Quantum Chromodynamics Sum Rules Research Articles

Charmoniumlike states with the exotic quantum number JPC=3−+

We apply the method of quantum chromodynamics (QCD) sum rules to study the qcq¯c¯ tetraquark states with the exotic quantum number JPC=3−+, and extract the mass of the lowest-lying state to be 4.49−0.41+0.45 GeV. To construct the relevant tetraquark currents we need to explicitly add the covariant derivative operator. Our systematic analysis of these interpolating currents indicates that: (a) this state readily decays into the P-wave [ρJ/ψ]/[ωJ/ψ] channel but not into the [ρχc2]/[ωχc2]/[J/ψf2(1270)] channels, and (b) it readily decays into the [D*D¯2*] channel but not into the P-wave [D*D¯*] channel. Published by the American Physical Society 2024

Chiral properties of the nucleon interpolating current and θ -dependent observables

We revisit the chiral properties of nucleon interpolating currents, and show that of the two leading order currents j1 and j2, only two linear combinations j1±j2 transform covariantly under the anomalous U(1)A symmetry. As a result, calculations of quantities which vanish by symmetry in the chiral limit may produce unphysical results if carried out with different linear combinations of the currents. This includes observables such as electric dipole moments, induced by the quantum chromodynamics (QCD) parameter θ, and the θ-dependence of the nucleon mass. For completeness, we also exhibit the leading order results for nucleon electric dipole moments (dn,p) induced by θ, and the nucleon magnetic moments (μn,p), when calculated using QCD sum rules for both the covariant choices of the nucleon interpolating current. The results in each channel, conveniently expressed as the ratios, dn,p/μn,p, are numerically consistent, and reflect the required physical dependence on θ. Published by the American Physical Society 2024

Interaction of exotic states in a hadronic medium: the Z c (3900) case

We investigate the interactions of the charged exotic state Z c (3900) in a hadronic medium composed of light mesons. We study processes such as Zcπ→DD¯ , Zcπ→D*D¯* , Zcπ→DD¯* and the inverse ones. Using effective Lagrangians and form factors calculated with Quantum Chromodynamics (QCD) sum rules (treating the Z c (3900) as a tetraquark) we estimate the vacuum and thermally-averaged cross-sections of these reactions. We find that the Z c (3900) has relatively large interaction cross sections with the constituent particles of the hadronic medium. After that, we use the production and suppression cross sections in a rate equation to estimate the time evolution of the Z c multiplicity. We include the Z c decay and regeneration terms The coalescence model is employed to compute the initial Z c multiplicity for the compact tetraquark configuration. Our results indicate that the combined effects of hadronic interactions, hydrodynamical expansion, decay and regeneration affect the final yield, which is bigger than the initial value. Besides, the dependence of the Z c final yield with the centrality, center-of-mass energy and the charged hadron multiplicity measured at midrapidity [dNch/dη(η<0.5)] is also investigated.

Investigation on the Ω(2012) from QCD sum rules

We study the recently observed Ω(2012) baryon in quantum chromodynamics (QCD) sum rules. We construct the P-wave Ω baryon currents with a covariant derivative, and perform spin projection to obtain the currents with total spin 1/2 and 3/2. We then apply the parity-projected QCD sum rules to separate the contributions of the positive and negative parity states. We extract the masses of JP=1/2− and 3/2− states to be M1/2−=2.07−0.07+0.07 GeV and M3/2−=2.05−0.10+0.09 GeV. Both results are in good agreement with the experimental result. Therefore, it is likely that the Ω(2012) is a negative parity state, which is interpreted as a P-wave excited state in the quark model. However, its spin is not determined in the present analysis, which can be done by detailed study on its decay properties. Published by the American Physical Society 2024

Doubly charmed pentaquark states in QCD sum rules

We have studied the mass spectra of doubly charmed pentaquark states in the Λc(*)D(*) and Σc(*)D(*) channels with JP=1/2±, 3/2±, and 5/2± within the framework of quantum chromodynamics sum rules. We use the parity projected sum rules to separate the contributions of negative and positive parities from the two-point correlations induced by the pentaquark interpolating currents. Our results show that the bound states of Pcc pentaquarks may exist in the ΛcD(12−), ΣcD(12−), ΣcD*(32−), Λc*D(32−), Λc*D*(52−) channels with negative-parity and ΣcD(12+), ΣcD*(32+), Σc*D(32+) channels with positive-parity, since their masses are predicted to be lower than the corresponding meson-baryon thresholds. However, they are still allowed to decay into the Ξcc(*)π final states via strong interaction. The triply charged Pcc+++(ccuud¯) and neutral Pcc0(ccddu¯) in the isospin quartet would definitely be pentaquark states due to their exotic charges. We suggest searching for these characteristic doubly charmed pentaquark signals in the Pcc+++→Ξcc(*)++π+/ρ+, Σc(*)++D(*)+ and Pcc0→Ξcc(*)+π−/ρ−, Σc(*)0D(*)0 decays in the near future. Published by the American Physical Society 2024

