Sum Rule Method Research Articles

Pseudoscalar-meson decuplet-baryon coupling constants in light cone QCD

Taking into account the $SU(3)_f$ breaking effects, the strong coupling constants of the $\pi$, $K$ and $\eta$ mesons with decuplet baryons are calculated within light cone QCD sum rules method. It is shown that all coupling constants, even in the case of $SU(3)_f$ breaking, are described in terms of only one universal function. It is shown that for $\Xi^{\ast 0} \to \Xi^{\ast 0} \eta $ transition violation of $SU(3)_f$ symmetry is very large and for other channels when $SU(3)_f$ symmetry is violated, its maximum value constitutes $10%\div15%$.

Nucleon QCD sum rules in nuclear matter including radiative corrections

We calculate the nucleon parameters in nuclear matter using the QCD sum rules method. The radiative corrections to only the leading operator product expansion terms are included, with the corrections of the order ${\ensuremath{\alpha}}_{s}$ beyond the logarithmic approximation taken into account. The density dependence of the influence of radiative corrections on the nucleon parameters is obtained. At saturation density, the radiative corrections increase the values of vector and scalar self-energies by about $40$ and $30$ MeV, respectively, which is much smaller than the result of a straightforward naive estimation. The results appear to be stable with respect to possible variations of the value of ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$.

Isgur-Wise functions and unitary representations of the Lorentz group: The baryon casej=0

We propose a group theoretical method to study Isgur-Wise (IW) functions. A current matrix element splits into a heavy quark matrix element and an overlap of the initial and final clouds, related to the IW functions, that contain the long distance physics. The light cloud belongs to the Hilbert space of a unitary representation of the Lorentz group. Decomposing into irreducible representations one obtains the IW function as an integral formula, superposition of irreducible IW functions with positive measures, providing positivity bounds on its derivatives. Our method is equivalent to the sum rule approach, but sheds another light on the physics and summarizes and gives all its possible constraints. We expose the general formalism, thoroughly applying it to the case j=0 for the light cloud, relevant to the semileptonic decay {lambda}{sub b}{yields}{lambda}{sub c}l{nu}{sub l}. In this case, the principal series of the representations contribute, and also the supplementary series. We recover the bound for the curvature of the j=0 IW function {xi}{sub {lambda}}(w) that we did obtain from the sum rule method, and we get new bounds for higher derivatives. We demonstrate also that if the lower bound for the curvature is saturated, then {xi}{sub {lambda}}(w) is completely determined, givenmore » by an explicit elementary function. We give criteria to decide if any Ansatz for the Isgur-Wise function is compatible or not with the sum rules. We apply the method to some simple model forms proposed in the literature. Dealing with a Hilbert space, the sum rules are convergent, but this feature does not survive hard gluon radiative corrections.« less

NtoΔtransition amplitudes from QCD sum rules

We present a calculation of the $N$ to $\ensuremath{\Delta}$ electromagnetic transition amplitudes using the method of QCD sum rules. A complete set of QCD sum rules is derived for the entire family of transitions from the baryon octet to decuplet. They are analyzed in conjunction with the corresponding mass sum rules using a Monte Carlo-based analysis procedure. The performance of each of the sum rules is examined using the criteria of operator product expansion convergence and ground-state dominance, along with the role of the transitions in intermediate states. Individual contributions from the $u$, $d$, and $s$ quarks are isolated and their implications in the underlying dynamics are explored. Valid sum rules are identified and their predictions are obtained. The results are compared with experiment and other calculations.

Spin content ofΛin QCD sum rules

We calculate the isoscalar axial-vector coupling constants of the {lambda} hyperon using the method of QCD sum rules. A determination of these coupling constants reveals the individual contributions of the u, d, and the s quarks to the spin content of {lambda}. Our results for the light-quark contributions are in agreement with those from experiment assuming flavor SU(3). We also find that the flavor-SU(3)-breaking effects are small and the contributions from the u and the d quarks to the {lambda} polarization are negatively polarized as in the flavor-SU(3) limit.

Mixed heavy quark hybrid mesons, decay puzzles, and RHIC

We estimate the energy of the lowest charmonium and upsilon states with hybrid admixtures using the method of QCD sum rules. Our results show that the ${\ensuremath{\Psi}}^{\ensuremath{'}}(2S)$ and $\ensuremath{\Upsilon}(3S)$ states both have about a 50% admixture of hybrid and meson components. From this we find explanations of both the famous $\ensuremath{\rho}\ensuremath{-}\ensuremath{\pi}$ puzzle for charmonium and the unusual pattern of $\ensuremath{\sigma}$ decays that have been found in $\ensuremath{\Upsilon}$ decays. Moreover, this picture can be used for predictions of heavy quark production with the octet model for RHIC.

