Narrow Results

We discuss the QCD sum-rule approach for the spacelike electromagnetic pion form factor in the O(α_s) approximation. We show that the nonlocality of the condensates is a key point to include nonperturbative contributions to the pion form factor. We compare our results with the Local-Duality predictions and show that the continuum threshold s₀(Q²) parameter is highly underestimated in the Local-Duality approach at Q² ≳ 2 GeV². Using our fit for this parameter, and applying the fractional analytic perturbation theory, we estimate with an accuracy of the order of 1% the contribution to the pion's form factor.

A general, and very basic introduction to QCD sum rules is presented, with emphasis on recent issues to be described at length in other papers in this issue. Collectively, these papers constitute the proceedings of the International Workshop on Determination of the Fundamental Parameters of QCD, Singapore, March 2013.

In this paper, we study the type scalar tetraquark state in detail with the QCD sum rules by calculating the contributions of the vacuum condensates up to dimension 10 in the operator product expansion, and obtain the value , which is the lowest mass for the hidden charmed tetraquark states from the QCD sum rules. Furthermore, we calculate the hadronic coupling constants G_Zcηcπ and G_ZcDD with the three-point QCD sum rules, then study the strong decays Z_c→η_cπ, DD, and observe that the total width Γ_Zc≈21 MeV. The present predictions can be confronted with the experimental data in the future at the BESIII, LHCb and Belle-II.

Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark–hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to s = 10 GeV² by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using e${}^{+}$e${}^{-}$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.

In this paper, we present preliminary results of the determination of the charm quark mass ${\widehat{m}}_c$ from QCD sum rules of moments of the vector current correlator calculated in perturbative QCD at ${𝒪}({\widehat{\alpha }}_s^3)$. Self-consistency between two different sum rules allow to determine the continuum contribution to the moments without requiring experimental input, except for the charm resonances below the continuum threshold. The existing experimental data from the continuum region is used, then, to confront the theoretical determination and reassess the theoretic uncertainty.

The temperature dependence of the sum of the QCD up- and down-quark masses, (m_u+m_d) and the pion decay constant, f${}_{\pi }$, are determined from two thermal finite energy QCD sum rules for the pseudoscalar-current correlator. This quark mass remains mostly constant for temperatures well below the critical temperature for deconfinement/chiral-symmetry restoration. As this critical temperature is approached, the quark mass increases sharply with increasing temperature. This increase is far more pronounced if the temperature dependence of the pion mass (determined independently from other methods) is taken into account. The behavior of f${}_{\pi }$(T) is consistent with the expectation from chiral symmetry, i.e. that it should follow the thermal dependence of the quark condensate, independently of the quark mass.

In this paper, the tensor–vector–pseudoscalar (TVP) type of vertices are analyzed with the QCD sum rules (QCDSR) and the local-QCD sum rules (SR) in the leading-order approximation and the hadronic coupling constants $G_{D_2^{\ast }{D}^{\ast }\pi }$, $G_{D_{s2}^{\ast }{D}^{\ast }K}$, $G_{B_2^{\ast }{B}^{\ast }\pi }$ and $G_{B_{s2}^{\ast }{B}^{\ast }K}$ together with the corresponding decay widths are then calculated. The results indicate that QCDSR as well as the local-QCDSR give a consistent description. The calculated strong decay widths and decay width ratios are compared with the available experimental and other theoretical values. Finally, the total widths $\mathrm{\Gamma }(D_2^{\ast }{(2460)}^0)$, $\mathrm{\Gamma }(D_{s2}^{\ast }(2573))$, $\mathrm{\Gamma }(B_2^{\ast }{(5747)}^0)$ and $\mathrm{\Gamma }(B_{s2}^{\ast }{(5840)}^0)$ are discussed in detail. The results show that these total widths are underestimated, especially for the tensor $B_2^{\ast }$ and $B_{s2}^{\ast }$ mesons where the obtained predictions are almost a factor of 2 lower than measured decay widths.

In this paper, we apply the method of QCD sum rules to study the doubly heavy tetraquark states $QQ\bar{q}\bar{n}$ with spin-parity $J^P=1^{+}$ and strangeness $S=0,-1$ using careful estimates of the Borel and threshold parameters involved. Masses of the doubly bottom and charmed tetraquarks with isospin $I=0,1/2,1$ are computed precisely via taking into account multifarious condensates up to dimension 10. Compared with the two-heavy meson thresholds, we find that all nonstrange doubly-bottom tetraquarks and a doubly-charmed tetraquarks associated with $J_3$ with $J^P=1^{+}$ are stable against strong decay into two bottom mesons while a doubly-charmed tetraquark associated with current $J_2$ is unstable against strong decay. By the way, weak decay widths of the doubly bottom tetraquarks are also given.

Using only independent high-scale OPE input, we investigate QCD sum rule constraints on two currently incompatible versions of the isovector vector spectral function, one obtained from electroproduction (EM) data, the other from hadronic τ decay data. Sum rules involving weighted integrals over the spectral function, from threshold to a variable upper endpoint s₀, are employed. It is shown that both the normalization and slope with respect to s₀ of the EM spectral integrals disagree with the corresponding OPE expectations, while both normalization and slope are in good agreement when hadronic τ decay data is used instead. These results favor determinations of the leading hadronic vacuum polarization contribution to a_μ obtained using the τ decay data, and hence Standard Model predictions for a_μ compatible with the current experimental determination.

