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.