$X_{0,1}$(2900) and $(D^{-}{K}^{+})$ invariant mass from QCD Laplace sum rules at NLO

Abstract

We revisit, improve and complete some recent estimates of the $0^{+}$ and $1^{-}$ open charm $(\bar{c}\bar{d})(us)$ tetraquarks and the corresponding molecules masses and decay constants from QCD spectral sum rules (QSSR) by using QCD Laplace sum rule (LSR) within stability criteria where the factorised perturbative NLO corrections and the contributions of quark and gluon condensates up to dimension-6 in the OPE are included. We confront our results with the $D^{-}{K}^{+}$ invariant mass recently reported by LHCb from $B^{+}\to D^{+}(D^{-}{K}^{+})$ decays. We expect that the bump near the $D^{-}{K}^{+}$ threshold can be originated from the $0^{++}(D^{-}{K}^{+})$ molecule and/or $D^{-}{K}^{+}$ scattering. The prominent $X_0$(2900) scalar peak and the bump $X_J(3150)$ (if $J=0$) can emerge from a {\it minimal mixing model}, with a tiny mixing angle ${\theta }_0\simeq (5.2\pm 1.9{)}^0$, between a scalar {\it Tetramole} (${{\mathcal{T}}_{\mathcal{M}}}_0$) (superposition of nearly degenerated hypothetical molecules and compact tetraquarks states with the same quantum numbers) having a mass $M_{{{\mathcal{T}}_{\mathcal{M}}}_0}$=2743(18) MeV and the first radial excitation of the $D^{-}{K}^{+}$ molecule with mass $M_{(DK{)}_1}=3678(310)$ MeV. In an analogous way, the $X_1$(2900) and the $X_J(3350)$ (if $J=1$) could be a mixture between the vector {\it Tetramole} $({{\mathcal{T}}_{\mathcal{M}}}_1)$ with a mass $M_{{{\mathcal{T}}_{\mathcal{M}}}_1}=2656(20)$ MeV and its first radial excitation having a mass $M_{({{\mathcal{T}}_{\mathcal{M}}}_1{)}_1}=4592(141)$ MeV with an angle ${\theta }_1\simeq (9.1\pm 0.6{)}^0$. A (non)-confirmation of the previous {\it minimal mixing models} requires an experimental identification of the quantum numbers of the bumps at 3150 and 3350 MeV.

28 pages, 15 Figures, 5 Tables - Version to appear in Nuclear Physics A after some minor corrections on proofs

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Cited by in corpus (36)

• An updated review of the new hadron states
• Hadronic molecules in B decays
• A study of the decays of $S-$wave ${\bar{D}}^{\ast }{K}^{\ast }$ hadronic molecules: the scalar $X_0(2900)$ and its spin partners $X_{J(J=1,2)}$
• Mass spectrum and strong decays of tetraquark $\bar{c}\bar{s}qq$ states
• Analysis of the $Z_{cs}(3985)$ as the axialvector tetraquark state
• Z_c -like spectra from QCD Laplace sum rules at NLO
• How to understand the $X(2900)$?
• Discriminating among interpretations for the $X(2900)$ states
• The $\mathbf{sQ}\bar{\mathbf{q}}\bar{\mathbf{q}}$ $(\mathbf{q}=\mathbf{u},\mathbf{d};\mathbf{Q}=\mathbf{c},\mathbf{b})$ tetraquarks in the chiral quark model
• The $T_{c\bar{s}}(2900)$ as a threshold effect from the interaction of the $D^{\ast }{K}^{\ast }$, $D_s^{\ast }\rho$ channels
• On the structures of new scalar resonances $T_{cs0}^a(2900{)}^{++}$ and $T_{cs0}^a(2900{)}^0$
• Vector resonance $X_1(2900)$ and its structure
• Modeling the resonance $T_{cs0}^a(2900{)}^{++}$ as a hadronic molecule $D^{\ast +}{K}^{\ast +}$
• Spectrum of the molecular tetraquarks: Unraveling the $T_{cs0}(2900)$ and $T_{c\bar{s}0}^a(2900)$
• Color flux-tube nature of the states $T_{cs}(2900)$ and $T_{c\bar{s}}^a(2900)$
• Unified description of the $Qs\bar{q}\bar{q}$ molecular bound states, molecular resonances and compact tetraquark states in the quark potential model
• The ${\bar{B}}^0\to D^{\ast +}{\bar{D}}^{\ast 0}{K}^{-}$ reaction to detect the $I=0,J^P=1^{+}$ partner of the $X_0(2866)$
• Possibility of $T_{c\bar{s}}(2900)$ as the resonance-like structure induced by threshold effects
• Prediction of possible $D{K}_1$ bound states
• Improved XTZ masses and mass ratios from Laplace Sum Rules at NLO
• Magnetic moment of the $X_1(2900)$ state in the diquark-antidiquark picture
• Looking for the exotic $X_0(2866)$ and its $J^P=1^{+}$ partner in the ${\bar{B}}^0\to D^{(\ast )+}{K}^{-}{K}^{(\ast )0}$ reactions
• Method to observe the $J^P=2^{+}$ partner of the $X_0(2866)$ in the $B^{+}\to D^{+}{D}^{-}{K}^{+}$ reaction
• Is the resonance $X_0(2900)$ a ground-state or radially excited scalar tetraquark $[ud][\overline{c}\overline{s}]$?
• Discovery of $T_{c\bar{s}0}^a(2900{)}^{0,++}$ implies new charmed-strange pentaquark system
• Double pole structures of $X_1(2900)$ as the $P$-wave ${\bar{D}}^{\ast }{K}^{\ast }$ resonances
• Next-to-Leading Order (NLO) Perturbative Effects in QCD Sum-Rule Analyses of Light Tetraquark Systems: A Case Study in the Scalar-Isoscalar Channel
• Possible Molecular Explanation for the Resonance $Y(4500)$
• $Z_c$ and $Z_{cs}$ systems with operator mixing at NLO in QCD sum rules
• Theoretical study of the open-flavor tetraquark $T_{c\bar{s}}(2900)$ in the process ${\bar{B}}_s^0\to K^0{D}^0{\pi }^0$
• $D_1(2420)$ and its interactions with a kaon: open charm states with strangeness
• $D^{(\ast )}{\bar{B}}^{(\ast )}$ dynamics in chiral effective field theory
• Baryons and baryoniums in the perspective of QCD sum rules
• Tests of the Z_c-like Laplace Sum Rule (LSR) results using FESR at NLO
• Strange pentaquark molecules in QCD sum rules
• Exotic hadrons associated with $b$-quark