The $X(3960)$, $X_0(4140)$, and other compact $cs\bar{c}\bar{s}$ states

We study the spectrum and rearrangement decays of S-wave $cs\bar{c}\bar{s}$ tetraquark states in a simplified quark model. The masses and widths are estimated by assuming that the $X(4140)$ is the lower $1^{++}$ $cs\bar{c}\bar{s}$ tetraquark. Comparing our results with experimental measurements, we find that the recently observed $X(3960)$ by LHCb can be assigned as the lowest $0^{++}$ $cs\bar{c}\bar{s}$ tetraquark state and the $X_0(4140)$ could be the second lowest $0^{++}$ $cs\bar{c}\bar{s}$ tetraquark. Predictions of ratios between partial widths for the involved tetraquarks are given. We call for searches for more $cs\bar{c}\bar{s}$ tetraquarks with $J^{PC}=1^{+-}$, $0^{++}$, and $2^{++}$.

[1]  Yan-Rui Liu,et al.  The hidden-charm pentaquark states in a mass splitting model , 2023, 2307.00539.

[2]  Han-qing Zheng,et al.  On the nature of X(3960) , 2023, The European Physical Journal C.

[3]  F. Guo,et al.  Understanding the 0++ and 2++ charmonium(-like) states near 3.9 GeV. , 2022, Science bulletin.

[4]  Zhi-Gang wang,et al.  Analysis of the X(3960) and related tetraquark molecular states via the QCD sum rules , 2022, AAPPS Bulletin.

[5]  H. Mutuk.  Molecular interpretation of X(3960) as $$D_s^+ D_s^-$$ state , 2022, The European Physical Journal C.

[6]  Jiaxing Zhao,et al.  Investigation of the tetraquark states in the improved chromomagnetic interaction model , 2022, Chinese Physics C.

[7]  Jun-Zhang Wang,et al.  Connection between near the $D_s^+D_s^-$ threshold enhancement in $B^+ \to D_s^+D_s^-K^+$ and conventional charmonium $\chi_{c0}(2P)$ , 2022, 2210.16720.

[8]  I. A. Monroy,et al.  Observation of a Resonant Structure near the D_{s}^{+}D_{s}^{-} Threshold in the B^{+}→D_{s}^{+}D_{s}^{-}K^{+} Decay. , 2022, Physical review letters.

[9]  Qi Huang,et al.  Charmoniumlike resonant explanation on the newly observed $X(3960)$ , 2022, 2209.05180.

[10]  V. Papadimitriou,et al.  Review of CMS contribution to Hadron Spectroscopy (Snowmass 2021 White Paper) , 2022, 2204.06667.

[11]  Hao Sun,et al.  The strong coupling g/ of X(4700)→J/ψϕ in the light-cone sum rules , 2022, Nuclear Physics B.

[12]  K. Azizi,et al.  Resonance $X(4630)$ , 2022, 2203.02542.

[13]  Satoshi X. Nakamura.  X structures in B+ → J/ψ ϕ K+ as one-loop and double-triangle threshold cusps , 2021, Physics Letters B.

[14]  F. Huang,et al.  Hidden charm tetraquark states in a diquark model , 2021, 2105.02397.

[15]  E. Santopinto,et al.  Quark Structure of the X (4500), X (4700) and χ c (4P,5P) States , 2021, Frontiers in Physics.

[16]  A. Turkan,et al.  Newly observed resonance $ X(4685) $: diquark-antidiquark picture , 2021, 2103.05515.

[17]  Xiang Liu,et al.  Newly observed X(4630): a new charmoniumlike molecule , 2021, The European Physical Journal C.

[18]  R. A. Mohammed,et al.  Observation of New Resonances Decaying to J/ψK^{+} and J/ψϕ. , 2021, Physical review letters.

[19]  R. A. Mohammed,et al.  Amplitude analysis of the B+→D+D−K+ decay , 2020, Physical Review D.

[20]  I. A. Monroy,et al.  A model-independent study of resonant structure in $B^+\to D^+D^-K^+$ decays , 2020, 2009.00025.

[21]  Yan-Rui Liu,et al.  Spectrum and rearrangement decays of tetraquark states with four different flavors , 2020, 2001.05287.

[22]  Hong Chen,et al.  Can the state Y(4626) be a P -wave tetraquark state [cs][c¯s¯] ? , 2019, Physical Review D.

[23]  Wei Hao,et al.  Canonical interpretation of the X(4140) state within the 3P0 model , 2019, Hadron Spectroscopy and Structure.

[24]  Yan-Rui Liu,et al.  Pc(4457)+ , Pc(4440)+ , and Pc(4312)+ : Molecules or compact pentaquarks? , 2019, Physical Review D.

