QCD Sum Rule Analysis Research Articles

Revisiting ΞQ-ΞQ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{Q}-\\Xi _{Q}^{\\prime }$$\\end{document} mixing in QCD sum rules

In this work, we perform a QCD sum rules analysis on ΞQ-ΞQ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{Q}-\\Xi _{Q}^{\\prime }$$\\end{document} mixing. Contributions from up to dimension-6 four-quark operators are considered. However, it turns out that only dimension-4 and dimension-5 operators contribute, which reveals the non-perturbative nature of mixing. In particular, we observe that only the diagrams with the two light quarks participating in gluon exchange contribute to the mixing. Our results indicate that the mixing angle θc=(1.2∼2.8)∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{c}=(1.2\\sim 2.8)^{\\circ }$$\\end{document} for the Q=c\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=c$$\\end{document} case and θb=(0.28∼0.34)∘\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{b}=(0.28\\sim 0.34)^{\\circ }$$\\end{document} for the Q=b\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$Q=b$$\\end{document} case. Our prediction of θc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\ heta _{c}$$\\end{document} is consistent with the most recent Lattice QCD result within error. Such a small mixing angle seems unlikely to resolve the tension between the recent experimental measurement from Belle and Lattice QCD calculation for the semileptonic decay Ξc0→Ξ-e+νe\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Xi _{c}^{0}\\rightarrow \\Xi ^{-} e^{+}\ u _{e}$$\\end{document}.

Mass predictions of triply heavy hybrid baryons via QCD sum rules

In this article, we study the mass spectrum of the low-lying triply heavy hybrid baryon, which consists of three valence heavy quarks in a color octet and one valence gluon, with spin-parity J^P=(frac{1}{2})^+ via QCD sum rules. This is the first study on the triply heavy hybrid baryons in the framework of QCD sum rules. After performing the QCD sum rule analysis, we find that the mass of cccg hybrid baryon lies in M_{cccg}= 5.91–6.13 GeV. As a byproduct, the mass of the triply bottom hybrid baryon state is extracted to be around M_{bbbg}= 14.62–14.82 GeV. The contributions up to dimension eight at the leading order of alpha _s (LO) in the operator product expansion are taken into account in the calculation. The triply charmed hybrid baryon predicted in this work can decay into one doubly charmed baryon and one charmed meson. Especially, we propose to search for cccg hybrid baryon with J^{P}= (1/2)^+ in the P-wave decay channels Xi _{cc}^{++} D^0, Xi _{cc}^{+} D^+, and Xi _{ccs}^{+} D_s^+, which may be accessible in future BelleII, Super-B, PANDA, and LHCb experiments.

Light double-gluon hybrid states from QCD sum rules

We study the double-gluon hybrid states with the quark-gluon contents $\bar q q gg$ ($q=u/d$) and $\bar s s gg$. We construct twelve double-gluon hybrid currents with various quantum numbers, five of which are found to be zero due to some internal symmetries between the two gluon fields. We use the rest seven currents to perform QCD sum rule analyses. Especially, the masses of the double-gluon hybrid states with the exotic quantum number $J^{PC} = 2^{+-}$ are calculated to be $M_{|\bar q q gg;2^{+-}\rangle} = 2.26^{+0.20}_{-0.25}$ GeV and $M_{|\bar s s gg;2^{+-}\rangle} = 2.38^{+0.19}_{-0.25}$ GeV. Their two- and three-meson decay patterns are also investigated.

QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic catalysis

In-medium masses of the $1S$ and $1P$ states of heavy quarkonia are investigated in the magnetized asymmetric nuclear medium, accounting for the Dirac sea effects, using a combined approach of chiral effective model and QCD sum rule method. Masses are calculated from the in-medium scalar and twist-2 gluon condensates, calculated within the chiral model. The gluon condensate is simulated through the scalar dilaton field, $\ensuremath{\chi}$ introduced in the model through a scale-invariance breaking logarithmic potential. Contribution of the Dirac sea is incorporated through the nucleonic tadpole diagrams. Treating the scalar fields as classical, the dilaton field, $\ensuremath{\chi}$, the isoscalar nonstrange $\ensuremath{\sigma}(\ensuremath{\sim}(⟨\overline{u}u⟩+⟨\overline{d}d⟩))$, strange $\ensuremath{\zeta}(\ensuremath{\sim}⟨\overline{s}s⟩)$ and isovector $\ensuremath{\delta}(\ensuremath{\sim}(⟨\overline{u}u⟩\ensuremath{-}⟨\overline{d}d⟩))$ fields, are obtained by solving their coupled equations of motion as derived from the chiral model Lagrangian. The effects of magnetic field are incorporated through the Dirac sea as well as the Landau energy levels of the protons, and the anomalous magnetic moments of the nucleons. The scalar fields modify appreciably with magnetic field due to the Dirac sea contribution. In-medium masses of the charmonium and bottomonium ground states are observed to have significant modifications with magnetic field due to the effects of (inverse) magnetic catalysis. In presence of an external magnetic field, there is mixing between the longitudinal component of the vector and the pseudoscalar mesons (PV mixing) in both quarkonia sectors, leading to a rise (drop) of the masses of $J/{\ensuremath{\psi}}^{||}({\ensuremath{\eta}}_{c})$ and ${\mathrm{\ensuremath{\Upsilon}}}^{||}(1S)({\ensuremath{\eta}}_{b})$ states. These might show in the experimental observables, e.g., the dilepton spectra in the noncentral, ultrarelativistic heavy ion collision experiments at RHIC and LHC, where the produced magnetic field is huge.

Next-to-leading order (NLO) perturbative effects in QCD sum-rule analyses of light tetraquark systems: A case study in the scalar-isoscalar channel

QCD sum-rule mass predictions for tetraquark states provide insights on the interpretations and internal structure of experimentally-observed exotic mesons. However, the overwhelming majority of tetraquark QCD sum-rule analyses have been performed at leading order (LO), which raises questions about the underlying theoretical uncertainties from higher-loop corrections. The impact of next-to-leading order (NLO) perturbative effects are systematically examined in scalar (JPC=0++) isoscalar light-quark tetraquark systems where comprehensive LO sum-rule analyses have been performed and NLO perturbative corrections to the correlators have previously been calculated. Using the scalar-isoscalar state as a detailed case study to illustrate the differences between LO and NLO analyses, it is shown that NLO effects in individual Laplace sum-rules are numerically significant and have an important role in improving the reliability of the sum-rule analyses by widening the Borel window. However, ratios of sum-rules are found to be less sensitive to NLO effects with the additional advantage of cancelling the anomalous dimension that emerges from the NLO corrections. NLO mass predictions based on these sum-rule ratios are thus remarkably robust despite the slow perturbative convergence of the underlying correlator. The mass predictions 0.52GeV<mσ<0.77GeV for the lightest scalar-isoscalar σ state are in good agreement with the four-quark interpretation of the f0(500), and the relative coupling strengths of the f0(980) and f0(500) to the tetraquark current agree with the pattern found in chiral Lagrangian analyses. Effects of the σ resonance width are studied for different models, including resonance shapes inspired by chiral Lagrangians.

Covalent hadronic molecules via QCD sum rules

After carefully examining Feynman diagrams corresponding to the $\bar D \Sigma_c$ hadronic molecular state, we propose a possible binding mechanism induced by shared light quarks. We systematically study its corresponding light-quark-exchange interaction using the method of QCD sum rules, and the obtained results suggest that there can be the $\bar D \Sigma_c$ covalent molecule of $I=1/2$. Our QCD sum rule analyses further indicate a model-independent hypothesis: the light-quark-exchange interaction is attractive when the shared light quarks are totally antisymmetric so that obey the Pauli principle.

