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Silvano Simula

Publications and source records attributed to Silvano Simula.

At least 109 records · Page 6Linked to original sources
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↗
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

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

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

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↗
arXiv2007

Systematic errors of bound-state parameters extracted by means of SVZ sum rules

This talk presents the results of our study of systematic errors of the ground-state parameters obtained by Shifman-Vainshtein-Zakharov (SVZ) sum rules. We use the harmonic-oscillator potential model as an example: in this case we know the exact solution for the polarization operator, which allows us to obtain both the OPE to any order and the parameters (masses and decay constants) of the bound states. We extract the parameters of the ground state by making use of the standard procedures of the method of QCD sum rules, and compare the obtained results with their known exact values. We show that if the continuum contribution to the polarization operator is not known and is modelled by some effective continuum threshold, the standard procedures adopted in sum rules do not allow one to gain control over the systematic errors of the extracted ground-state parameters.

hep-ph↗
arXiv2007

Systematic errors of transition form factors extracted by means of light-cone sum rules

This talk presents results of our study of heavy-to-light transition form factors extracted with the help of light-cone sum rules. We employ a model with scalar particles interacting via massless-boson exchange and study the heavy-to-light correlator, relevant for the extraction of the transition form factor. We calculate this correlator in two different ways: by making use of the Bethe-Salpeter wave function of the light bound state and by making use of the light-cone expansion. This allows us to calculate the full correlator and separately the light-cone contribution to it. In this way we show that the off-light cone contributions are not suppressed compared to the light-cone one by any large parameter. Numerically, the difference between the value of the form factor extracted from the full correlator and from the light-cone contribution to this correlator is found to be about 20-30% in a wide range of masses of the particles involved in the decay process.

hep-ph↗
arXiv2007

Can one control systematic errors of QCD sum rule predictions for bound states?

We study the possibility to control systematic errors of the ground-state parameters obtained by Shifman-Vainshtein-Zakharov (SVZ) 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 QCD 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 modelled by an effective continuum, the method of sum rules does not allow to control the systematic errors of the extracted ground-state parameters.

hep-ph↗
arXiv2007

Light quark masses and pseudoscalar decay constants from Nf=2 twisted mass QCD

We present the results of the lattice QCD calculation of the average up-down and strange quark masses and of the light meson pseudoscalar decay constants, recently performed with Nf=2 dynamical fermions by the ETM Collaboration. The simulation is carried out at a single value of the lattice spacing with the twisted mass fermionic action at maximal twist, which guarantees automatic O(a)-improvement of the physical quantities. Quark masses are renormalized by implementing the non perturbative RI-MOM renormalization procedure. Our results for the light quark masses are m_{ud}^{MSbar}(2 Gev)=3.85 +- 0.12 +- 0.40 MeV, m_s^{MSbar}(2 Gev)=105 +- 3 +- 9 MeV and m_s/m_{ud}=27.3 +- 0.3 +- 1.2. We also obtain f_K=161.7 +- 1.2 +- 3.1 MeV and the ratio f_K/f_pi=1.227 +- 0.009 +- 0.024. From this ratio, by using the experimental determination of Gamma(K -> mu {bar nu}_mu (gamma))/Gamma(pi -> mu {bar nu}_mu (gamma)) and the average value of |V_{ud}| from nuclear beta decays, we obtain |V_{us}|=0.2192(5)(45), in agreement with the determination from K_{l3} decays and the unitarity constraint.

hep-lat↗
arXiv2007

Systematic errors of bound-state parameters obtained with SVZ sum rules

We study systematic errors of the ground-state parameters obtained by Shifman-Vainshtein-Zakharov (SVZ) 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 modelled by an effective continuum, the method of sum rules does not allow to control the systematic uncertainties of the extracted ground-state parameters.

hep-ph↗
arXiv2007

Systematic uncertainties of hadron parameters obtained with QCD sum rules

We study the uncertainties of the determination of the ground-state parameters from Shifman-Vainshtein-Zakharov (SVZ) 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 $Π(μ)$, which allows one to obtain both the OPE to any order and the spectrum of states. We start with the OPE for $Π(μ)$ and analyze the extraction of the square of the ground-state wave function, $R\propto|Ψ_0(\vec r=0)|^2$, from an SVZ sum rule, setting the mass of the ground state $E_0$ equal to its known value and treating the effective continuum threshold as a fit parameter. We show that in a limited ``fiducial'' range of the Borel parameter there exists a solution for the effective threshold which precisely reproduces the exact $Π(μ)$ for any value of $R$ within the range $0.7 \le R/R_0 \le 1.15$ ($R_0$ is the known exact value). Thus, the value of $R$ extracted from the sum rule is determined to a great extent by the contribution of the hadron continuum. Our main finding is that in the cases where the hadron continuum is not known and is modeled by an effective continuum threshold, the systematic uncertainties of the sum-rule procedure cannot be controlled.

hep-ph↗
arXiv2007

Heavy-to-light form factors: sum rules on the light cone and beyond

We report the first systematic analysis of the off-light-cone effects in sum rules for heavy-to-light form factors. These effects are investigated in a model based on scalar constituents, which allows a technically rather simple analysis but has the essential features of the analogous QCD calculation. The correlator relevant for the extraction of the heavy-to-light form factor is calculated in two different ways: first, by adopting the full Bethe-Salpeter amplitude of the light meson and, second, by performing the expansion of this amplitude near the light cone $x^2=0$. We demonstrate that the contributions to the correlator from the light-cone term $x^2=0$ and the off-light-cone terms $x^2\ne 0$ have the same order in the $1/m_Q$ expansion. The light-cone correlator, corresponding to $x^2=0$, is shown to systematically overestimate the full correlator, the difference being $\sim Λ_{\rm QCD}/δ$, with $δ$ the continuum subtraction parameter of order 1 GeV. Numerically, this difference is found to be 10-20%.

hep-ph↗
arXiv2006

Dispersion representations and anomalous singularities of the triangle diagram

We discuss dispersion representations for the triangle diagram $F(p_1^2,p_2^2,q^2)$, the single dispersion representation in $q^2$ and the double dispersion representation in $p_1^2$ and $p_2^2$, with special emphasis on the appearance of the anomalous singularities and the anomalous cuts in these representations. For the double dispersion representation in $p_1^2$ and $p_2^2$, the appearance of the anomalous cut in the region $q^2>0$ is demonstrated, and a new derivation of the anomalous double spectral density is given. We point out that the double spectral representation is particularly suitable for applications in the region of $p_1^2$ and/or $p_2^2$ above the two-particle thresholds. The dispersion representations for the triangle diagram in the nonrelativistic limit are studied and compared with the triangle diagram of the nonrelativistic field theory.

hep-ph↗
arXiv2006

Chiral properties of the constituent quark model

We show that, in a model based exclusively on constituent-quark degrees of freedom interacting via a potential, the full axial current is conserved if the spectrum of \bar QQ states contains a massless pseudoscalar. The current conservation emerges nonperturbatively if the model satisfies certain constraints on (i) the axial coupling g_A of the constituent quark and (ii) the \bar QQ potential at large distances. We define the chiral point of the constituent quark model as that set of values of the parameters (such as the masses of the constituent quarks and the couplings in the \bar QQ potential) for which the mass of the lowest pseudoscalar \bar QQ bound state vanishes. At the chiral point the main signatures of the spontaneously broken chiral symmetry are shown to be present, namely: the axial current is conserved, the decay constants of the excited pseudoscalar bound states vanish, and the pion decay constant has a nonzero value.

hep-ph↗