[25]  Yan-Rui Liu,et al.  Pentaquark and Tetraquark States , 2019, Progress in Particle and Nuclear Physics.

[26]  Yan-Rui Liu,et al.  Systematic studies of charmonium-, bottomonium-, and Bc -like tetraquark states , 2018, Physical Review D.

[27]  Hongxia Huang,et al.  Hidden charmed states and multibody color flux-tube dynamics , 2017, Physical Review D.

[28]  Yan-Rui Liu,et al.  Hidden-charm pentaquarks and their hidden-bottom and $B_c$-like partner states , 2017, 1701.03873.

[29]  Yubing Dong,et al.  X (4140 ), X (4274 ), X (4500 ), and X (4700 ) in the relativized quark model , 2016, 1607.05570.

[30]  R. Zhu.  Hidden charm octet tetraquarks from a diquark-antidiquark model , 2016, 1607.02799.

[31]  L. Maiani,et al.  Interpretation of Axial Resonances in J/psi-phi at LHCb , 2016, 1607.02405.

[32]  Zhi-Gang wang.  Scalar tetraquark state candidates: X(3915), X(4500) and X(4700) , 2016, 1606.05872.

[33]  Hua-Xing Chen,et al.  Understanding the internal structures of X(4140), X(4274), X(4500) and X(4700) , 2016, 1606.03179.

[34]  Yan-Rui Liu,et al.  Heavy-flavored tetraquark states with the Q Q Q ̄ Q ̄ configuration , 2016, 1605.01134.

[35]  Zhi-Gang wang,et al.  Tetraquark state candidates: $Y(4140)$, $Y(4274)$ and $X(4350)$ , 2015, 1502.04619.

[36]  Yan-Rui Liu.  Heavy quark spin selection rules in meson-antimeson states , 2013, 1304.7467.

[37]  Xiang Liu,et al.  Novel charmonium-like structures in the J / ? ? and J / ? ? invariant mass spectra , 2010, 1011.1045.

[38]  R. Molina,et al.  Radiative decays of the Y(3940), Z(3930), and the X(4160) as dynamically generated resonances , 2010, 1010.0587.

[39]  Y. Simonov,et al.  Channel coupling in heavy quarkonia: Energy levels, mixing, widths, and new states , 2010 .

[40]  Y. J. Kim,et al.  Evidence for a new resonance and search for the Y(4140) in the gammagamma-->phiJ/psi process. , 2009, Physical review letters.

[41]  Chengping Shen,et al.  XYZ particles at Belle , 2009, 0912.2386.

[42]  Gui-Jun Ding.  Possible molecular states of $D^{*}_{s}\bar{D}^{*}_{s}$ system and Y(4140) , 2009, 0904.1782.

[43]  M. Nielsen,et al.  A QCD sum rule calculation for the Y(4140) narrow structure , 2009, 0903.5540.

[44]  T. Gutsche,et al.  Hadronic molecule structure of the Y(3940) and Y(4140) , 2009, 0903.5424.

[45]  N. Mahajan.  Y(4140): Possible options , 2009, 0903.3107.

[46]  Xiang Liu,et al.  Y(4143) is probably a molecular partner of Y(3930) , 2009, 0903.2529.

[47]  R. Workman.  Amplitude Analysis , 1998, nucl-th/9807053.

[48]  Y. Simonov,et al.  The scalar exotic resonances X(3915), X(3960), X(4140) , 2023 .

[49]  H. Ke,et al.  Threshold effects as the origin of Z cs ( 4000 ) , Z cs ( 4220 ) and X ( 4700 ) observed in B + → J /ψφ K + , 2021 .

[50]  I. Babuschkin,et al.  Observation of J / Structures Consistent with Exotic States from Amplitude Analysis of B+ j /K+ Decays , 2017 .

[51]  A. Korytov,et al.  Observation of a peaking structure in the J /ψφ mass spectrum from B ± → J /ψφ K ± decays , 2014 .

[52]  G. Sciolla,et al.  Study of B ± , 0 → J/ψK + K − K ± , 0 and search for B 0 → J/ψφ at B A B AR , 2014 .

[53]  J. S. Lee,et al.  Observation of the Y(4140) structure in the J/ψ φ Mass Spectrum in B+- ---> J/ψ φ K decays , 2011 .

[54]  P. Barria,et al.  Evidence for a Narrow Near-Threshold Structure in the J/ψφ Mass Spectrum in B + → J/ψφK + Decays , 2009 .

[55]  Particle Data Group.  Review of Particle Physics , 1998 .

[56]  The explanation of some exotic states in the cs ¯ c ¯ s tetraquark system , 2022 .

[57]  Edinburgh Research Explorer Search for the X(4140) state in B+J/K+ decays with the D0 detector , 2022 .