ϕ meson properties in nuclear matter from QCD sum rules with chirally separated four-quark condensates

The modification of the $\ensuremath{\phi}$ meson spectrum in nuclear matter is studied in an updated QCD sum rule analysis, taking into account recent improvements in properly treating the chiral invariant and breaking components of four-quark condensates. Allowing both mass and decay width to change at finite density, the QCD sum rule analysis determines certain combinations of changes for these parameters that satisfy the sum rules equally well. A comprehensive error analysis, including uncertainties related to the behavior of various condensates at linear order in density, the employed renormalization scale and perturbative corrections of the Wilson coefficients, is used to compute the allowed ranges of these parameter combinations. We find that the $\ensuremath{\phi}$ meson mass shift in nuclear matter is especially sensitive to the strange sigma term ${\ensuremath{\sigma}}_{sN}$, which determines the decrease of the strange quark condensate in nuclear matter. Specifically, we obtain a linear relation between the width ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}$ and mass shift $\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}$ given as ${\mathrm{\ensuremath{\Gamma}}}_{\ensuremath{\phi}}=a\mathrm{\ensuremath{\Delta}}{m}_{\ensuremath{\phi}}+b{\ensuremath{\sigma}}_{sN}+c$ with $a=({3.947}_{\ensuremath{-}0.130}^{+0.139})$, $b=({0.936}_{\ensuremath{-}0.177}^{+0.180})$ and $c=\ensuremath{-}({7.707}_{\ensuremath{-}5.679}^{+4.791})\text{ }\text{ }\mathrm{MeV}$.

Mixing of X and Y states from QCD sum rules analysis * *Supported by NSFC (11175153, 11205093) and the Natural Sciences and Engineering Research Council of Canada (NSERC)

We study and states as mixed states in QCD sum rules. By calculating the two-point correlation functions of pure states of their corresponding currents, we review the mass and coupling constant predictions of , , and states. By calculating the two-point mixed correlation functions of and currents, we estimate the mass and coupling constants of the corresponding "physical state" that couples to both and currents. Our results suggest that for states, the and components are more likely to mix, while for and states, there is less mixing between and . Our results suggest the Y series of states have more complicated components.

QCD sum rules analysis of weak decays of doubly heavy baryons: the brightarrow c processes

A comprehensive study of brightarrow c weak decays of doubly heavy baryons is presented in this paper. The transition form factors as well as the pole residues of the initial and final states are respectively obtained by investigating the three-point and two-point correlation functions in QCD sum rules. Contributions from up to dimension-6 operators are respectively considered for the two-point and three-point correlation functions. The obtained form factors are then applied to a phenomenological analysis of semi-leptonic decays.

Monte-Carlo based QCD sum rules analysis of X 0(2900) and X 1(2900)

Motivated by the very recent discovery of fully open-flavor exotic states X 0(2900) and X 1(2900) by the LHCb collaboration [], we study possible interpretations of these exotic states by QCD sum rules method. We have calculated mass and decay constant by traditional QCD sum rules analysis and Monte-Carlo based analysis. X 0(2900) and X 1(2900) are studied in molecular and diquark–antidiquark tetraquark pictures, respectively. Obtained mass results agree well with the masses observed in the experiment. We also made a Monte-Carlo based analysis within QCD sum rules for the mass and decay constant distributions to investigate the possible assignments for the structures of X 0(2900) and X 1(2900).

New Λb(6072)0 state as a 2S bottom baryon

As a result of continuous developments, the recent experimental searches lead to the observations of new particles at different hadronic channels. Among these hadrons are the excited states of the heavy baryons containing single bottom or charmed quark in their valance quark content. The recently observed $\Lambda_b(6072)^0$ state is one of these baryons and possibly $2S$ radial excitation of the $\Lambda_b$ state. Considering this information from the experiment, we conduct a QCD sum rule analysis on this state and calculate its mass and current coupling constant considering it as a $2S$ radially excited $\Lambda_b$ resonance. For completeness, in the analyses, we also compute the mass and current coupling constant for the ground state $\Lambda_b^0$ and its first orbital excitation. We also consider the $\Lambda_c^+$ counterpart of each state and attain their mass, as well. The obtained results are consistent with the experimental data as well as existing theoretical predictions.