P -wave fully charm and fully bottom tetraquark states

We have studied the mass spectra of the P-wave fully charm and fully bottom tetraquark states in the framework of quantum chromodynamics (QCD) sum rules. We construct the interpolating currents by inserting the covariant derivative operator D↔μ between the S-wave diquark and antidiquark fields. The excitation structures show that the pure λ-mode excited P-wave fully heavy tetraquarks exist for the quantum numbers JPC=1−−,1−+,2−−,2−+, and 3−−, while it is difficult to separate the λ-mode and ρ-mode excitations in the 0−+ channel. Within three Lorentz indices, there is no pure λ-mode excited P-wave fully charm/bottom tetraquark operators with JPC=0−− and 3−+. Our results support that the recent observed X(6900) and X(7200) resonances could be interpreted as the P-wave fully charm ccc¯c¯ tetraquark states with JPC=1−+ and 2−+, respectively. Some P-wave fully bottom bbb¯b¯ tetraquark states are predicted to be lower than the di-ηb(1S) and di-ϒ(1S) mass thresholds. Hopefully our calculations will be useful for identifying the nature of new exotic tetraquark states. Published by the American Physical Society 2024

Forward-backward asymmetries in in the Bethe-Salpeter equation approach * *Supported by National Natural Science Foundation of China (11905117, 11775024)

Using the Bethe-Salpeter equation (BSE), we investigate the forward-backward asymmetries in in the quark-diquark model. This approach provides precise form factors that are different from those of quantum chromodynamics (QCD) sum rules. We calculate the rare decay form factors for b and investigate the (integrated) forward-backward asymmetries in these decay channels. We observe the integrated , , , and ; the hadron side asymmetries ; the lepton-hadron side asymmetries ; and the longitudinal polarization fractions .

1Dand 2D Ξ b and Λ b baryons * *Supported by the Fundamental Research Funds for the Central Universities (016MS133), Natural Science Foundation of HeBei Province (A2018502124)

Recently, scientists have achieved significant progress in experiments searching for excited and baryons such as , , , , , , and . Motivated by these achievements, we systematically analyze the and states of and baryons using the method of quantum chromodynamics sum rules. By constructing three types of interpolating currents, we calculate the masses and pole residues of these heavy baryons with different excitation modes: , , and . Subsequently, we decode the inner structures of , , , and and favor assigning these states as the baryons with the quantum numbers and , , , and , respectively. In addition, the predictions for the masses and pole residues of the other and and baryons in this paper will be useful for studying D-wave bottom baryons in the future.

Improved analysis of the rare decay processes of Λ b

It is noted that in the new Particle Data Group (PDG) version the rare decays of the baryon have been revised with more accuracy. The new results show that most of the existing theoretical results on the process are larger than those of experiments. With the improved higher-order light-cone distribution amplitudes of the Λ baryon, we reanalyze the process in the framework of light-cone quantum chromodynamics sum rules and the branching ratio is estimated to be , which is consistent with the new experimental result. Furthermore, another process is also analyzed in the same frame. The final branching ratio is calculated to be , which is in good accordance with the data from the PDG and other theoretical predictions.

