Sum Rule Approach Research Articles

Exact Sum-Rule Approach to Polarizability and Asymptotic van der Waals Functionals─Derivation of Exact Single-Particle Benchmarks

Using a sum-rule approach, we develop an exact theoretical framework for polarizability and asymptotic van der Waals correlation energy functionals of small isolated objects. The functionals require only monomer ground-state properties as input. Functional evaluation proceeds via solution of a single position-space differential equation, without the usual summations over excited states or frequency integrations. Explicit functional forms are reported for reference physical systems, including atomic hydrogen and single electrons subject to harmonic confinement, and immersed in a spherical-well potential. A direct comparison to the popular Vydrov-van Voorhis density functional shows that the best performance is obtained when density decay occurs at atomic scales. The adopted sum-rule approach implies general validity of our theory, enabling exact benchmarking of van der Waals density functionals and direct inspection of the subtle long-range correlation effects that constitute a major challenge for approximate (semi)local density functionals.

Resonance X(4630)

We investigate the structure $X(4630)$ discovered by the LHCb Collaboration in the process ${B}^{+}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\phi}{K}^{+}$ as a resonance in the $J/\ensuremath{\psi}\ensuremath{\phi}$ mass distribution. We explore this resonance as a diquark-antidiquark state $X=[cs][\overline{c}\overline{s}]$ with spin-parities ${J}^{\mathrm{PC}}={1}^{\ensuremath{-}+}$. Its mass and current coupling are calculated using the QCD two-point sum rule method by taking into account vacuum condensates up to dimension 10. We also study decays of this tetraquark to mesons $J/\ensuremath{\psi}\ensuremath{\phi}$, ${\ensuremath{\eta}}_{c}{\ensuremath{\eta}}^{(\ensuremath{'})}$ and ${\ensuremath{\chi}}_{c1}{\ensuremath{\eta}}^{(\ensuremath{'})}$, and compute partial widths of these channels. To this end, we employ the light-cone sum rule approach and technical methods of soft-meson approximation to extract strong coupling at relevant tetraquark-meson-meson vertices. Our predictions for the mass $m=(4632\ifmmode\pm\else\textpm\fi{}60)\text{ }\text{ }\mathrm{MeV}$ and width $\mathrm{\ensuremath{\Gamma}}=(159\ifmmode\pm\else\textpm\fi{}31)\text{ }\text{ }\mathrm{MeV}$ of $X$ are in a very nice agreement with recent measurements of the LHCb Collaboration. These results allow us to interpret the resonance $X(4630)$ as the tetraquark $X$ with spin-parities ${J}^{\mathrm{PC}}={1}^{\ensuremath{-}+}$.

The semi-leptonic [formula omitted] transition to tensor meson of negative parity in the QCD sum rules approach

The semi-leptonic transition of B¯s→Ds2ℓν¯ to tensor meson of negative parity JP=2− is examined in the content of the QCD sum rules approach. The three-point correlation function is used to calculate the transition form-factors of the hadronic matrix element involved in these channels. With these transition form-factors, the predicted branching ratios are estimated as: BR[B¯s→Ds2eν¯e]=4.32−2.0+2.0×10−3, BR[B¯s→Ds2μν¯μ]=4.29−2.0+2.0×10−3, and BR[B¯s→Ds2τν¯τ]=3.1−1.4+1.4×10−4. We also calculated the leptonic angular spectra and leptonic forward-backward asymmetries. The effect of the leptonic decay constant fDs2 on these observables is also considered. The obtained orders of the branching ratios in this work are indicating that these channels can be investigated at LHCb in the near future.

A_1(1260)-meson longitudinal twist-2 distribution amplitude and the Drightarrow a_1(1260)ell ^+nu _ell decay processes