Hidden-bottom and -charm hexaquark states in QCD sum rules

In this paper, we investigate the spectra of the prospective hidden-bottom and -charm hexaquark states with quantum numbers J^{PC }= 0^{++}, 0^{-+}, 1^{++} and 1^{--} in the framework of QCD sum rules. By constructing appropriate interpreting currents, the QCD sum rules analyses are performed up to dimension 12 of the condensates. Results indicate that there exist two possible baryonium states in b-quark sector with masses 11.84 pm 0.22 GeV and 11.72 pm 0.26 GeV for 0^{++} and 1^{--}, respectively. The corresponding hidden-charm partners are found lying respectively at 5.19 pm 0.24 GeV and 4.78 pm 0.23 GeV. Note that these baryonium states are all above the dibaryon thresholds, which enables their dominant decay modes could be measured at BESIII, BELLEII, and LHCb detectors.

QCD sum rule studies of s s {bar{s}} {bar{s}} tetraquark states with J^{PC} = 1^{+-}

We apply the method of QCD sum rules to study the structure X newly observed by the BESIII Collaboration in the phi eta ^prime mass spectrum in 2.0–2.1 GeV region in the J/psi rightarrow phi eta eta ^prime decay. We construct all the s s {bar{s}} {bar{s}} tetraquark currents with J^{PC} = 1^{+-}, and use them to perform QCD sum rule analyses. One current leads to reliable QCD sum rule results and the mass is extracted to be 2.00^{+0.10}_{-0.09} GeV, suggesting that the structure X can be interpreted as an s s {bar{s}} {bar{s}} tetraquark state with J^{PC} = 1^{+-}. The Y(2175) can be interpreted as its s s {bar{s}} {bar{s}} partner having J^{PC} = 1^{--}, and we propose to search for the other two partners, the s s {bar{s}} {bar{s}} tetraquark states with J^{PC} = 1^{++} and 1^{-+}, in the eta ^prime f_0(980), eta ^prime K {bar{K}}, and eta ^prime K {bar{K}}^* mass spectra.

Exploratory study of χc1(4140) and like states in QCD sum rules

In this work, we chose three molecular and three diquark–antidiquark currents with the quark content cc¯ss¯ and JPC=0++,1++,2++, and estimated the masses and the meson coupling constants of the ground states coupling to these currents in the framework of QCD sum rules. In operator product expansion, we considered the terms including dimension eight, and we performed pole contribution tests carefully. According to our results, all of these currents couple to the ground states with degenerate masses which are in 10 MeV vicinity of χc1(4140). Therefore, with a QCD sum rules analysis, it is not possible to conclude that χc1(4140) has a dominant molecular or diquark–antidiquark content. However, there may be three states degenerate in mass, with positive charge conjugation and different isospins.

Revisiting [formula omitted] as a 0+ tetraquark state from QCD sum rules

Stimulated by the renewed observation of Ds0⁎(2317) signal and its updated mass value 2318.3±1.2±1.2MeV/c2 in the process e+e−→Ds⁎+Ds0⁎(2317)−+c.c. by BESIII Collaboration, we devote to reinvestigate Ds0⁎(2317) as a 0+ tetraquark state from QCD sum rules. Technically, four different possible currents are adopted and high condensates up to dimension 12 are included in the operator product expansion (OPE) to ensure the quality of QCD sum rule analysis. In the end, we obtain the mass value 2.37−0.36+0.50GeV with the factorization parameter ρ=1 (or 2.23−0.24+0.78GeV with ρ=3) for the scalar–scalar current, which agrees well with the experimental data of Ds0⁎(2317) and could support its explanation as a 0+ scalar–scalar tetraquark state. The final result for the axial–axial configuration is calculated to be 2.51−0.43+0.61GeV with ρ=1 (or 2.52+0.76−0.52GeV with ρ=3), which is still consistent with the mass of Ds0⁎(2317) considering the uncertainty, and then the possibility of Ds0⁎(2317) as a axial–axial tetraquark state can not be excluded. For the pseudoscalar–pseudoscalar and the vector–vector cases, their unsatisfactory OPE convergence makes that it is of difficulty to find rational work windows to further acquire hadronic masses.

