicit P-wave between the diquark and antidiquark pairs.We observed that the Cγα⊗↔∂μ⊗γαC(or Cγα⊗↔Dμ⊗γαC)type current with fully-strange quarks couples potentially to a tetraquark state with a mass 2.16±0.14GeV,which supports assigning Y(2175)/ϕ(2170)as the diquark-antidiquark type tetraquark state with JPC=1−−.The qsˉqˉs and ssˉsˉs vector tetraquark states with the structure Cγμ⊗↔∂α⊗γαC+Cγα⊗↔∂α⊗γμ(or Cγμ⊗↔Dα⊗γαC+Cγα⊗↔Dα⊗γμ)are consistent with X(2200)and X(2400),respectively,which lie in the region from 2.20 to 2.40GeV.The central values of the masses of the fully-strange vector tetraquark states with an explicit P-wave are approximately 2.16−3.13GeV(or 2.16−3.16GeV).Predictions for other fully-light vector tetraquark states with and without hidden-strange are also presented.

Search for hidden-charm tetraquark with strangeness in e^(+)e^(−)→K^(+)D_(s)^(∗−) D^(∗0 )+ c.c.

We report a search for a heavier partner of the recently observed Z_(cs)(3985)^(-) state,denoted as Z_(cs)^('-),in the process e^(+)e^(−)→K^(+)D_(s)^(∗−) D^(∗0 )+ c.c.,based on e^(*)e^(-)collision data collected at the center-of-mass energies of √s=4.661,4.682 and 4.699 GeV with the BESIII detector.The Z_(cs)^('-) is of interest as it is expected to be a candidate for a hidden-charm and open-strange tetraquark.A partial-reconstruction technique is used to isolate K^(+)recoil-mass spectra,which are probed for a potential contribution from Z_(cs)^('-)→D_(s)^(∗−) D^(∗0 )+ c.c.We find an excess of Z_(cs)^('-)→D_(s)^(*-)-D^(*0)(c.c.)candidates with a significance of 2.1o,after considering systematic uncertainties,at a mass of(4123.5±0.7_(sat)±4.7_(syst.))MeV/c^(2).As the data set is limited in size,the upper limits are evaluated at the 90%confidence level on the product of the Born cross sections(σ^(Borm))and the branching fraction(B)of Z_(cs)^('-)→D_(s)^(*-)-D^(*0),under different assumptions of the Z_(cs)^('-) mass from 4.120 to 4.140 MeV and of the width from 10 to 50 MeV at the three center-of-mass energies.The upper limits of σ^(Born).B are found to be at the level of O(1)pb at each energy.Larger data samples are needed to confirm the Z_(cs)^('-) state and clarify its nature in the coming years.

Double-heavy tetraquarks with strangeness in the chiral quark model

Recently,some progress has been made in the experiments on double-heavy tetraquarks,such as T_(cc)reported by the LHCb Collaboration and Xccssreported by the Belle Collaboration.Coming on the heels of our previous work about T_(cc) and T_(bb), we present a study on the bound and resonance states of their companions,QQqs(Q=c,b;q=u,s) tetraquarks with strange flavor in the chiral quark model.Two pictures,meson-meson and diquark-antidiquark ones,and their couplings were considered in our calculations.Isospin violation was neglected herein.Our numerical analysis indicated that the states ccus with 1/2(1^(+)) ald bbus with 1/2(1^(+)) are the most promising stable states against strong interactions.Besides,we found several resonance states for the double-heavy strange tetraquarks with the real scaling method.

Mass spectra of doubly heavy tetraquarks in diquark-antidiquark picture

Inspired by the recent observation of the first doubly charmed tetraquark T_(cc),we apply the linear Regge relation and mass scaling to study low-lying mass spectra of the doubly heavy tetraquark in a heavy-diquark−light-antidiquark picture.The measured data and other compatible estimates of ground-state masses of doubly heavy baryons are employed to evaluate masses of heavy diquark M_(QQ)(Q=c,b)and the D/D_(s) meson masses are used in mass scaling to determine the hyperfine mass splitting.Our mass computation indicates that all low-lying states of doubly heavy tetraquarks are unstable against strong decays to two heavy-light mesons,except for the ground states of nonstrange bb tetraquarks.

