QCD Sum Rules Research Articles

Global analysis of hadronic two-body B decays in the perturbative QCD approach

Based on the flavor structure of four-quark effective operators, we develop an automatic computation program to calculate hadronic two-body $B$ meson decay amplitudes, and apply it to their global analysis in the perturbative QCD (PQCD) approach. Fitting the PQCD factorization formulas for $B\to PP,VP$ decays at leading order in the strong coupling $\alpha_s$ to measured branching ratios and direct CP asymmetries, we determine the Gegenbauer moments in light meson light-cone distribution amplitudes (LCDAs). It is found that most of the fitted Gegenbauer moments of the twist-2 and twist-3 LCDAs for the pseudoscalar meson $P$ ($P=\pi$, $K$) and vector meson $V$ ($V=\rho$, $K^*$) agree with those derived in QCD sum rules. The shape parameter for the $B_s$ meson distribution amplitude and the weak phase $\phi_3(\gamma)=(75.1\pm2.9)^\circ$ consistent with the value in Particle Data Group are also obtained. It is straightforward to extend our analysis to higher orders and higher powers in the PQCD approach, and to the global determination of LCDAs for other hadrons.

QCD sum rules for parameters of the B -meson distribution amplitudes

We obtain new estimates for the parameters $\lambda_{E}^2$, $\lambda_H^2$ and their ratio $\mathcal{R} = \lambda_{E}^2/\lambda_H^2$, which appear in the second moments of the $B$-meson light-cone distribution amplitudes defined in the heavy-quark effective field theory. The computation is based on two-point QCD sum rules for the diagonal correlation function and includes all contributions up to mass dimension seven in the operator-product expansion. For the ratio we get $\mathcal{R} = (0.1 \pm 0.1)$ with $\lambda_H^2 = (0.15 \pm 0.05) \, \text{GeV}^2$ and $\lambda_E^2 = (0.01 \pm 0.01) \, \text{GeV}^2$.

Doubly charged vector tetraquark [formula omitted

We explore properties of the doubly charged vector tetraquark ZV++=[cu][s‾d‾] built of four quarks of different flavors using the QCD sum rule methods. The mass and current coupling of ZV++ are computed in the framework of the QCD two-point sum rule approach by taking into account quark, gluon and mixed vacuum condensates up to dimension 10. The full width of this tetraquark is saturated by S-wave ZV++→π+Ds1(2460)+, ρ+Ds0⁎(2317)+, and P-wave ZV++→π+Ds+,K+D+ decays. Strong couplings required to find partial widths of aforementioned decays are calculated in the context of the QCD light-cone sum rule method and a soft-meson approximation. Our predictions for the mass m=(3515±125) MeV and full width Γfull=156−30+56 MeV of ZV++ are useful to search for this exotic meson in various processes. Recently, the LHCb collaboration discovered neutral states X0(1)(2900) as resonance-like peaks in D−K+ invariant mass distribution in the decay B+→D+D−K+. We argue that mass distribution of D+K+ mesons in the same B decay can be used to observe the doubly charged scalar ZS++ and vector ZV++ tetraquarks.

The Radiative Δ(1600) → γN Decay in the Light-Cone QCD Sum Rules

Within the framework of the light-cone QCD sum rules method (LCSR’s), the radiative Δ(1600)→γN decay is studied. In particular, the magnetic dipole moment GM1(0) and the electric quadrupole moment GE1(0) are estimated. We also calculate the ratio REM=−GE1(0)GM1(0) and the decay rate. The predicted multipole moments and the decay rate strongly agree with the existing experimental results as well as with the other available phenomenological approaches.

Universal Scale Factors: A Bridge Between Chiral Lagrangians and QCD Sum-Rules

Chiral Lagrangian mesonic fields can be connected to QCD quark operators via matrix operators containing scale factors. These scale factor matrices are shown to be constrained by chiral symmetry, resulting in a universal scale factor for each chiral Lagrangian nonet. QCD sum-rules, combined with mixing angles from Chiral Lagrangian analyses, are used to determine the scale factors for the a0 isotriplet and K*0 isodoublet scalar mesons. The resulting scale factors verify the universality property, providing a validation of the scale factor matrices connecting Chiral Lagrangian mesonic fields and quark operators.

