arXiv subjects

K. Schilcher

Publications and source records attributed to K. Schilcher.

At least 37 records · Page 2Linked to original sources

arXiv2011

Hadronic contribution to the muon g-2: a theoretical determination

The leading order hadronic contribution to the muon g-2, $a_μ^{HAD}$, is determined entirely from theory using an approach based on Cauchy's theorem in the complex squared energy s-plane. This is possible after fitting the integration kernel in $a_μ^{HAD}$ with a simpler function of $s$. The integral determining $a_μ^{HAD}$ in the light-quark region is then split into a low energy and a high energy part, the latter given by perturbative QCD (PQCD). The low energy integral involving the fit function to the integration kernel is determined by derivatives of the vector correlator at the origin, plus a contour integral around a circle calculable in PQCD. These derivatives are calculated using hadronic models in the light-quark sector. A similar procedure is used in the heavy-quark sector, except that now everything is calculable in PQCD, thus becoming the first entirely theoretical calculation of this contribution. Using the dual resonance model realization of Large $N_{c}$ QCD to compute the derivatives of the correlator leads to agreement with the experimental value of $a_μ$. Accuracy, though, is currently limited by the model dependent calculation of derivatives of the vector correlator at the origin. Future improvements should come from more accurate chiral perturbation theory and/or lattice QCD information on these derivatives, allowing for this method to be used to determine $a_μ^{HAD}$ accurately entirely from theory, independently of any hadronic model.

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arXiv2011

QCD sum rule determination of the charm-quark mass

QCD sum rules involving mixed inverse moment integration kernels are used in order to determine the running charm-quark mass in the $\bar{MS}$ scheme. Both the high and the low energy expansion of the vector current correlator are involved in this determination. The optimal integration kernel turns out to be of the form $p(s) = 1 - (s_0/s)^2$, where $s_0$ is the onset of perturbative QCD. This kernel enhances the contribution of the well known narrow resonances, and reduces the impact of the data in the range $s \simeq 20 - 25 GeV^2$. This feature leads to a substantial reduction in the sensitivity of the results to changes in $s_0$, as well as to a much reduced impact of the experimental uncertainties in the higher resonance region. The value obtained for the charm-quark mass in the $\bar{MS}$ scheme at a scale of 3 GeV is $\bar{m}_c (3 GeV) = 987 \pm 9 MeV$, where the error includes all sources of uncertainties added in quadrature.

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arXiv2010

Charm-quark mass from weighted finite energy QCD sum rules

The running charm-quark mass in the $\bar{MS}$ scheme is determined from weighted finite energy QCD sum rules (FESR) involving the vector current correlator. Only the short distance expansion of this correlator is used, together with integration kernels (weights) involving positive powers of $s$, the squared energy. The optimal kernels are found to be a simple {\it pinched} kernel, and polynomials of the Legendre type. The former kernel reduces potential duality violations near the real axis in the complex s-plane, and the latter allows to extend the analysis to energy regions beyond the end point of the data. These kernels, together with the high energy expansion of the correlator, weigh the experimental and theoretical information differently from e.g. inverse moments FESR. Current, state of the art results for the vector correlator up to four-loop order in perturbative QCD are used in the FESR, together with the latest experimental data. The integration in the complex s-plane is performed using three different methods, fixed order perturbation theory (FOPT), contour improved perturbation theory (CIPT), and a fixed renormalization scale $μ$ (FMUPT). The final result is $\bar{m}_c (3\, {GeV}) = 1008\,\pm\, 26\, {MeV}$, in a wide region of stability against changes in the integration radius $s_0$ in the complex s-plane.

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arXiv2010

New Sum Rule Determination of the Nucleon Mass

A new QCD calculation of the mass of the nucleon is presented. It makes use of a polynomial kernel in the dispersion integrals tailored to practically eliminate the contribution of the unknown 1/2+ and 1/2- continuum. This approach avoids the arbitrariness and other drawbacks attached to the Borel kernel used in previous sum rules calculations. Our method yields stable results for the nucleon mass and coupling for standard values of the condensates. The prediction of the nucleon mass m_{N}=(0.945 \pm .045) GeV is in good agreement with experiment.

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arXiv2010

Chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner relation

The next to leading order chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner (GMOR) relation are obtained using the pseudoscalar correlator to five-loop order in perturbative QCD, together with new finite energy sum rules (FESR) incorporating polynomial, Legendre type, integration kernels. The purpose of these kernels is to suppress hadronic contributions in the region where they are least known. This reduces considerably the systematic uncertainties arising from the lack of direct experimental information on the hadronic resonance spectral function. Three different methods are used to compute the FESR contour integral in the complex energy (squared) s-plane, i.e. Fixed Order Perturbation Theory, Contour Improved Perturbation Theory, and a fixed renormalization scale scheme. We obtain for the corrections to the GMOR relation, $δ_π$, the value $δ_π= (6.2, \pm 1.6)%$. This result is substantially more accurate than previous determinations based on QCD sum rules; it is also more reliable as it is basically free of systematic uncertainties. It implies a light quark condensate $<0|\bar{u} u|0> \simeq <0|\bar{d} d|0> \equiv <0|\bar{q} q|0>|_{2\,\mathrm{GeV}} = (- 267 \pm 5 MeV)^3$. As a byproduct, the chiral perturbation theory (unphysical) low energy constant $H^r_2$ is predicted to be $H^r_2 (ν_χ= M_ρ) = - (5.1 \pm 1.8)\times 10^{-3}$, or $H^r_2 (ν_χ= M_η) = - (5.7 \pm 2.0)\times 10^{-3}$.