In the paper, we investigate the moments langle xi _{2;a_1}^{Vert ;n}rangle of the axial-vector a_1(1260)-meson distribution amplitude by using the QCD sum rules approach under the background field theory. By considering the vacuum condensates up to dimension-six and the perturbative part up to next-to-leading order QCD corrections, its first five moments at an initial scale mu _0=1~{mathrm{GeV}} are langle xi _{2;a_1}^{Vert ;2}rangle |_{mu _0} = 0.223 pm 0.029, langle xi _{2;a_1}^{Vert ;4}rangle |_{mu _0} = 0.098 pm 0.008, langle xi _{2;a_1}^{Vert ;6}rangle |_{mu _0} = 0.056 pm 0.006, langle xi _{2;a_1}^{Vert ;8}rangle |_{mu _0} = 0.039 pm 0.004 and langle xi _{2;a_1}^{Vert ;10}rangle |_{mu _0} = 0.028 pm 0.003, respectively. We then construct a light-cone harmonic oscillator model for a_1(1260)-meson longitudinal twist-2 distribution amplitude phi _{2;a_1}^{Vert }(x,mu ), whose model parameters are fitted by using the least squares method. As an application of phi _{2;a_1}^{Vert }(x,mu ), we calculate the transition form factors (TFFs) of Drightarrow a_1(1260) in large and intermediate momentum transfers by using the QCD light-cone sum rules approach. At the largest recoil point (q^2=0), we obtain A(0) = 0.130_{ - 0.013}^{ + 0.015}, V_1(0) = 1.898_{-0.121}^{+0.128}, V_2(0) = 0.228_{-0.021}^{ + 0.020}, and V_0(0) = 0.217_{ - 0.025}^{ + 0.023}. By applying the extrapolated TFFs to the semi-leptonic decay D^{0(+)} rightarrow a_1^{-(0)}(1260)ell ^+nu _ell , we obtain {mathcal {B}}(D^0rightarrow a_1^-(1260) e^+nu _e) = (5.261_{-0.639}^{+0.745}) times 10^{-5}, {mathcal {B}}(D^+rightarrow a_1^0(1260) e^+nu _e) = (6.673_{-0.811}^{+0.947}) times 10^{-5}, {mathcal {B}}(D^0rightarrow a_1^-(1260) mu ^+ nu _mu )=(4.732_{-0.590}^{+0.685}) times 10^{-5}, {mathcal {B}}(D^+ rightarrow a_1^0(1260) mu ^+ nu _mu )=(6.002_{-0.748}^{+0.796}) times 10^{-5}.

Hadronic molecule model for the doubly charmed state {T}_{cc}^{+}

The mass, current coupling, and width of the doubly charmed four-quark meson {T}_{cc}^{+} are explored by treating it as a hadronic molecule {M}_{cc}^{+}equiv {D}^0{D}^{ast +} . The mass and current coupling of this molecule are calculated using the QCD two-point sum rule method by including into analysis contributions of various vacuum condensates up to dimension 10. The prediction for the mass m = (4060 ± 130) MeV exceeds the two-meson D0D∗+ threshold 3875.1 MeV, which makes decay of the molecule {M}_{cc}^{+} to a pair of conventional mesons D0D∗+ kinematically allowed process. The strong coupling G of particles at the vertex {M}_{cc}^{+}{D}^0{D}^{ast +} is found by applying the QCD three-point sum rule approach, and used to evaluate the width of the decay {M}_{cc}^{+}to {D}^0{D}^{ast +} . Obtained result for the width Γ = (3.8 ± 1.7) MeV demonstrates that {M}_{cc}^{+} is wider than the resonance {T}_{cc}^{+} .

Helicity form factors and the decays * *Supported in part by the National Natural Science Foundation of China (11765007, 11625520, 11947406, 12047564), the Project of Guizhou Provincial Department of Science and Technology (KY[2019]1171), the Project of Guizhou Provincial Department of Education (KY[2021]030), the China Postdoctoral Science Foundation (2019TQ0329, 2020M670476), the Chongqing Graduate Research and Innovation Foundation (ydstd1912), the Fundamental Research

In this paper, we calculate the helicity form factors (HFFs) up to twist-4 accuracy by using the light-cone sum rules (LCSR) approach. After extrapolating those HFFs to the physically allowable region, we investigate the -meson two-body decays and semi-leptonic decays , where stand for light pseudoscalar and vector mesons, respectively. The branching fractions can be derived using the CKM matrix element and the lifetime from the Particle Data Group, and we obtain , , , , and . We then obtain and , which agree with the LHCb measured value within -error. We also obtain , which like other theoretical predictions, is consistent with the LHCb measured value within -error. These imply that the HFFs under the LCSR approach are also applicable to the meson two-body decays and semi-leptonic decays , and the HFFs obtained using LCSR in a new way implies that there may be new physics in the semi-leptonic decays.

