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.

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.

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.

A family of double-beauty tetraquarks:Axial-vector state T^-bb;us^-

The spectroscopic parameters and decay channels of the axial-vector tetraquark Tho(in what follows,TAV)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 m=(10215±250)MeV 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 T AV b:s^-→v10 b:s^-M decays of T AV b:s^-.In these processes,Z-b:s^-is a scalar tetraquark[be][us^-]built of a colo-triplet diquark and an antidiquark,whereas M is one of the vector mesonsρ^-,K^*(892),D^*(2010)^-,and D^*s-.To caleulate the partial w idths of these decays,we use the QCD three-point sum rule approach and evaluate the weak transition form factors Gi(i=0,1,2,3),which govem these processes.The full widthΓfull=(12.9±2.1)×10^-8 MeV and the mean lifetimeτ=5.1+0.99-0.71 fs of the tetraquark TAV are computed us-ing the aforementioned weak decays.The obtained information about the parametersof TAY and Zh,is useful for experimental investigations of these double-heavy exotic mesons.

Discovery potentials of double-charm tetraquarks

In this study,we investigate the discovery potential of double-charm tetraquarks■.We find that their production cross sections at the LHCb with■TeV reach O(10^(4))pb,which indicates that the LHCb has collected O(10^(8))such particles.Through the decay channels of■or■or■(if unstable),it is highly expected that they get discovered at the LHCb in the near future.We also discuss the productions and decays of the double-charm tetraquarks at future Tera-Z factories.

Strong decays of fully-charm tetraquarks into di-charmonia

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,our results suggest that the broad structure around 6.2–6.8 GeV can be interpreted as an S-wave cccc tetraquark state with JPC=0++or 2++,and the narrow structure around 6.9 GeV can be interpreted as a P-wave one with JPC=0-+or 1-+.These structures were observed in the di-J=w invariant mass spectrum,and we propose to confirm them in the di-gc;J/ψhc;ηcχc0,and ηcχc1channels.We also propose to search for their partner states having the negative charge-conjugation parity in the J/ψηc;J/ψχc0;J/ψχc1,and ηchc channels.

Qq^- Q ^- q＇ States in Chiral SU（3） Quark Model

We study the masses of Qq^- Q ^- q＇ states with J^PC=0^＋＋,1＋＋ and 2^＋＋ in the chiral SU（3）quark model, where Q is the heavy quark （c or b） and q （q＇） is the light quark （u, d or s）. According to our numerical results, it is improbable to make the interpretation of [cn^-C^-n]1＋＋ and [cn^-C^-n]2＋＋ （n = u, d） states as X（3872） and Y（3940）, respectively. However, it is interesting to find the tetraquarks in the bq^-b^-q＇ system.

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.

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.

X(3960),X0(4140),and other compact cs■states

We studied the spectrum and rearrangement decays of S-wave cs■tetraquark states in a simplified quark model.The masses and widths were estimated by assuming that X(4140)is the lower 1^(++)cs■tetraquark.Comparing our results with experimental measurements,we found that X(3960),recently observed by LHCb,can be considered the lowest 0^(++)sc■tetraquark state and X0(4140)could be the second lowest 0^(++)cs■tetraquark.Predictions of ratios between partial widths for the involved tetraquarks are provided in this paper.We aim to identify more cs■tetraquarks with J^(PC)=1^(+-),0^(++),and 2^(++).

Strong decay of Y(4230)→ J/ψ f0(980) in light cone sum rules

In this study,we assign the tetraquark state for the Y(4230) resonance and investigate the mass and decay constant of Y(4230) in the framework of SVZ sum rules through a different calculation technique.Then,we calculate the strong coupling gYJ/ψf0 by considering soft-meson approximation techniques within the framework of light cone sum rules,and we use the strong coupling gYJ/ψf0 to obtain the width of the decay Y(4230)→J/ψf0(980).Our prediction for the mass agrees with the experimental measurement,and that for the decay width of Y(4230)→J/ψf0(980) is within the upper limit.

Magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states in the diquark-antidiquark picture

The magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states are calculated within the QCD light-cone sum rules.The compact diquark-antidiquark interpolating currents and the distribution amplitudes of the on-shell photon are used to extract the magnetic and quadrupole moments of these states.The magnetic moments are acquired asμZ_(c)=0.50+0.22−0.22μN,μZ_(c)^(1)=1.22+0.34−0.32μN,andμZ_(c)^(2)=2.40+0.53−0.48μN for the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states,respectively.The magnetic moments evaluated for the Z_(c)4020)+,Z_(c)(4050)+,and Z_(c)(4600)+states are sufficiently large to be experimentally measurable.The magnetic moment is an excellent platform for studying the internal structure of hadrons governed by the quark-gluon dynamics of QCD because it is the leading-order response of a bound system to a weak external magnetic field.The quadrupole moment results are DZ_(c)=(0.20+0.05−0.04)×10^(−3)fm^(2),DZ_(c)^(1)=(0.57+0.07−0.08)×10^(−3)fm^(2),and DZ_(c)^(2)=(0.30+0.05−0.04)×10^(−3)fm^(2)for the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states,respectively.We obtain a non-zero,but small,value for the quadrupole moments of the Z_(c)states,which indicates a non-spherical charge distribution.The nature and internal structure of these states can be elucidated by comparing future experimental data on the magnetic and quadrupole moments of the Z_(c)(4020)^(+),Z_(c)(4050)^(+),and Z_(c)(4600)^(+)states with the results of the present study.

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.

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.

Exotic states with QQQ′Q′configuration

In the framework of a non-relativistic quark model,we have calculated the masses of the QQQ′Q′(Q=c,b,s and Q′=c,b,s)tetraquark states.Using the linear and quadratic confinement potentials inside a Cornell-type potential along with all possible spin and color configurations,the Schrodinger equation masses of these tetraquark states have been calculated.Based on our numerical analysis,linear confinement and quadratic confinement produce acceptable results.Models that use linear confinement estimate charmonium-like tetraquark mass close to experimental data,as well as bottomonium-like tetraquark mass below the threshold of their meson-meson channels.

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.

Production of X_(eses)in heavy ion collisions

The yields of X_(cscs)with its two possible configurations,i.e.,the hadronic molecular state and tetraquark state,for Pb-Pb collisions at√sNN=5.02 TeV is studied.A volume effect is found from the centrality distribution of X_(cscs),which could help to distinguish the inner structure of X_(cscs).We also show the rapidity and the transverse momentum distributions of X_(cscs) production as well as its elliptic flow coefficient as a function of the transverse momentum.

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.