Spin-3/2pentaquark in QCD sum rules

The QCD sum rule method is formulated for the strangeness $+1$ pentaquark baryon with isospin $I=0$ and spin-parity ${J}^{\ensuremath{\pi}}={\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$. The spin-$\frac{3}{2}$ states are considered to be narrower than the spin-$\frac{1}{2}$ ones, and thus may provide a natural explanation for the experimentally observed narrow width of ${\ensuremath{\Theta}}^{+}$. In order to obtain reliable results in QCD sum rule calculations, we stress the importance of establishing a wide Borel window, where convergence of the operator product expansion and sufficient low-mass strength of the spectral function are guaranteed. To this end, we employ the difference of two independent correlators so that the high-energy continuum contribution is suppressed. The stability of the physical quantities against the Borel mass is confirmed within the Borel window. It is found that the sum rule gives positive evidence for the $(I,{J}^{\ensuremath{\pi}})=(0,{\frac{3}{2}}^{+})$ state with a mass of about $1.4\ifmmode\pm\else\textpm\fi{}0.2\text{ }\text{ }\mathrm{GeV}$, while we cannot extract any evidence for the $(0,{\frac{3}{2}}^{\ensuremath{-}})$ state.

SemileptonicBmeson decays into a highly excited charmed meson doublet

We study the heavy quark effective theory prediction for semileptonic $B$ decays into an orbital excited $F$-wave charmed doublet, the ($2^{+}$, $3^{+}$) states ($D^{*'}_{2}$, $D_{3}$), at the leading order of heavy quark expansion. The corresponding universal form factor is estimated by using the QCD sum rule method. The decay rates we predict are $\Gamma_{B\to D^{*'}_{2}\ell\overline{\nu}}=1.85\times10^{-19} {GeV}$ and $\Gamma_{B\to D_{3}\ell\overline{\nu}}=1.78\times10^{-19} {GeV}$. The branching ratios are $\mathcal {B}(B\to D_{2}^{*'}\ell\overline{\nu})=4.6\times10^{-7}$ and $\mathcal {B}(B\to D_{3}\ell\overline{\nu})=4.4\times10^{-7}$, respectively.

Effective continuum threshold in dispersive sum rules

We study the accuracy of the bound-state parameters obtained with the method of dispersive sum rules, one of the most popular theoretical approaches in nonperturbative QCD and hadron physics. We make use of a quantum-mechanical potential model since it provides the only possibility to probe the reliability and the accuracy of this method: one obtains the bound-state parameters from sum rules and compares these results with the exact values calculated from the Schr\"odinger equation. We investigate various possibilities to fix the crucial ingredient of the method of sum rules---the effective continuum threshold---and propose modifications which lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method. Although the rigorous control of systematic uncertainties in the method of sum rules remains unfeasible, the application of the proposed procedures in QCD promises a considerable increase of the actual accuracy of the extracted hadron parameters.

Dynamical properties of dipolar Fermi gases

In this paper, we investigate the dynamical properties of a one-component Fermi gas with dipole–dipole interaction between particles. Using a variational function based on the Thomas–Fermi density distribution in phase space representation, the total energy is described as a function of deformation parameters in both real and momentum spaces. Various thermodynamic quantities of a uniform dipolar Fermi gas are derived, and then instability of this system is discussed. For a trapped dipolar Fermi gas, the collective oscillation frequencies are derived with the energy-weighted sum rule method. The frequencies for the monopole, quadrupole, radial and axial modes are calculated, and softening against collapse is shown as the dipolar strength approaches the critical value. Finally, we investigate the expansion dynamics of the Fermi gas and show how the dipolar interaction manifests itself in the shape of an expanded cloud.

Distribution amplitudes of Σ and Λ and their electromagnetic form factors

Based on QCD conformal partial wave expansion to leading order conformal spin accuracy, we present the light-cone distribution amplitudes (DAs) of Σ and Λ baryons up to twist 6. It is concluded that fourteen independent DAs are needed to describe the valence three-quark states of the baryons at small transverse separations. The nonperturbative parameters relevant to the DAs are determined within the framework of QCD sum rule method. With the obtained DAs, a simple investigation on the electromagnetic form factors of these baryons are given. The magnetic moments of the baryons are estimated by fitting the magnetic form factor with the dipole formula.

Accuracy of bound-state form factors extracted from dispersive sum rules

We discuss the extraction of form factors from three-point sum rules making use of a harmonic-oscillator model, where we derive the exact expression for the relevant correlator. We determine the form factor of the ground state by the standard procedures adopted in the method of sum rules, and compare the obtained results with the known exact values. We show that the uncontrollable uncertainty in the extracted value of the form factor is typically much larger than that for the decay constant. In the example considered, we find the uncontrolled systematic error in the extracted form factor to exceed the 10% level.

Hadron form factors from sum rules for vacuum-to-hadron correlators

We analyse the extraction of the bound-state form factor from vacuum-to-hadron correlator, which is the basic object for the calculation of hadron form factors in the method of light-cone sum rules in QCD. We study this correlator in quantum mechanics, calculate it exactly, and derive the corresponding OPE. We then apply the standard procedures of QCD sum rules to isolate the ground-state form factor from this correlator. We demonstrate that fixing the effective continuum threshold, one of the key ingredients of the sum-rule calculation of bound-state parameters, poses a serious problem for sum rules based on vacuum-to-hadron correlators.

