arXiv subjects

Wolfgang Lucha

Publications and source records attributed to Wolfgang Lucha.

At least 127 records · Page 7Linked to original sources

arXiv2010

Decay constants of heavy pseudoscalar mesons from QCD sum rules

We revisit the sum-rule extraction of the decay constants of the D, Ds, B, and Bs mesons from the two-point correlator of heavy-light pseudoscalar currents. We use the operator product expansion for this correlator expressed in terms of the MSbar heavy-quark mass, for which the perturbative expansion exhibits a reasonable convergence. Our main emphasis is laid on the control over the uncertainties in the decay constants, related both to the input QCD parameters and to the limited accuracy of the method of sum-rules. This becomes possible due to the application of our procedure of extracting hadron observables that involves as novel feature dual thresholds depending on the Borel parameter. For charmed mesons, we find the decay constants f_D=206.2\pm 7.3(OPE)\pm 5.1(syst) MeV and f_Ds=245.3\pm 15.7(OPE)\pm 4.5(syst) MeV. For beauty mesons, the decay constants turn out to be extremely sensitive to the precise value of mb(mb). By requiring our sum-rule estimate to match the average of the lattice results for f_B, a very accurate value mb(mb)=4.245\pm 0.025 GeV is extracted, leading to f_B=193.4\pm 12.3(OPE)\pm 4.3(syst) MeV and f_Bs=232.5\pm 18.6(OPE)\pm 2.4(syst) MeV.

hep-ph↗

arXiv2010

Bethe-Salpeter Equations with Instantaneous Confinement: Establishing Stability of Bound States

Salpeter equations with potential functions rising to infinity in configuration space do not automatically predict stable bound states. For this to happen, also the Lorentz behaviour of the involved Bethe-Salpeter kernels is crucial. At least for interaction potentials of harmonic-oscillator form analytic scrutinies of Salpeter equations with confining interactions may identify those Bethe-Salpeter kernels which describe bound states free from the notorious instabilities encountered in numerical evaluations. Such truly confining kernels can be singled out systematically by requesting the resulting bound-state energy spectra to be both real and discrete.

hep-ph↗

arXiv2010

Effective Continuum Thresholds for Quark-Hadron Duality in Dispersive Sum Rules

Modifying the standard approaches to nonperturbative QCD based on Borel-transformed dispersive sum rules by allowing the effective continuum thresholds required for the implementation of quark-hadron duality to depend on the Borel parameters and on any relevant momentum promises to provide higher accuracy and reliable error estimates for the extracted predictions of hadron characteristics. A careful analysis reveals that the exact effective continuum thresholds do indeed exhibit dependence on the Borel parameter (and on external momenta) and that they are not universal but vary with the correlators under consideration. The striking similarity of our hadron-parameter extraction procedures in QCD, on the one hand, and quantum-theoretical potential models, on the other hand, calls for application of the proposed techniques in QCD.

hep-ph↗

arXiv2010

Extraction of bound-state parameters from dispersive sum rules

The procedure of extracting the ground-state parameters from vacuum-to-vacuum and vacuum-to-hadron correlators within the method of sum rules is considered. The emphasis is laid on the crucial ingredient of this method - the effective continuum threshold. A new algorithm to fix this quantity is proposed and tested. First, a quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of the sum-rule method is used as a study case. In this model, our algorithm is shown to lead to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. As a next step, it is demonstrated that the procedures of extracting the ground-state decay constant in the potential model and in QCD are quantitatively very close to each other. Therefore, the application of the proposed algorithm in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.

hep-ph↗

arXiv2010

Klein-Gordon lower bound to the semirelativistic ground-state energy

For the class of attractive potentials V(r) <= 0 which vanish at infinity, we prove that the ground-state energy E of the semirelativistic Hamiltonian H = \sqrt{m^2 + p^2} + V(r) is bounded below by the ground-state energy e of the corresponding Klein--Gordon problem (p^2 + m^2)ϕ= (V(r) -e)^2ϕ. Detailed results are presented for the exponential and Woods--Saxon potentials.