Modern status of heavy quark sum rules in QCD

We briefly report the modern status of heavy quark sum rules (HQSR) based on stability criteria by emphasizing the recent progresses for determining the QCD parameters (αs, mc,b and gluon condensates) where their correlations have been taken into account. The results: αs(MZ) = 0.1181(16)(3), m‾c(m‾c)=1286(16)MeV, m‾b(m‾b)=4202(7)MeV, 〈αsG2〉 = (6.49±0.35)×10−2 GeV4, 〈g3G3〉 = (8.2±1.0)×GeV2〈αsG2〉 and the ones from recent light quark sum rules are summarized in Table 2. One can notice that the SVZ value of 〈αsG2〉 has been underestimated by a factor 1.6, 〈g3G3〉 which is much bigger than the instanton liquid model estimate, while the four-quark condensate which mixes under renormalization is incompatible with the vacuum saturation by a factor (2 ∼ 4). The uses of HQSR for molecules and tetraquarks states are commented.

A review of quarkonia under strong magnetic fields

We review the properties of quarkonia under strong magnetic fields. The main phenomena are (i) mixing between different spin eigenstates, (ii) quark Landau levels and deformation of wave function, (iii) modification of $\bar{Q}Q$ potential, and (iv) the motional Stark effect. For theoretical approaches, we review (i) constituent quark models, (ii) effective Lagrangians, (iii) QCD sum rules, and (iv) holographic approaches.

Ds -meson leading-twist distribution amplitude within the QCD sum rules and its application to the Bs→Ds transition form factor

We make a detailed study of the ${D}_{s}$-meson leading-twist light-cone distribution amplitude ${\ensuremath{\phi}}_{2;{D}_{s}}$ by using the QCD sum rules within the framework of the background field theory. To improve the precision, its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;{D}_{s}}$ are calculated up to dimension-six condensates. At the scale $\ensuremath{\mu}=2\text{ }\text{ }\mathrm{GeV}$, we obtain $⟨{\ensuremath{\xi}}^{1}{⟩}_{2;{D}_{s}}=\ensuremath{-}{0.261}_{\ensuremath{-}0.020}^{+0.020}$, $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;{D}_{s}}={0.184}_{\ensuremath{-}0.012}^{+0.012}$, $⟨{\ensuremath{\xi}}^{3}{⟩}_{2;{D}_{s}}={\ensuremath{-}0.111}_{\ensuremath{-}0.012}^{+0.007}$, and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;{D}_{s}}={0.075}_{\ensuremath{-}0.005}^{+0.005}$. Using those moments, the ${\ensuremath{\phi}}_{2;{D}_{s}}$ is then constructed by using the light-cone harmonic oscillator model. As an application, we calculate the transition form factor ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ within the light-cone sum rules (LCSR) approach by using a right-handed chiral current, in which the terms involving ${\ensuremath{\phi}}_{2;{D}_{s}}$ dominate the LCSR. It is noted that the extrapolated ${f}_{+}^{{B}_{s}\ensuremath{\rightarrow}{D}_{s}}({q}^{2})$ agrees with the lattice QCD prediction. After extrapolating the transition form factor to the physically allowable ${q}^{2}$ region, we calculate the branching ratio and the CKM matrix element, which give $\mathcal{B}({\overline{B}}_{s}^{0}\ensuremath{\rightarrow}{D}_{s}^{+}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}})=({2.03}_{\ensuremath{-}0.49}^{+0.35})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2}$ and $|{V}_{cb}|=({40.00}_{\ensuremath{-}4.08}^{+4.93})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Analysis of the [formula omitted] hexaquark molecular state with the QCD sum rules

In this work, we construct the color-singlet-color-singlet type six-quark pseudoscalar current to investigate the Ξ‾ccΞcc hexaquark molecular state with the QCD sum rules, the predicted mass MX∼7.2GeV supports assigning the X(7200) to be the Ξ‾ccΞcc hexaquark molecular state with the quantum numbers JPC=0−+. The X(7200) can decay through fusions of the c¯c and q¯q pairs, we can search for the X(7200) and explore its properties in the J/ψJ/ψ, χc1χc1, D⁎D¯⁎ and D1D¯1 invariant mass spectrum in the future.

Analysis of the Hidden-charm Tetraquark molecule mass spectrum with the QCD sum rules

In this paper, we investigate the mass spectrum of the ground state hidden-charm tetraquark molecular states without strange, with strange and with hidden-strange via the QCD sum rules in a comprehensive way and revisit the assignments of the [Formula: see text], [Formula: see text], [Formula: see text] states in the scenario of tetraquark molecular states consistently based on the QCD sum rules.