Light meson emissions of selected charmonium-like states within compact tetraquark configurations

We adopt the quark pair creation model to investigate the light meson emissions of several charmoniumlike states.The quark pair creation model is applied to four-body systems,and we calculate the pion/kaon emissions of X(4700),Z_(c)(4430),Y(4230),Y(4360),Y(4390),and Y(4660)within compact tetraquark configurations.We find that the pion/kaon decay widths of X(4700)and Z_(c)(4430)the resonances Y(4230),Y(4360),Y(4390),and Y(4660)cay behaviors will provide useful information for future experimental searches and theoretical interpretations.

D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)

We study the mass spectra of D-wave excited cscs tetraquark states with J^(PC)=1^(++)and 1^(+-)in both symmetric 6cs@6cs and antisymmetric 3cs@3cs color configurations using the QCD sum rule method.We construct the D-wave diquark-antidiquark type of cscs tetraquark interpolating currents in various excitation structures with(L_(λ),Lp{p_(1),p_(2)})=(2,0(0,0),(1,1(1,0),(1,1(0,1),(0,2(1,1),(0,2(2,0),(0,2(0,2).Our results support the interpretation of the recently observed X(4685)resonance as a D-wave cscs tetraquark state with JPC-1++in the(2,O(0,O))or(0,2(2,O))excitation mode,although some other possible excitation structures cannot be excluded exhaustively within theoretical errors.Moreover,our results provide the mass relations 6_(ρρ)<3_(λλ)<3_(λρ)<3_(ρρ)and 6pp<3au<6aa<3pp for the positive and negative C-parity D-wave cscs tetraquarks,respectively.We suggest searching for these possible D-wave cscs tetraquarks in both the hidden-charm channels J/o and nc,as well as open-cham channes such as D_(s)D_(x)nd D_(s)D_(s1).

Investigation of the tetraquark states QqQq in the improved chromomagnetic interaction model

In the framework of the improved chromomagnetic interaction model,we complete a systematic study of the S-wave tetraquark states QqQq(Q=c,b,and q=u,d,s)with different quantum numbers:J^(PC)=0^(+(+)),1^(+(±)),and 2^(+(+)).The mass spectra of tetraquark states are predicted,and the possible decay channels are analyzed by considering both the angular momentum and C-parity conservation.The recently observed hidden-charm tetraquark states with strangeness,such as Z_(cs)(3985)^(-),X(3960),and Z_(cs)(4220)^(+),can be well explained in our model.Additionally,according to the wave function of each tetraquark state,we find that the low-lying states of each QqQq configuration have a large overlap to the QQ and qq meson basis,instead of the Qq and qQ meson basis.This indicates that one can search these tetraquark states in future experiments via the channel of QQ and qq mesons.

A non-relativistic model for the[cc]■ tetraquark

We use a non-relativistic model to study the spectroscopy of a tetraquark composed of [cc]■ in a diquark-antidiquark configuration.By numerically solving the Schr?dinger equation with a Cornell-inspired potential,we separate the four-body problem into three two-body problems.Spin-dependent terms(spin-spin,spin-orbit and tensor)are used to describe the splitting structure of the ■ spectrum and are also extended to the interaction between diquarks.Recent experimental data on charmonium states are used to fix the parameters of the model and a satisfactory description of the spectrum is obtained.We find that the spin-dependent interaction is sizable in the diquark-antidiquark system,despite the heavy diquark mass,and also that the diquark has a finite size if treated in the same way as the ■ systems.We find that the lowest S-wave T 4c tetraquarks might be below their thresholds of spontaneous dissociation into low-lying charmonium pairs,while orbital and radial excitations would be mostly above the corresponding charmonium pair thresholds.Finally,we repeat the calculations without the confining part of the potential and obtain bound diquarks and bound tetraquarks.This might be relevant to the study of exotic charmonium in the quark-gluon plasma.The T 4c states could be investigated in the forthcoming experiments at the LHC and BelleⅡ.

Doubly heavy tetraquarks in an extended chromomagnetic model

Using an extended chromomagnetic model,we perform a systematic study of the masses of doubly heavy tetraquarks.We find that the ground states of the doubly heavy tetraquarks are dominated by the color-triplet ■configuration,which is opposite to that of fully heavy tetraquarks.The combined results suggest that the color-triplet configuration becomes more important when the mass difference between the quarks and antiquarks increases.We find three stable states that lie below the thresholds of two pseudoscalar mesons.They are the I^(P)=01^(+)nnbb tetraquark,I^(P)=1^(+)nncb tetraquark,and J^(P)=1^(+)nsbb tetraquark.

