QCD Sum Rule Analysis Research Articles

(g − 2)μ and α(M2Z) re-evaluated using new precise data

We update our standard model predictions for g − 2 of the muon and for the hadronic contributions to the running of the QED coupling, Δα(5)had(M2Z). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2π channel and from the energy region just below 2 GeV. In particular, for the e+e− → π+π− contribution we include the recent ‘radiative return’ data from KLOE and BaBar. We also include the recent BaBar data on other exclusive channels. We make a detailed study of the effect of replacing the measurements of the inclusive cross section, σ(e+e− → hadrons), by the sum of the exclusive channels in the energy interval GeV, which includes a QCD sum-rule analysis of this energy region. Our favoured prediction for the muon anomalous magnetic moment is (g − 2)/2 = (11 659 182.8 ± 4.9) × 10−10 which is 3.3 σ below the present world-average measurement. We compare our g − 2 value with other recent calculations. Our prediction for the QED coupling, obtained via Δα(5)had(MZ2) = (276.26 ± 1.38) × 10−4 , is α(M2Z)−1 = 128.944 ± 0.019.

Charm Mass Determination from QCD Sum Rules: A Revision of the Classical Method

In this work we take a revised look at the charm quark mass determination from QCD sum rules analyses. On the theoretical side we use the most up to date calculations (amounting to up \({O(\alpha_s^3)}\) expressions) and on the experimental side, to our knowledge, the most complete data set (maximum coverage of the energy spectrum). We reconsider the estimate of perturbative uncertainties (due to truncation of the series in α s ) proposing four alternative methods (equivalent in perturbation theory) to determine the \({\rm{\overline{MS}}}\) charm quark mass. We also use a very robust method to combine data from different experiments when systematic correlated errors are mainly due to normalization. This allows to use experimental data up to 10.5GeV, and to quantify statistic and systematic experimental errors in a meaningful way.

A Bayesian Approach to QCD Sum Rules

QCD sum rules are analyzed with the help of the Maximum Entropy Method. We develop a new technique based on the Bayesion inference theory, which allows us to directly obtain the spectral function of a given correlator from the results of the operator product expansion given in the deep euclidean 4-momentum region. The most important advantage of this approach is that one does not have to make any a priori assumptions about the functional form of the spectral function, such as the "pole + continuum" ansatz that has been widely used in QCD sum rule studies, but only needs to specify the asymptotic values of the spectral function at high and low energies as an input. As a first test of the applicability of this method, we have analyzed the sum rules of the rho-meson, a case where the sum rules are known to work well. Our results show a clear peak structure in the region of the experimental mass of the rho-meson. We thus demonstrate that the Maximum Entropy Method is successfully applied and that it is an efficient tool in the analysis of QCD sum rules.

ππcontribution to the QCD sum rules for the light tetraquark

We perform a QCD sum rule analysis for the ${f}_{0}$ light tetraquark taking into account the contribution arising from the two pion intermediate state. With the interpolating currents of the different chiral combinations of scalar and pseudoscalar diquarks, it is demonstrated that the interpolating current with maximum chirality has a large coupling to the two pion state, but the current with zero chirality interacts only weekly with this state. Taking into account the form factor in the ${f}_{0}$-two pion vertex, it is shown that the ${f}_{0}$ coupling to the two pion state leads to an increase of the lightest tetraquark mass by a value of about 100 MeV. The analysis of the resulting sum rule shows that the $\ensuremath{\sigma}({f}_{0}(600))$-meson state might be treated as the four-quark bound state in the instanton field which has a rather strong coupling to the two pion state.

$D_sD^*$ Molecule as an Axial Meson

We use QCD sum rules to study the possible existence of a $D_s\bar{D}^*+ D_s^*\bar{D}$ molecule with the quantum number $J^P=1^+$. We consider the contributions of condensates up to dimension eight and work at leading order in $\alpha_s$. We obtain $m_{D_sD^*}=(3.96\pm0.10) \GeV$ around 100 MeV above the mass of the meson X(3872). The proposed state is a natural generalized state to the strangeness sector of the X(3872), which was also found to be consistent with a multiquark state from a previous QCD sum rule analysis.

QCD sum rule analysis of the rare radiativeBc→Ds*γdecay

In this work, the radiative ${B}_{c}\ensuremath{\rightarrow}{D}_{s}^{*}\ensuremath{\gamma}$ decay is investigated in the framework of QCD sum rules. The transition form factors responsible for the decay are calculated. The total branching ratio for this decay is estimated to be in the order of ${10}^{\ensuremath{-}5}$, so this decay can be measurable at LHC in the near future.

Light cone QCD sum rules analysis of the axial [formula omitted] transition form factors

The axial N − Δ ( 1232 ) transition form factors are calculated within the light cone QCD sum rules method. A comparison of our results with the predictions of lattice theory and quark model is presented.

QCD sum rule study of the masses of light tetraquark scalar mesons

We study the low-lying scalar mesons of light u, d, s flavors in the QCD sum rule. Having all possible combinations of tetraquark currents in the local form, QCD sum rule analysis has been carefully performed. We found that using the appropriate tetraquark currents, the masses of σ, κ, f0 and a0 mesons appear in the region of 0.6–1 GeV with the expected ordering. The results are compared with that of the conventional q¯q currents, where the masses are considerably larger.