Analysis of Zcs (3985) as the axialvector tetraquark state * *Supported by National Natural Science Foundation of China (11775079)

In this study, we choose the scalar and axialvector diquark operators in the color antitriplet as the fundamental building blocks to construct four-quark currents and investigate the diquark-antidiquark type axialvector tetraquark states in the framework of the QCD sum rules. The predicted tetraquark mass is in excellent agreement with the experimental value from the BESIII collaboration, which supports identifying as the cousin of with quantum numbers . We take into account the light flavor mass-breaking effect to estimate the mass spectrum of the diquark-antidiquark type hidden-charm tetraquark states with strangeness according to previous studies.

Investigation of Pcs(4459)0 pentaquark via its strong decay to ΛJ/Ψ

Recently the observation of a new pentaquark state, the hidden-charmed strange $P_{cs}(4459)^0$, was reported by the LHCb Collaboration. The spin-parity quantum numbers of this state were not determined as a result of insufficient statistics. To shed light on its quantum numbers, we investigate its decay, $P_{cs}(4459)^0 \rightarrow J/\psi \Lambda $, the mode that this state has been observed, within the QCD sum rule framework. We obtain the width of this decay assigning the spin-parity quantum numbers of $P_{cs}(4459)^0$ state as $J^P=\frac{1}{2}^-$ and its substructure as diquark-diquark-antiquark. To this end, we first calculate the strong coupling constants defining the considered decay and then use them in the width calculations. The obtained width is consistent with the experimental observation, confirming the quantum numbers $J^P=\frac{1}{2}^-$ and compact pentaquark nature for $P_{cs}(4459)^0$ state.

About the exotic structure of Zcs

Very recently a new hadronic structure around 3.98 GeV was observed in BESIII experiment. From its decay modes, it is reasonable for people to assign it to the category of exotic state, say Zcs+, the stranged-parter of Zc(3900). This finding indicates for the first time the tetraquark with strange quark in hidden-charm sector, and hence has a peculiar importance. By virtue of the QCD Sum Rule technique, we analyze the Zcs+ about its possible configuration and physical properties, and find it could be configured as a mixture of two types of structures, [1c]c¯u⊗[1c]s¯c and [1c]c¯c⊗[1c]s¯u, or [3c]c¯u⊗[3¯c]s¯c and [3c]c¯c⊗[3¯c]s¯u, with JP=1+. Physically, it then appears to be the emergence of a compound of four possible currents in each configuration, which tells that the single current evaluation of hadron spectroscopy and their decay properties are sometimes not enough. We find that in both cases the energy spectra may fit well with the experimental observation within the uncertainties, i.e. 3.98 GeV, while be noted that the molecular state is not favored by vector-meson-exchange model. Various Zcs+(3980) decay modes are evaluated, which are critical for pinning down its configuration and left for experimental verification. We also predict the mass of Zcs0, the neutral partner of Zcs+(3980), and analyze its dominant decay probabilities.

Toward the existence of the odderon as a three-gluon bound state

Inspired by the evidence of the odderon exchange recently observed by the D0 and TOTEM Collaborations, a QCD sum rule investigation is performed to study the odderon as a three-gluon bound state. There may exist six lowest-lying three-gluon odderons with the quantum numbers $J^{PC} = 1/2/3^{\pm-}$. We systematically construct their interpolating currents, and calculate their mass spectra. To verify their existence, we propose to search for the spin-3 odderons in their $VVV$ and $VVP$ decay channels directly at LHC, with $V$ and $P$ light vector and pseudoscalar mesons respectively.

Mass spectra of NΩ dibaryons in the S13 and S25 channels

We study the mass spectra of the $N\mathrm{\ensuremath{\Omega}}$ dibaryons in the $^{3}{S}_{1}$ and $^{5}{S}_{2}$ channels with ${J}^{P}={1}^{+}$ and ${2}^{+}$, respectively, by using the method of QCD sum rules. We construct two dibaryon interpolating currents in the molecular picture and calculate their correlation functions and spectral densities up to dimension-16 condensates. Our results indicate that there may exist an $N\mathrm{\ensuremath{\Omega}}$ dibaryon bound state in the $^{5}{S}_{2}$ channel with a binding energy of about 21 MeV. The masses of the $^{3}{S}_{1}$ $N\mathrm{\ensuremath{\Omega}}$ dibaryons with ${J}^{P}={1}^{+}$ are predicted to be higher than the $N\mathrm{\ensuremath{\Omega}}$ and $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ thresholds and thus, can decay into these final states directly in S wave. The $N\mathrm{\ensuremath{\Omega}}(^{5}{S}_{2})$ dibaryon bound state can decay into the octet-octet final states $\mathrm{\ensuremath{\Lambda}}\mathrm{\ensuremath{\Xi}}$ and $\mathrm{\ensuremath{\Sigma}}\mathrm{\ensuremath{\Xi}}$ in D wave via the quark rearrangement mechanism. The existence of these $N\mathrm{\ensuremath{\Omega}}$ dibaryons may be identified in the relativistic heavy-ion collision experiments in the future.