Analysis of Z_(cs)(3985)as the axialvector tetraquark state

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 ccus in the framework of the QCD sum rules.The predicted tetraquark massM_(Z)=3.99±0.09GeV is in excellent agreement with the experimental value 3985.2^(+2.1)_(-2.0)±1.7 MeV from the BESⅢ collaboration,which supports identifying Z_{cs}(3985) as the cousin of Z_(c)(3900) with quantum numbers J^(PC)=1^(+-).We take into account the light flavor SU(3) mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

Scalar or Vector Tetraquark State Candidate: Z_c(4100)

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 than4.1 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).

Vector hidden-bottom tetraquark candidate: Y(10750)

In this article,we take the scalar diquark and antidiquark operators as the basic constituents,and construct the Cγ5■γ5C type tetraquark current to study Y（10750） with the QCD sum rules.The predicted mass MY=10.75±0.10 GeV and width ΓY=33.60-9.45+16.64 MeV support the assignment of Y（10750） as the diquark-antidiquark type vector hidden-bottom tetraquark state,with a relative P-wave between the diquark and antidiquark constituents.

0^+ tetraquark states from improved QCD sum rules:delving into X(5568)

In order to investigate the possibility of the recently observed X（5568） being a 0＋ tetraquark state, we make an improvement to the study of the related various configuration states in the framework of the QCD sum rules. Particularly, to ensure the quality of the analysis, condensates up to dimension 12 are included to inspect the convergence of operator product expansion （OPE） and improve the final results of the studied states. We note that some condensate contributions could play an important role on the OPE side. By releasing the rigid OPE convergence criterion, we arrive at the numerical value 5.57-0.23＋0.35 GeV for the scalar-scalar diquark-antidiquark 0＋ state, which agrees with the experimental data for the X（5568） and could support its interpretation in terms of a 0＋ tetraquark state with the scalar-scalar configuration. The corresponding result for the axial-axial current is calculated to be 5.77-0.33＋0.44 GeV, which is still consistent with the mass of X（5568） in view of the uncertainty. The feasibility of X（5568） being a tetraquark state with the axial-axial configuration therefore cannot be definitely excluded. For the pseudoscalar-pseudoscalar and the vector-vector cases, their unsatisfactory OPE convergence make it difficult to find reasonable work windows to extract the hadronic information.

The ■ tetraquark states and the structure of X(2239) observed by the BESⅢ collaboration

We investigate the mass spectrum of the ■ tetraquark states in the relativized quark model.By solving the Schr?dinger-like equation with the relativized potential,the masses of S-and P-wave ■ tetraquarks are obtained.The screening effects are also taken into account.It is found that the resonant structureX（2239）observed in thee+e-→K+K-process by the BESIII collaboration can be assigned as a P-wave 1--■ tetraquark state.Furthermore,the radiative transition and the strong decay behavior of this structure are also estimated,which can provide helpful information for future experimental searches.

Can X(5568) be a tetraquark state?

Very recently, the D0 collaboration has reported the observation of a narrow structure, X（5568）, in the decay process X（5568）→ Bs^0π^±using the 10.4fb^-1 data of pp collision at √s= 1.96 TeV. This structure is of great interest since it is the first hadronic state with four different valence quark flavors, b, s, u, d. In this work,we investigate tetraquarks with four different quark flavors. Based on the diquark-antidiquark scheme, we study the spectroscopy of the tetraquarks with one heavy bottom/charm quark and three light quarks. We find that the lowest-lying S-wave state, a tetraquark with the flavor [su][bd] and the spin-parity J^P= 0^＋, is about 150 MeV higher than the X（5568）. Further detailed experimental and theoretical studies of the spectrum, production and decays of tetraquark states with four different flavors are vital to gain a better understanding of the nature and classification of hadron exotic states.

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states ao（980）, f0（980）,k, within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the ＂fall apart＂ mechanism.

Production of Tetraquark State T_(cc) at B-Factories

We study production of the tetraquark state Tcc via virtual photon at the B-factories in the QCD factorization framework. We predict the cross section of tetraquark state production in the leading order at the B-factories.