Mass calculations of light quarkonium, exotic JPC=0+− hybrid mesons from Gaussian sum rules

We extend previous calculations of leading-order correlation functions of spin-0 and spin-1 light quarkonium hybrids to include QCD condensates of dimensions five and six, with a view to improving the stability of QCD sum-rules analyses in previously unstable channels. Based on these calculations, prior analyses in the literature, and its phenomenological importance, we identify the exotic $J^{PC}=0^{+-}$ channel as the most promising for detailed study. Using Gaussian sum-rules constrained by the H\"older inequality, we calculate masses of light (nonstrange and strange) quarkonium hybrid mesons with $J^{PC}=0^{+-}$. We consider single narrow, single wide, and double narrow resonance models, and find that the double narrow resonance model yields the best agreement between QCD and phenomenology. In both non-strange and strange cases, we find hybrid masses of $2.60$ GeV and $3.57$ GeV.

Charmonium ground and excited states at finite temperature from complex Borel sum rules

Charmonium spectral functions in vector and pseudoscalar channels at finite temperature are investigated through the complex Borel sum rules and the maximum entropy method. Our approach enables us to extract the peaks corresponding to the excited charmonia, ψ′ and ηc′, as well as those of the ground states, J/ψ and ηc, which has never been achieved in usual QCD sum rule analyses. We show the spectral functions in vacuum and their thermal modification around the critical temperature, which leads to the almost simultaneous melting (or peak disappearance) of the ground and excited states.

Ground State Mass Predictions of Heavy-Light Hybrids from QCD Sum-Rule Analysis (JP = {0±,1±})

We present QCD Laplace sum-rule predictions of ground state masses of heavy-light open-flavour hybrid mesons. Having computed leading-order diagonal correlation functions, including up to dimension six gluon condensate contributions, we extract hybrid mass predictions for all JP∈{0±,1±}, and explore possible mixing effects with conventional meson states. Similarities are found in the mass hierarchy in both charm and bottom systems with some exceptions that are discussed.

Hidden bottom pentaquark states with spin 3/2 and 5/2

Theoretical investigations of the pentaquark states which were recently discovered provide important information on their nature and structure. It is necessary to study the spectroscopic parameters like masses and residues of particles belong to the class of pentaquarks and ones having similar structures. The mass and pole residue are quantities which emerge as the main input parameters in exploration of the electromagnetic, strong and weak interactions of the pentaquarks with other hadrons in many frameworks. This work deals with a QCD sum rule analysis of the spin-$3/2$ and spin-$5/2$ bottom pentaquarks with both positive and negative parities aiming to evaluate their masses and residues. In calculations, the pentaquark states are modeled by molecular-type interpolating currents: for particles with $J=5/2$ a mixing current is used. We compare the results obtained in this work with the existing predictions of other theoretical studies. The predictions on the masses may shed light on experimental searches of the bottom pentaquarks.

Hunting for exotic doubly hidden-charm/bottom tetraquark states

We develop a moment QCD sum rule method augmented by fundamental inequalities to study the existence of exotic doubly hidden-charm/bottom tetraquark states made of four heavy quarks. Using the compact diquark–antidiquark configuration, we calculate the mass spectra of these tetraquark states. There are 18 hidden-charm ccc¯c¯ tetraquark currents with JPC=0++, 0−+, 0−−, 1++, 1+−, 1−+, 1−−, and 2++. We use them to perform QCD sum rule analyses, and the obtained masses are all higher than the spontaneous dissociation thresholds of two charmonium mesons, which are thus their dominant decay modes. The masses of the corresponding hidden-bottom bbb¯b¯ tetraquarks are all below or very close to the thresholds of the ϒ(1S)ϒ(1S) and ηb(1S)ηb(1S), except one current of JPC=0++. Hence, we suggest to search for the doubly hidden-charm states in the J/ψJ/ψ and ηc(1S)ηc(1S) channels.