The matrix element of the isoscalar axial vector current, , between nucleon states is computed using the external field QCD sum rule method. The external field induced correlator, , is calculated from the spectrum of the isoscalar axial vector meson states. Since it is difficult to ascertain, from QCD sum rule for hyperons, the accuracy of validity of flavor SU(3) symmetry in hyperon decays when strange quark mass is taken into account, we rely on the empirical validity of Cabbibo theory to determine the matrix element between nucleon states. Combining with our calculation of and the well-known nucleon β-decay constant allows us to determine occurring in the Bjorken sum rule. The result is in reasonable agreement with experiment. We also discuss the role of the anomaly in maintaining flavor symmetry and validity of OZI rule.

It is shown that QCD sum rules in the planar limit lead to a certain relation between four important quantities: ρ-meson mass, weak π-meson decay constant, quark and gluon condensates. As a byproduct an explanation for the dominance of ρρ-decay for the f₀(1370)-meson is proposed.

We describe the present status of the pion distribution amplitude as it originated from two sources: (i) a nonperturbative approach, based on QCD sum rules with nonlocal condensates and (ii) a NLO QCD analysis of the CLEO data on F^γγ*^π(Q²), supplemented by the recent high-precision lattice calculations of the second moment of the pion distribution amplitude.

The pentaquark width is calculated in QCD sum rules. The higher dimension operators contribution is accounted. It is shown, that Γ_Θ should be very small, less than 1 MeV.

In this paper, we assume that there exists a pseudoscalar molecular state and study its mass with the molecule-type interpolating current in details using the QCD sum rules. The numerical result disfavors identifying the charmonium-like state Y(4274) as the molecule.

The structure of the D_s1(2460) meson has not yet been exactly known in the quark model. Considering the D_s1 meson as a conventional meson, we investigate the strong form factors and coupling constants g_Ds1D*K and in the framework of the three point QCD sum rules. Any future experimental measurement on these form factors as well as coupling constants g_Ds1D*K and and their comparison with the obtained results in the present work can give considerable information about the structure of this meson.

In this paper, we calculate the mass modifications of the vector and axial vector mesons D*, B*, D₁ and B₁ in the nuclear matter with the QCD sum rules, and obtain the mass-shifts δM_D* = -71 MeV, δM_B* = -380 MeV, δM_D1 = 72 MeV, δM_B1 = 264 MeV, and the scattering lengths a_D* = -1.07 fm, a_B* = -7.17 fm, a_D1 = 1.15 fm and a_B1 = 5.03 fm for the D*N, B*N, D₁N and B₁N interactions, respectively.

In this paper, we tentatively assign the Y(4140), Y(4274) and X(4350) to be the scalar and tensor tetraquark states, respectively, and study them with the QCD sum rules. In the operator product expansion, we take into account the vacuum condensates up to dimension-10. In calculations, we use the formula to determine the energy scales of the QCD spectral densities. The numerical results favor assigning the Y(4140) to be the J^PC = 2⁺⁺ diquark–antidiquark type tetraquark state, and disfavor assigning the Y(4274) and X(4350) to be the 0⁺⁺ or 2⁺⁺ tetraquark states.

In this paper, we assume the $Z_c(4200)$ as the color octet–octet type axial-vector molecule-like state, and construct the color octet–octet type axial-vector current to study its mass and width with the QCD sum rules. The numerical values $M_{Z_c(4200)}=4.19\pm 0.08\mathrm{\text{GeV}}$ and ${\Gamma }_{Z_c(4200)}\approx 334\mathrm{\text{MeV}}$ are consistent with the experimental data $M_{Z_c(4200)}=4196_{-29}^{+31}{}_{-13}^{+17}\mathrm{\text{MeV}}$ and ${\Gamma }_{Z_c(4200)}=370_{-70}^{+70}{}_{-132}^{+70}\mathrm{\text{MeV}}$, and support assigning the $Z_c(4200)$ to be the color octet–octet type molecule-like state with $J^{PC}=1^{+-}$. Furthermore, we discuss the possible assignments of the $Z_c(3900)$, $Z_c(4200)$ and $Z(4430)$ as the diquark–antidiquark type tetraquark states with $J^{PC}=1^{+-}$.

The calculation of the mass of light scalar isosinglet meson within the Shifman–Vainshtein–Zakharov (SVZ) sum rules is revisited. We develop simple analytical methods for estimation of hadron masses in the SVZ approach and try to reveal the origin of their numerical values. The calculations of hadron parameters in the SVZ sum rules are known to be heavily based on a choice of the perturbative threshold. This choice requires some important ad hoc information. We show analytically that the scalar mass under consideration has a lower and upper bound which are independent of this choice: $0.78\lesssim m_s\lesssim 1.28$ GeV.

The large-$N_c$ masses of light vector, axial, scalar and pseudoscalar mesons are calculated from QCD spectral sum rules for a particular ansatz interpolating the radial Regge trajectories. The ansatz includes a linear part plus exponentially degreasing corrections to the meson masses and residues. The form of corrections was proposed some time ago for consistency with analytical structure of Operator Product Expansion of the two-point correlation functions. We revised that original analysis and found the second solution for the proposed sum rules. The given solution describes better the spectrum of vector and axial mesons.