Resonance contributions in B^-rightarrow K^+K^-pi ^- within the light-cone sum rule approach

In this work, we study the resonance contributions to the decay B^-rightarrow K^+K^-pi ^-, which is dominated by the scalar f_0(980), K_0^*(1430), vector rho (1450), phi (1020), K^*(892) and tensor f_2(1270) resonances. The three-body decay is reduced to various quasi two-body decays, where the B meson firstly decays into a resonance and a pion or a kaon, subsequently the resonance decays into the other two final-state mesons. The quasi two-body decays are calculated within the light-cone sum rule approach utilizing the leading twist B meson light-cone distribution amplitudes. Finally, the decay branching fraction contributions from each resonance is calculated. Some of them are compatible with experiment or previous theoretical works. Including the effects of non-resonant and final-state interactions, we also evaluate the total branching fraction.

Investigating the K1(1270) – K1(1400) Mixing Angle via QCD Sum Rules

In this work, we investigated the mixing between strange axial vector mesons K1(1270) and K1(1400) by using QCD Sum Rules approach. Since these states couple to the same interpolating currents, we defined them in terms of orbital angular momentum eigen states K1A and K1B. By using the axial vector and tensor interpolating currents which are almost purely coupling to K1A and K1B, and then employing the orthogonality of the physical states, we obtained an analytical expression for the K1 mixing angle. We performed a Monte Carlo based numerical analysis to estimate the value of the mixing angle.

Newly observed exotic doubly charmed meson [formula omitted

In this work, we treat the newly observed doubly charmed four-quark state Tcc+ as an axial-vector tetraquark with content ccu‾d‾, and calculate its spectroscopic parameters and width. The mass and current coupling of the tetraquark Tcc+ are found by means of the QCD two-point sum rule method by taking into account quark, gluon and mixed condensates up to dimension 10. The width of the Tcc+ is evaluated using partial widths of decay processes Tcc+→T˜π0 and Tcc+→Tcc;u‾u‾0π+, where T˜=ccu‾d‾ and Tcc;u‾u‾0 are scalar tetraquarks. To compute the partial width of the first process, we apply the QCD three-point sum rule approach and exact numerical value of the strong coupling g that corresponds to the vertex Tcc+T˜π0. The width of the second decay is estimated using isospin symmetry and the prediction obtained for the first channel. Our results for the mass m=(3868±124)MeV and width Γ=(489±92)keV of the tetraquark Tcc+ are in a nice agreement with recent measurements of the LHCb collaboration.

Eta ^{(prime )}-meson twist-2 distribution amplitude within QCD sum rule approach and its application to the semi-leptonic decay D_s^+ rightarrow eta ^{(prime )}ell ^+ nu _ell

In this paper, we make a detailed discussion on the eta and eta ^prime -meson leading-twist light-cone distribution amplitude phi _{2;eta ^{(prime )}}(u,mu ) by using the QCD sum rules approach under the background field theory. Taking both the non-perturbative condensates up to dimension-six and the next-to-leading order (NLO) QCD corrections to the perturbative part, its first three moments langle xi ^n_{2;eta ^{(prime )}}rangle |_{mu _0} with n = (2, 4, 6) can be determined, where the initial scale mu _0 is set as the usual choice of 1 GeV. Numerically, we obtain langle xi _{2;eta }^2rangle |_{mu _0} =0.231_{-0.013}^{+0.010}, langle xi _{2;eta }^4 rangle |_{mu _0} =0.109_{ - 0.007}^{ + 0.007}, and langle xi _{2;eta }^6 rangle |_{mu _0} =0.066_{-0.006}^{+0.006} for eta -meson, langle xi _{2;eta '}^2rangle |_{mu _0} =0.211_{-0.017}^{+0.015}, langle xi _{2;eta '}^4 rangle |_{mu _0} =0.093_{ - 0.009}^{ + 0.009}, and langle xi _{2;eta '}^6 rangle |_{mu _0} =0.054_{-0.008}^{+0.008} for eta '-meson. Next, we calculate the D_srightarrow eta ^{(prime )} transition form factors (TFFs) f^{eta ^{(prime )}}_{+}(q^2) within QCD light-cone sum rules approach up to NLO level. The values at large recoil region are f^{eta }_+(0) = 0.476_{-0.036}^{+0.040} and f^{eta '}_+(0) = 0.544_{-0.042}^{+0.046}. After extrapolating TFFs to the allowable physical regions within the series expansion, we obtain the branching fractions of the semi-leptonic decay, i.e. D_s^+rightarrow eta ^{(prime )}ell ^+ nu _ell , i.e. {{mathcal {B}}}(D_s^+ rightarrow eta ^{(prime )} e^+nu _e)=2.346_{-0.331}^{+0.418}(0.792_{-0.118}^{+0.141})times 10^{-2} and {{mathcal {B}}}(D_s^+ rightarrow eta ^{(prime )} mu ^+nu _mu )=2.320_{-0.327}^{+0.413}(0.773_{-0.115}^{+0.138})times 10^{-2} for ell = (e, mu ) channels respectively. And in addition to that, the mixing angle for eta -eta ' with varphi and ratio for the different decay channels {{mathcal {R}}}_{eta '/eta }^ell are given, which show good agreement with the recent BESIII measurements.