Charm meson couplings in Hard-Wall holographic QCD

In phenomenology of quantum chromodynamics (QCD), charmed meson vertices are useful tools to study the final-state re-scattering effects in the hadronic B decays. The strong couplings of charm mesons vertices, are related to the basic parameters in the heavy quark effective Lagrangian. Here, the four-flavor Hard-Wall holographic QCD is illustrated to evaluate the couplings of (D^{_{-(*-)}}, {bar{D}}^{_0}, a_{1}^{_-}), (D^{_{-(*-)}}, {bar{D}}^{_0}, b_{1}^{_-}), (D_{s}^{_{-(*-)}},{bar{D}}^{_{0}}, K_{1A}^{_-}), (D_{s}^{_{-(*-)}}, {bar{D}}^{_{0}}, K_{1B}^{_{-(*-)}}), (D_{s}^{_{+(*+)}}, {D}^{_+}, K_{1A}^{_0}), (D_{s}^{_{+(*+)}}, {D}^{_+}, K_{1B}^{_0}), (D^{_{-(*-)}}, {bar{D}}^{_{0(*0)}}, rho ^{_-}), (D_{s}^{_{-(*-)}}, {bar{D}}^{_{0(*0)}}, K^{_{*-}}), ({D}^{_{0(*0)}}, {bar{D}}^{_{0(*0)}}, psi ), (D_{1}^{_-}, {bar{D}}_{1}^{_0}, pi ^{_-}), (D_{s1}^{_-}, {bar{D}}_{1}^{_0}, K^{_{-}}), ({D}_{1}^{_0}, {bar{D}}_{1}^{_0}, eta _{c}), (psi , D^{_{0(*0)}}, D^{_{+}}, pi ^{_-}), (psi , D^{_{0(*0)}}, {bar{D}}^{_0}, pi ^{_0}), (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K^{_{0}}), (psi , D^{_{0(*0)}}, D^{_{+}}, a_{1}^{_-}), (psi , D^{_{0(*0)}}, D^{_{+}}, b_{1}^{_-}), (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K_{1B}^{_{0}}) and (psi , D_{s}^{_{+(*+)}}, D^{_{-}}, K_{1B}^{_{0}}) vertices. Moreover, the values of the masses of D^{_{0(*0)}}, D_{s}^{_{-(*-)}}, omega , psi , D_{1}^{_{0}}, D_{1}^{_{-}}, K^{0}, eta _{c}, D_{s1}^{_{-}} and chi _{_{c1}} as well as the decay constant of pi ^{-}, D^{_{-(*-)}}, K^{-}, rho ^{-}, D_{1}^{_{-}}, a_{1}^{-} and D_{s}^{_{-(*-)}} are estimated in this study. A comparison is also made between our results and the experimental values of the masses and decay constants. Our results for strong couplings are also compared with the three point sum rule (3PSR) and light-cone QCD sum rule (LCSR) predictions.

A family of double-beauty tetraquarks: Axial-vector state * *The work of K. A, B. B., and H. S was Supported in part by the TUBITAK (119F050)

The spectroscopic parameters and decay channels of the axial-vector tetraquark (in what follows, ) 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 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 decays of . In these processes, is a scalar tetraquark built of a color-triplet diquark and an antidiquark, whereas M is one of the vector mesons , , , and . To calculate the partial widths of these decays, we use the QCD three-point sum rule approach and evaluate the weak transition form factors ( ), which govern these processes. The full width and the mean lifetime of the tetraquark are computed using the aforementioned weak decays. The obtained information about the parameters of and is useful for experimental investigations of these double-heavy exotic mesons.

Identifying the Λb(6146)0 and Λb(6152)0 as D-Wave Bottom Baryons

We study the Λ b ( 6146 ) 0 and Λ b ( 6152 ) 0 recently observed by LHCb using the method of Quantum Chromodynamics (QCD) sum rules within the framework of heavy quark effective theory. Our results suggest that they can be interpreted as D-wave bottom baryons of J P = 3 / 2 + and 5 / 2 + respectively, both of which contain two λ -mode excitations. We also investigate other possible assignments containing ρ -mode excitations. We extract all the parameters that are necessary to study their decay properties when using the method of light-cone sum rules. We predict masses of their strangeness partners to be m Ξ b ( 3 / 2 + ) = 6.26 − 0.14 + 0.11 GeV and m Ξ b ( 5 / 2 + ) = 6.26 − 0.14 + 0.11 GeV with the mass splitting Δ M = m Ξ b ( 5 / 2 + ) − m Ξ b ( 3 / 2 + ) = 4.5 − 1.5 + 1.9 MeV, and propose to search for them in future CMS, EIC, and LHCb experiments.

Review of Charmonium and Bottomonium Quark State Production via Relativistic Heavy Ion Collisions

This is a review of the production of heavy quark states via relativistic heavy ion collisions in RHIC. The heavy quarks here are c, charm quark, and b, bottom quark. The states are charmonium meson states Ψ ( n S ) , with n = 1,2 and upsilon meson states Υ ( m S ) , with m = 1,2,3. Quantum Chromodynamics (QCD) sum rules were used to derive the result that the Ψ ( 2 S ) and Υ ( 3 S ) are mixed hybrid states, which increase their production cross sections. We also review the Ψ ( n S ) and Υ ( m S ) production cross sections via Cu-Cu and Au-Au collisions, which are very important for this review of the production of heavy quark states in RHIC. The possible detection of the Quark Gluon Plasma (QGP) is also reviewed.

Analysis of Ds⁎D⁎K⁎ and Ds1D1K⁎ Vertices in Three-Point Sum Rules

In this study, the coupling constants of Ds⁎D⁎K⁎ and Ds1D1K⁎ vertices were determined within the three-point Quantum chromodynamics sum rules method with and without consideration of the SUf(3) symmetry. The coupling constants were calculated for off-shell charm and K⁎ cases. Considering the nonperturbative effect of the correlation function, as the most important contribution, the quark-quark, quark-gluon, and gluon-gluon condensate corrections were estimated and were compared with other predictive methods.