Light Scalar Mesons in the QCD Sum Rule

We study the light scalar mesons in the QCD sum rule. We find that there are five independent scalar tetraquark currents in the local form, and we perform QCD sum rule analysis using both these currents and their combinations. Compared with the sum rules by conventional \bar{q} q currents, our result supports a tetraquark structure for low-lying scalar mesons.

Instanton interpolating current for σ-tetraquark

Abstract We perform a QCD sum rule analysis for the light scalar meson σ ( f 0 ( 600 ) ) with a tetraquark current related to the instanton picture for QCD vacuum. We demonstrate that instanton current, including equal weights of scalar and pseudoscalar diquark–antidiquarks, leads to a strong cancelation between the contributions of high dimension operators in the operator product expansion (OPE). Furthermore, in the case of this current direct instanton contributions do not spoil the sum rules. Our calculation, obtained from the OPE up to dimension 10 operators, gives the mass of σ-meson around 780 MeV.

Exotic tetraquarkuds¯s¯ofJP=0+in the QCD sum rule

We study a QCD sum rule analysis for an exotic tetraquark ud bar[s] bar[s] of J^P=0^+ and I = 1. We construct q q bar[q] bar[q] currents in a local product form and find that there are five independent currents for this channel. Due to high dimensional nature of the current, it is not easy to form a good sum rule when using a single current. This means that we do not find any sum rule window to extract reliable results, due to the insufficient convergence of the OPE and to the exceptional important role of QCD continuum. Then we examine sum rules by using currents of linear combinations of two currents among the independent ones. We find two reasonable cases that predict a mass of the tetraquark around 1.5 GeV.

QCD sum rule analysis of the pentaquark

We perform a QCD sum rule calculation to determine the mass and the parity of the lowest lying pentaquark state. We include operators up to dimension $d=13$ in the OPE and the direct instanton contributions. We find evidence for a positive parity state. The contribution from operators of dimension $d>5$ is instrumental in determining the parity of the state and achieving the convergence of the sum rule.

QCD sum rules for the anticharmed pentaquark

We present a QCD sum rule analysis for the anti-charmed pentaquark state with and without strangeness. While the sum rules for most of the currents are either non-convergent or dominated by the $DN$ continuum, the one for the non-strange pentaquark current composed of two diquarks and an antiquark, is convergent and has a structure consistent with a positive parity pentaquark state after subtracting out the $DN$ continuum contribution. Arguments are presented on the similarity between the result of the present analysis and that based on the constituent quark models, which predict a more stable pentaquark states when the antiquark is heavy.

ηc-glueball mixing and resonance X(1835)

The mixing of ${\ensuremath{\eta}}_{c}$ and the lowest mass pseudoscalar glueball is estimated within the framework of the instanton liquid model. It is demonstrated that the mixing is large and may explain the difference between the observed mass of the glueball candidate X(1835) and the theoretical prediction of the QCD sum rule analysis.

ρ-meson form factors and QCD sum rules

We present predictions for \ensuremath{\rho}-meson form factors obtained from the analysis of QCD sum rules in next-to-leading order of perturbation theory. The radiative corrections turn out to be sizeable and should be taken into account in rigorous theoretical analysis.

Pion form factor and QCD sum rules: case of pseudoscalar current

We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of pseudoscalar pion currents. The essential instanton contribution is reanalysed with account for present more accurate values of parameters entering Single Instanton Approximation (SIA). The theoretical curve obtained for Q2 dependence of pion form factor is in a good agreement with existing experimental data. To calculate NLO corrections for double spectral densities we developed an effective computational technique. The details of the method together with the results for pion form factor in a more theoretically clean case of axial interpolating currents will be presented elsewhere.

Pion form factor and QCD sum rules: case of axial current

We present an analysis of QCD sum rules for pion form factor in next-to-leading order of perturbation theory for the case of axial-vector pion currents. The theoretical predictions for Q2-dependence of pion form factor are in good agreement with available experimental data. It is shown, that NLO corrections are large in this case and should be taken into account in rigorous theoretical analysis.

Instanton and higher-loop perturbative contributions to the QCD sum-rule analysis of pseudoscalar gluonium

Instanton effects and three-loop perturbative contributions are incorporated into QCD sum-rule analyses of pseudoscalar ( J PC =0 −+) gluonium. Gaussian sum-rules are shown to be superior to Laplace sum-rules in optimized predictions for pseudoscalar gluonium states in the presence of instanton contributions. The Gaussian sum-rule analysis yields a pseudoscalar mass of (2.65±0.33) GeV and width bounded by Γ<530 MeV. The Laplace sum-rules provide corroborating evidence in support of the ≈2.7 GeV mass scale.

QCD sum rules for heavy baryons

We construct heavy baryon currents from the heavy quark limit of baryonic Bethe-Salpeter wave functions. We discuss the one-loop renormalization of these heavy baryon currents as well as their two-point correlators up to the order ${1/m}_{Q}.$ For the special case of the spin (3/2,5/2) doublet, we extract mass values from a QCD sum-rule analysis.

QCD sum rule analysis of the coupling constant g???

We employ QCD sum rules to calculate the coupling constant gωσγ by studying the three point ωσγ-correlation function. Our result complements the analysis of this coupling constant utilizing the experimental value of the ω →π0π0γ decay rate studied within the framework of chiral perturbation theory including vector meson and σ meson intermediate states.