QCD sum rules study of meson-baryon sigma terms

The pion-baryon sigma terms and the strange-quark condensates of the octet and the decuplet baryons are calculated by employing the method of QCD sum rules. We evaluate the vacuum-to-vacuum transition matrix elements of two baryon interpolating fields in an external isoscalar-scalar field and use a Monte Carlo-based approach to systematically analyze the sum rules and the uncertainties in the results. We extract the ratios of the sigma terms, which have rather high accuracy and minimal dependence on QCD parameters. We discuss the sources of uncertainties and comment on possible strangeness content of the nucleon and the Delta.

Mass and magnetic moments of the heavy flavored baryons with [formula omitted] in light cone QCD sum rules

Inspired by the results of recent experimental discoveries for charm and bottom baryons, the masses and magnetic moments of the heavy baryons with J P = 3 / 2 + containing a single heavy quark are studied within light cone QCD sum rules method. Our results on the masses of heavy baryons are in good agreement with predictions of other approaches, as well as with the existing experimental values. Our predictions on the masses of the states, which are not yet discovered in the experiments, can be tested in the future experiments. A comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is presented.

Parity-violating nuclear force as derived from QCD sum rules

Parity-violating nuclear force, as may be accessed from parity-violation studies in nuclear systems, represents an area of nonleptonic weak interactions that has been the subject of experimental investigations for several decades. In the simple meson-exchange picture, a parity-violating nuclear force may be parametrized as arising from the exchange of $\ensuremath{\pi},\ensuremath{\rho},\ensuremath{\omega}$, or other mesons with strong meson-nucleon coupling at one vertex and weak parity-violating meson-nucleon coupling at the other vertex. The QCD sum rule method allows for a fairly complicated, but nevertheless straightforward, leading-order loop-contribution determination of the various parity-violating $\mathrm{MNN}$ couplings starting from QCD (with the nontrivial vacuum) and Glashow-Salam-Weinberg electroweak theory. We continue our earlier investigation of the parity-violating $\ensuremath{\pi}\mathit{NN}$ coupling (by Henley, Hwang, and Kisslinger) to other parity-violating couplings. Our predictions are in reasonable overall agreement with the results estimated on phenomenological grounds, such as in the now classic paper of Desplanques, Donoghue, and Holstein, in the global experimental fit of Adelberger and Haxton, or the effective field theory thinking of Ramsey-Musolf and Page.

Study of systematic errors of bound-state parameters in SVZ sum rules

We study systematic errors of the ground-state parameters obtained from Shifman—Vainshtein—Zakharov sum rules, making use of the harmonic-oscillator potential model as an example. In this case, one knows the exact solution for the polarization operator, which allows one to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We determine the parameters of the ground state making use of the standard procedures of the method of sum rules and compare the obtained results with the known exact values. We show that, in the situation when the continuum contribution to the polarization operator is not known and is modeled by an effective continuum, the method of sum rules does not allow one to control the systematic uncertainties of the extracted ground-state parameters.

Octet baryon magnetic moments from QCD sum rules

A comprehensive study is made for the magnetic moments of octet baryons in the method of QCD sum rules. A complete set of QCD sum rules is derived using the external-field method and generalized interpolating fields. For each member, three sum rules are constructed from three independent tensor structures. They are analyzed in conjunction with the corresponding mass sum rules. The performance of each of the sum rules is examined using the criteria of operator product expansion convergence and ground-state dominance, along with the role of the transitions in intermediate states. Individual contributions from the $u$, $d$, and $s$ quarks are isolated and their implications in the underlying dynamics are explored. Valid sum rules are identified and their predictions are obtained. The results are compared with experiment and previous calculations.

Magnetic moments of heavyΞQbaryons in light cone QCD sum rules

The magnetic moments of heavy ${\ensuremath{\Xi}}_{Q}$ baryons containing a single charm or bottom quark are calculated in the framework of the light cone QCD sum rules method. A comparison of our results with the predictions of other approaches, such as relativistic and nonrelativistic quark models, the hypercentral model, chiral perturbation theory, and soliton and skyrmion models, is presented.

Pion distribution amplitude from holographic QCD and the electromagnetic form factorFπ(Q2)

The holographic QCD prediction for the pion distribution amplitude (DA) ${\ensuremath{\varphi}}_{\mathrm{hol}}(u)$ is used to compute the pion spacelike electromagnetic form factor ${F}_{\ensuremath{\pi}}({Q}^{2})$ within the QCD light-cone sum rule method. In calculations the pion's renormalon-based model twist-4 DA, as well as the asymptotic twist-4 DA are employed. Obtained theoretical predictions are compared with experimental data and with results of the holographic QCD.