math-ph↗

arXiv2009

Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models

We compare the extraction of the ground-state decay constant from the two-point correlator in QCD and in potential models and show that the results obtained at each step of the extraction procedure follow a very similar pattern. We prove that allowing for a Borel-parameter-dependent effective continuum threshold yields two essential improvements compared to employing a Borel-parameter-independent quantity: (i) It reduces considerably the (unphysical) dependence of the extracted bound-state mass and the decay constant on the Borel parameter. (ii) In a potential model, where the actual value of the decay constant is known from the Schroedinger equation, a Borel-parameter-dependent threshold leads to an improvement of the accuracy of the extraction procedure. Our findings suggest that in QCD a Borel-parameter dependent threshold leads to a more reliable and accurate determination of bound-state characteristics by the method of sum rules.

hep-ph↗

arXiv2009

Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators

We study the extraction of the ground-state parameters from vacuum-to-vacuum correlators. We work in quantum-mechanical potential model which provides the only possibility to probe the reliability and the actual accuracy of this method: one obtains the bound-state parameters from the correlators by the standard procedures adopted in the method of sum rules and compares these results with the exact values calculated from the Schroedinger equation. We focus on the crucial ingredient of the method of sum rules - the effective continuum threshold - and propose a new algorithm to fix this quantity. In a quantum-mechanical model, our procedure leads to a remarkable improvement of the accuracy of the extracted ground-state parameters compared to the standard procedures adopted in the method and used in all previous applications of dispersive sum rules in QCD. The application of the proposed procedure in QCD promises a considerable increase of the accuracy of the extracted hadron parameters.

hep-ph↗

arXiv2009

Effective continuum threshold for vacuum-to-bound-state correlators

We formulate a new algorithm for obtaining the effective continuum threshold in vacuum-to-bound-state correlators - the basic objects for the calculation of hadron form factors in the method of light-cone sum rules in QCD. The effective continuum threshold is one of the key ingredients of the method which to a large extent determines the value of the form factor extracted from the relevant correlator. In a quantum-mechanical potential model, where the exact form factor is known, the application of our algorithm is shown to lead to a dramatic increase of the accuracy of the extracted form factor compared to the standard procedures adopted in the method of sum rules in QCD. Moreover, the application of our algorithm considerably enlarges the range of the momentum transfer where the form factor may be extracted from the correlator.

hep-ph↗

arXiv2009

Semirelativistic N-boson systems bound by attractive pair potentials

We establish bounds on the energy of a system of N identical bosons bound by attractive pair potentials and obeying the semirelativistic Salpeter equation. The lower bound is provided by a `reduction', with the aid of Jacobi relative coordinates, to a suitably scaled one-body Klein-Gordon problem. Complementary upper energy bounds are provided by means of a Gaussian trial function. Detailed results are presented for the exponential pair potential V(r) = -v\exp(-r/a).

math-ph↗

arXiv2009

The 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 Schrödinger 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.

hep-ph↗

arXiv2008

Pion form factor from local-duality QCD sum rule

We present our recent results for the pion elastic form factor [1] obtained within a local-duality three-point sum rule (a Borel sum rule in the limit of an infinite Borel parameter). Our analysis includes the O(1) and O(α_s) contributions and is therefore applicable in a broad range of spacelike momentum transfers. Our results demonstrate in essentially model-independent way that the O(1) term, which provides the subleading 1/Q^4 power correction at asymptotically large momentum transfers, contributes more than half of the pion form factor in the region Q^2 \le 20 GeV^2. To probe the accuracy of local-duality sum rules for form factors, we apply precisely the same procedures to extract the form factor in a quantum-mechanical potential model. Comparison of the exact form factor known in this model with the result of the sum-rule calculation gives a probe of the systematic error of the method. In our example this error is found to be at the level of 10-20%. We expect similar systematic errors for form factors obtained from local-duality sum rules in QCD.

hep-ph↗

arXiv2008

How reliable are bound-state parameters obtained from QCD sum rules?