Zooming in on Multiquark Hadrons within QCD Sum-Rule Approaches

Aiming at self-consistent descriptions of multiquark hadrons (such as tetraquarks, pentaquarks, hexaquarks) by means of QCD sum rules, we note that the totality of contributions to two-point or three-point correlation functions that involve, respectively, either two or just a single operator capable of interpolating the particular multiquark under study can be straightforwardly disentangled into two disjoint classes defined by unambiguously identifiable members. The first is formed by so-called multiquark-phile contributions which indeed might support multiquarks. In the case of flavour-exotic tetraquarks, by definition composed of four (anti–) quarks of mutually different flavours, a tetraquark-phile contribution has to exhibit two or more gluon exchanges of appropriate topology. The second consists of contributions evidently not bearing any relation to multiquarks; these must be discarded when studying multiquarks by QCD sum rules. The first class only should enter the “multiquark-adequate” QCD sum rules for exotic hadrons.

A closer look at observables from exclusive semileptonic B \u2192 (\u03c0, \u03c1)\u2113\u03bd\u2113 decays

This article analyses the available inputs in B → πℓνℓ and B → ρℓνℓ decays which include the measured values of differential rate in different q2-bins (lepton invariant mass spectrum), lattice, and the newly available inputs on the relevant form-factors from the light-cone sum rules (LCSR) approach. We define different fit scenarios, and in each of these scenarios, we predict a few observables in the standard model (SM). For example, R(M)=frac{mathcal{B}left(Bto M{ell}_i{nu}_{ell_i}right)}{mathcal{B}left(Bto M{ell}_j{nu}_{ell_j}right)},{R}_{ell_j}^{ell_i}(M)=frac{mathcal{B}left(Bto {ell}_i{nu}_{ell_i}right)}{mathcal{B}left(Bto M{ell}_j{nu}_{ell_j}right)} with M = π or ρ and ℓi,j = e, μ or τ. We also discuss the new physics (NP) sensitivities of all these observables and obtain bounds on a few NP Wilson coefficients in b → uτντ decays using the available data. We have noted that the data at present allows sizeable NP contributions in this mode. Also, we have predicted a few angular observables relevant to these decay modes.

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.

Improved light-cone harmonic oscillator model for the pionic leading-twist distribution amplitude

In this paper, we study the pion leading-twist distribution amplitude (DA) ${\ensuremath{\phi}}_{2;\ensuremath{\pi}}(x,\ensuremath{\mu})$ by improving the traditional light-cone harmonic oscillator model within the reconstruction of the function ${\ensuremath{\varphi}}_{2;\ensuremath{\pi}}(x)$. In order to constrain the model parameters, we calculate its moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ in the framework of the QCD background field theory sum rule up to tenth order. Considering the fact that the sum rule of the zeroth moment $⟨{\ensuremath{\xi}}^{0}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$ cannot be normalized, we suggest a more reasonable sum rule formula for $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$. Then, we obtain the values of $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}$ with $n=(2,4,6,8,10)$ at the initial scale ${\ensuremath{\mu}}_{0}=1\text{ }\text{ }\mathrm{GeV}$. The first two moments are $⟨{\ensuremath{\xi}}^{2}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.271\ifmmode\pm\else\textpm\fi{}0.013$ and $⟨{\ensuremath{\xi}}^{4}{⟩}_{2;\ensuremath{\pi}}{|}_{{\ensuremath{\mu}}_{0}}=0.138\ifmmode\pm\else\textpm\fi{}0.010$, and the corresponding Gegenbauer moments are ${a}_{2}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.206\ifmmode\pm\else\textpm\fi{}0.038$ and ${a}_{4}^{2;\ensuremath{\pi}}({\ensuremath{\mu}}_{0})=0.047\ifmmode\pm\else\textpm\fi{}0.011$, respectively. After fitting the moments $⟨{\ensuremath{\xi}}^{n}{⟩}_{2;\ensuremath{\pi}}{|}_{\ensuremath{\mu}}$, we obtain the appropriate model parameters by using the least squares method. The resultant behavior for the twist-2 pion DA is closer to the AdS/QCD and lattice results, but narrower than that obtained using the Dyson-Schwinger equation. Furthermore, we calculate the pion-photon transition form factors (TFFs) and $B\ensuremath{\rightarrow}\ensuremath{\pi}$ TFFs within the light-cone sum rule approach, which conform with experimental and theoretical results.