Masses of the bottom-charm hybrid states

Quantum Chromodynamics (QCD) sum rules are used to study the mass spectrum of bottom-charm hybrid systems. The correlation functions and the spectral densities are calculated up to dimension six condensates at leading order of αs for several JP quantum numbers. After performing the QCD sum rule analysis, we predict the masses of the JP = 0−, 0+, 1−, 1+, 2−, 2+ bottom-charm hybrids. These mass predictions show a similar supermultiplet structure as the bottomonium and charmonium hybrids. Using the QCD sum rule mass predictions we analyze the possible hadronic decay patterns of the , and hybrids including the open-flavor and hidden-flavor mechanisms.

Dynamical mass generation of vector mesons from QCD trace anomaly

Mass formulas for the light-vector mesons written in terms of the gluon condensate i.e., the trace anomaly in quantum chromodynamics (QCD), are derived on the basis of finite energy QCD sum rules. We utilize sum rules with $s^n$ and $s^{n+1/2}$ weights, which relate the energy-weighted spectral sums to the vacuum expectation values of certain commutation relations. After evaluating the commutation relations, the sum rules with $s^n$ weights are reduced to the familiar ones obtained from the operator product expansion (OPE). On the other hand, the sum rules with $s^{n+1/2}$ weights cannot be derived from OPE. They give new relations between the spectral sums and QCD vacuum fluctuations. To derive simple mass formula, we adopt the pole + continuum Ansatz for the spectral function, and solve coupled equations given by the sum rules with $s^{0,1}$ weights and the new sum rule with $s^{1/2}$ weight. Application of our approach to the axial-vector meson is also discussed.

The axial anomaly and consistency of the finite-width light-cone local duality sum rule for the form factor of the transition γ* γ* → π0

The pion transition form factor at the photon mass-shell of q21 = q22 = 0 is fixed by the axial anomaly, which may serve as a criterion in checking the consistency of the underlying quantum chromodynamics (QCD). We choose to work in the symmetric kinematical region where two photons have the same virtualities and hope to reproduce the experimental value of from light-cone QCD sum rules instead of direct extrapolation of the QCD expression to such a low-energy scale. The form factor of the transition γ*γ* → π0 is investigated in the framework of the zero- and finite-width light-cone local duality QCD sum rules. The expression of the pion transition form factor at large t is independent of the twist-two and twist-three pion distribution amplitudes; therefore a more accurate conclusion may be reached. The influence of the light quark mass and the ωρπ coupling constant to our sum rules is also considered. The consistency between the axial anomaly, the intermediate hadronic structure and the QCD perturbative dynamics is tested to be true within a reasonable region of input parameters.

Spin Structure of the Nucleon at Low Q 2 Region

The spin structure of the nucleon can play a key testing ground for the Quantum Chromo-Dynamics(QCD) at wide kinematic ranges from smaller to large four momentum transfer Q2. It is far more challenging to understand the QCD at small Q2 region due to the non-perturbative nature. Jefferson Lab has been one of the major experimental facilities for the spin structure with its polarized electron beams and various polarized targets. A few QCD sum rules have been compared with the measured spin structure functions g1 and g2 at low Q2 and the most surprising results have been obtained for the spin polarizabilities, γ0 and δLT.

THE FORM FACTOR OF ργ*→π0IN THE FINITE-WIDTH LIGHT-CONE LOCAL DUALITY SUM RULE

The form factor of the transition ργ*→π0is investigated by analyzing the γγ*→π0transition in the framework of the light-cone local duality quantum chromodynamics sum rules. Both finite- and zero-width forms for the low-energy physical absorptive part of the γγ*→π0transition are considered. The numerical results for the transition form factor Fρπ(Q2) in the asymptotic form and the CZ one of the pion distribution amplitude are obtained respectively, the difference between the finite- and zero-width form is not big but still distinguishable. It is found that the results for the form factor Fρπ(Q2) from CZ, asymptotic and the flat pion DAs are compatible with the predictions of perturbative QCD. Our results will be helpful to distinguish the shape of the pion DA of twist-two, when the concrete information of the experimental data for the transition ργ*→π0are provided.

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B and Bs mesons from the two-point correlator of heavy–light pseudoscalar currents. We use the operator product expansion of this correlator expressed in terms of the heavy-quark mass for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input quantum chromodynamics (QCD) parameters and to the limited intrinsic accuracy of the method of QCD sum rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants and . For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of . By requiring our sum-rule estimate to match the average of the lattice results for fB, a very accurate value is extracted, leading to fB = (193.4 ± 12.3(OPE) ± 4.3(syst)) MeV and .