We discuss the extraction of ground-state parameters, such as decay constants and form factors, from two- and three-point dispersive sum rules, making use of a quantum-mechanical potential model. This model provides a unique possibility to probe the reliability and the accuracy of the method of sum rules: one obtains the bound-state parameters by the standard procedures adopted in sum rules, and compares these results with the exact values, known in the potential model. We demonstrate the presence of uncontrollable uncertainties in the ground-state parameters obtained from sum rules and estimate their magnitude. The uncontrolled uncertainties in ground-state form factors are shown to be typically much larger than those in the decay constants. In the example presented, the uncontrolled systematic error in the extracted form factor is found to exceed the 10% level.

hep-ph↗

arXiv2008

Extracting Hadron Parameters from Dispersive Sum Rules

Puzzled or surprised by the almost incredible accuracy occasionally claimed in the literature to be achievable for numerical outcomes of QCD sum-rule analyses, we scrutinized the usual procedure employed for the extraction of the parameters of individual bound states from dispersive sum rules by taking advantage of the exact solvability of a quantum-mechanical harmonic-oscillator model: It turns out that the determination of the ground-state parameters (that is, decay constant and form factor) by requiring independence from the Borel mass in its stability window does not necessarily yield their exact numerical values. For instance, the comparison of the sum-rule predictions for bound-state parameters with their numerical values known precisely in our harmonic-oscillator model reveals that standard sum-rule procedures underestimate the ground-state decay constant by some 4% and its form factor by almost 15%; such systematic uncertainties cannot be inferred from our correlators' accuracy better than 1% in the window of Borel stability: they are uncontrollable.

hep-ph↗

arXiv2008

Full Salpeter Equation with Confining Interactions: Analytic Stability Proof

The most popular 3-dimensional reduction of the Bethe-Salpeter formalism for the description of bound states within quantum field theory is the Salpeter equation, found as the instantaneous limit of the Bethe-Salpeter framework if allowing, in addition, for free propagation of the bound-state constituents. Unfortunately, depending on the Lorentz nature of the Bethe-Salpeter kernel, supposedly stable results of Salpeter's equation with confining interactions exhibit (un-)expected instabilities, probably related to Klein's paradox. Clearly, bound states may be regarded as stable if, for appropriate interactions, their mass eigenvalues belong to a real and discrete (part of the) spectrum that is bounded from below. Some general features of the eigenvalue spectra of any Salpeter equation are well-established: all bound-state masses squared are real and, for a large class of sufficiently reasonable Bethe-Salpeter kernels - which includes all interactions of phenomenological relevance for QCD -, the spectrum of mass eigenvalues consists, in the complex bound-state mass plane, at most of real pairs of opposite sign and imaginary points. For time-component vector harmonic-oscillator kernels, a straightforward stability proof is given.

hep-ph↗

arXiv2008

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 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.

hep-ph↗

arXiv2008

Light-cone expansion of heavy-to-light form factors

We present the results of our recent systematic study of the light-cone expansion of heavy-to-light transition form factors in a model with scalar constituents [1]. We show that the higher-twist contributions (represented in this model by off-light-cone effects) all have the same behaviour in the 1/m_Q expansion. The suppression parameter of the higher-twist contributions compared to the lower-twist contributions is, in general, the inverse Borel parameter β. The only exception here is the case of the leading and the subleading twists: they are of the same order in 1/βbecause of an extra suppression of the leading-twist contribution to the form factor.

hep-ph↗

arXiv2008

Semirelativistic stability of N-boson systems bound by 1/r pair potentials

We analyze a system of self-gravitating identical bosons by means of a semirelativistic Hamiltonian comprising the relativistic kinetic energies of the involved particles and added (instantaneous) Newtonian gravitational pair potentials. With the help of an improved lower bound to the bottom of the spectrum of this Hamiltonian, we are able to enlarge the known region for relativistic stability for such boson systems against gravitational collapse and to sharpen the predictions for their maximum stable mass.

hep-th↗

arXiv2008

Pion form factor at spacelike momentum transfers from local-duality QCD sum rule

We study the pion form factor in a broad range of spacelike momentum transfers within the local-duality version of QCD sum rules. We make use of the recently calculated two-loop double spectral density of the $ $ correlator including O(1) and $O(α_s)$ terms, which allows us to give predictions for the pion form factor and to study the interplay between the nonperturbative and perturbative contributions to the pion form factor without any reference to the pion distribution amplitude. Our results demonstrate the dominance of the nonperturbative contribution to the form factor up to relatively large values of the momentum transfer: namely, the nonperturbative O(1) term, which provides the $1/Q^4$ power correction, gives more than half of the pion form factor in the region $Q^2 \le 20$ GeV$^2$.

hep-ph↗