Extending the application of the light-cone sum rules method to low momenta using QCD renormalization-group summation: Theory and phenomenology

We show that using renormalization-group summation to generate the QCD radiative corrections to the $\pi-\gamma$ transition form factor, calculated with lightcone sum rules (LCSR), renders the strong coupling free of Landau singularities while preserving the QCD form-factor asymptotics. This enables a reliable applicability of the LCSR method to momenta well below 1 GeV$^2$. This way, one can use the new preliminary BESIII data with unprecedented accuracy below 1.5 GeV$^2$ to fine tune the prefactor of the twist-six contribution. Using a combined fit to all available data below 3.1 GeV$^2$, we are able to determine all nonperturbative scale parameters and a few Gegenbauer coefficients entering the calculation of the form factor. Employing these ingredients, we determine a pion distribution amplitude with conformal coefficients $(b_2,b_4)$ that agree at the $1\sigma$ level with the data for $Q^2 \leqslant 3.1$ GeV$^2$ and fulfill at the same time the lattice constraints on $b_2$ at N$^3$LO together with the constraints from QCD sum rules with nonlocal condensates.The form-factor prediction calculated herewith reproduces the data below 1 GeV$^2$ significantly better than analogous predictions based on a fixed-order power-series expansion in the strong coupling constant.

Gluonic tetracharm configuration of X(6900)

Recently, a new hadronic structure at around 6.9 GeV was observed in an LHCb experiment. From its limited yet known decay mode, one could still determine that it contains at least four charm quarks and hence belongs to the category of exotic state. This finding indicates for the first time the tetracharm exotic states and is therefore quite importance. In this letter, we propose a nature hybrid interpretation for the structure of X(6900), i.e. in [3¯c]cc⊗[8c]G⊗[3c]c¯c¯ configuration with JPC=0++, and by using the QCD Sum Rule technique we performed mass spectrum calculation. The results showed that the observed X(6900) could be a gluonic tetracharm state, and some other structures may exist, e.g., one around 7.2 GeV in the tetracharm hybrid configuration and with JPC=0−+. We also predict the tetrabottom hybrid states, leaving for future experiment.

Bound State Solution Schrödinger Equation for Extended Cornell Potential at Finite Temperature

In this paper, we study the finite temperature-dependent Schrödinger equation by using the Nikiforov-Uvarov method. We consider the sum of the Cornell, inverse quadratic, and harmonic-type potentials as the potential part of the radial Schrödinger equation. Analytical expressions for the energy eigenvalues and the radial wave function are presented. Application of the results for the heavy quarkonia and B c meson masses are in good agreement with the current experimental data except for zero angular momentum quantum numbers. Numerical results for the temperature dependence indicates a different behaviour for different quantum numbers. Temperature-dependent results are in agreement with some QCD sum rule results from the ground states.

Tensor form factors of [formula omitted] state via light-cone QCD

We have achieved the isovector and isoscalar tensor form factors of the N(1535) state in the framework of the light-cone QCD sum rule approach. In numerical computations, we have considered the most general forms of the interpolating current for the nucleon and the tensor current together with the distribution amplitudes of the N(1535) resonance. We have shown that the squared momentum transfer, Q2, dependence of N(1535) tensor form factors is characterized by a multipole fit function. Our results provide a perspective of the momentum dependence of the tensor form factors and can help to improve our understanding of the internal structure of nucleon states.

Establishing the first hidden-charm pentaquark with strangeness

We study the P_{cs}(4459)^0 recently observed by LHCb using the method of QCD sum rules. Our results support its interpretation as the {{bar{D}}}^* varXi _c hadronic molecular state of either J^P=1/2^- or 3/2^-. Within the hadronic molecular picture, the three LHCb experiments observing P_c and P_{cs} states (Aaij et al., Phys Rev Lett 115:072001, 2015; Aaij et al., Phys Rev Lett 122:222001, 2019; Aaij et al., arXiv:2012.10380 [hep-ex], 2012) can be well understood as a whole. This strongly supports the existence of hadronic molecules, whose studies can significantly improve our understanding on the construction of the subatomic world. To verify this picture, we propose to further investigate the P_{cs}(4459)^0 to examine whether it can be separated into two states, and to search for the {{bar{D}}} varXi _c molecular state of J^P=1/2^{-}.