New scalar resonance X 0(2900) as a molecule: mass and width

We explore features of the scalar structure X 0(2900), which is one of the two resonances discovered recently by LHCb in the D − K + invariant mass distribution in the decay B + → D + D − K +. We treat X 0(2900) as a hadronic molecule composed of the conventional mesons and K ∗0 and calculate its mass, coupling and width. The mass and coupling of X 0(2900) are determined using the QCD two-point sum rule method by taking into account quark, gluon, and mixing vacuum condensates up to dimension 15. The decay of this structure to final state D − K + is investigated in the context of the light-cone sum rule approach supported by a soft-meson technique. To this end, we evaluate strong coupling G corresponding to vertex X 0 D − K +, which allows us to find width of the decay X 0(2900) → D − K +. Obtained predictions for the mass of the hadronic molecule and for its width Γ = (49.6 ± 9.3) MeV can be considered as arguments in favor of molecule interpretation of X 0(2900).

Implications of new physics in B → K 1 μ + μ − decay processes

Recently, several discrepancies at the level of (2–3)σ have been observed in the decay processes mediated by flavour changing neutral current (FCNC) transitions b → sℓ + ℓ −, which may be considered as the smoking-gun signal of new physics (NP). These intriguing hints of NP have attracted a lot of attention and many attempts are being made to find the possible NP signature in other related processes, which are mediated through the same quark-level transitions. In this work, we perform a comprehensive analysis of the FCNC decays of the B meson to axial vector mesons K 1(1270) and K 1(1400), which are an admixture of the 13 P 1 and 11 P 1 states K 1A and K 1B , in a model independent framework. Using the B → K 1 form factors evaluated in the light cone sum rule approach, we investigate the rare exclusive semileptonic decays B → K 1(1270)μ + μ − and B → K 1(1400)μ + μ −. Considering all the possible relevant operators for b → sℓ + ℓ − transitions, we study their effects on various observables such as branching fractions, the lepton flavor universality violating ratio , forward–backward asymmetries, and lepton polarization asymmetries of these processes. These results will not only enhance the theoretical understanding of the mixing angle but also serve as a good tool for probing NP.

A closer look at the extraction of |Vub| from B \u2192 \u03c0\u2113\u03bd

To extract the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |Vub|, we have re-analyzed all the available inputs (data and theory) on the B → πℓν decays including the newly available inputs on the form-factors from light cone sum rule (LCSR) approach. We have reproduced and compared the results with the procedure taken up by the Heavy Flavor Averaging Group (HFLAV), while commenting on the effect of outliers on the fits. After removing the outliers and creating a comparable group of data-sets, we mention a few scenarios in the extraction of |Vub|. In all those scenarios, the extracted values of |Vub| are higher than that obtained by HFLAV. Our best results for |Vub|exc. are (3.94 ± 0.14) × 10−3 and left({3.93}_{-0.15}^{+0.14}right) × 10−3 in frequentist and Bayesian approaches, respectively, which are consistent with that extracted from inclusive decays |Vub|inc. within 1 σ confidence interval.

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 $|{V}_{cb}|=({40.00}_{\ensuremath{-}4.08}^{+4.93})\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

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.

Fully heavy pentaquark states

Developing the calculation techniques to fivefold heavy hadrons, we perform the study of novel fully-heavy $QQQQ\bar{Q}$ pentaquark states by the QCD sum rule approach that is firmly based on the QCD basic theory. Numerically, masses of fully-heavy pentaquark states are calculated to be $7.41^{+0.27}_{-0.31}~\mbox{GeV}$ for $cccc\bar{c}$ and $21.60^{+0.73}_{-0.22}~\mbox{GeV}$ for $bbbb\bar{b}$, respectively. In experiment, these predicted all-heavy pentaquark states could be searched for in the $\Omega_{QQQ}\eta_{Q}$ invariant mass spectrum.