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arXiv2009

Confronting QCD with the experimental hadronic spectral functions from tau-decay

The (non-strange) vector and axial-vector spectral functions extracted from $τ$-decay by the ALEPH collaboration are confronted with QCD in the framework of a Finite Energy QCD sum rule (FESR) involving a polynomial kernel tuned to suppress the region beyond the kinematical end point where there is no longer data. This effectively allows for a QCD FESR analysis to be performed beyond the region of the existing data. Results show excellent agreement between data and perturbative QCD in the remarkably wide energy range $s = 3 - 10 {GeV}^2$, leaving room for a dimension $d$ =4 vacuum condensate consistent with values in the literature. A hypothetical dimension $d$=2 term in the Operator Product Expansion is found to be extremely small, consistent with zero. Fixed Order and Contour Improved perturbation theory are used, with both leading to similar results within errors. Full consistency is found between vector and axial-vector channel results.

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arXiv2008

Up and down quark masses from Finite Energy QCD sum rules to five loops

The up and down quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector divergences, to five loop order in Perturbative QCD (PQCD), and including leading non-perturbative QCD and higher order quark mass corrections. This FESR is designed to reduce considerably the systematic uncertainties arising from the (unmeasured) hadronic resonance sector, which in this framework contributes less than 3-4% to the quark mass. This is achieved by introducing an integration kernel in the form of a second degree polynomial, restricted to vanish at the peak of the two lowest lying resonances. The driving hadronic contribution is then the pion pole, with parameters well known from experiment. The determination is done in the framework of Contour Improved Perturbation Theory (CIPT), which exhibits a very good convergence, leading to a remarkably stable result in the unusually wide window $s_0 = 1.0 - 4.0 {GeV}^2$, where $s_0$ is the radius of the integration contour in the complex energy (squared) plane. The results are: $m_u(Q= 2 {GeV}) = 2.9 \pm 0.2 $ MeV, $m_d(Q= 2 {GeV}) = 5.3 \pm 0.4$ MeV, and $(m_u + m_d)/2 = 4.1 \pm 0.2$ Mev (at a scale Q=2 GeV).

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arXiv2008

Strange quark condensate from QCD sum rules to five loops

It is argued that it is valid to use QCD sum rules to determine the scalar and pseudoscalar two-point functions at zero momentum, which in turn determine the ratio of the strange to non-strange quark condensates $R_{su} = \frac{<\bar{s} s>}{<\bar{q} q>}$ with ($q=u,d$). This is done in the framework of a new set of QCD Finite Energy Sum Rules (FESR) that involve as integration kernel a second degree polynomial, tuned to reduce considerably the systematic uncertainties in the hadronic spectral functions. As a result, the parameters limiting the precision of this determination are $Λ_{QCD}$, and to a major extent the strange quark mass. From the positivity of $R_{su}$ there follows an upper bound on the latter: $\bar{m_{s}} (2 {GeV}) \leq 121 (105) {MeV}$, for $Λ_{QCD} = 330 (420) {MeV} .$

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arXiv2008

Determination of QCD condensates from tau-decay data

We have used the latest data from the ALEPH Collaboration to extract values for QCD condensates up to dimension d=12 in the V-A channel and up to dimension d=8 in the V, A and V+A channels. Performing 2- and 3-parameter fits, we obtain new results for the correlations of condensates. The results are consistent among themselves and agree with most of the previous results found in the literature.

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arXiv2007

QCD vacuum condensates from tau-lepton decay data

The QCD vacuum condensates in the Operator Product Expansion are extracted from the final ALEPH data on vector and axial-vector spectral functions from $τ$-decay. Weighted Finite Energy Sum Rules are employed in the framework of both Fixed Order and Contour Improved Perturbation Theory. An overall consistent picture satisfying chirality constraints can be achieved only for values of the QCD scale below some critical value $Λ\simeq350 {MeV}$. For larger values of $Λ$, perturbation theory overwhelms the power corrections. A strong correlation is then found between $Λ$ and the resulting values of the condensates. Reasonable accuracy is obtained up to dimension $d=8$, beyond which no meaningful extraction is possible.

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arXiv2006

QCD condensates of dimension D=6 and D=8 from hadronic tau-decays

The high-precision data from hadronic tau decays allows one to extract information on QCD condensates. Using the finalized ALEPH data, we obtain a more rigorous determination of the dimension 6 and 8 condensates for the V-A correlator. In particular, we find that the recent data fix a certain linear combination of these QCD condensates to a precision at the level of O(2%). Our approach relies on more general assumptions than alternative approaches based on finite energy sum rules.

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arXiv2005

D and D_{S} decay constants from QCD duality at three loops

We compute the decay constants of the pseudoscalar mesons D and D_{s} using a linear combination of finite energy sum rules which minimize the contribution of the unknown continuum spectral function. We employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running charm quark mass. The theoretical uncertainties arising from the QCD asymptotic expansion are quite relevant in this case due to the relative small scale of the charm mass. We obtain the following results: f_{D}=177 \pm 21 MeV and f_{D_{s}}=205 \pm 22 MeV. These results, within the error bars, are in good agreement with estimates obtained using Borel transform QCD sum rules, but somewhat smaller than results of recent lattice computations.

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arXiv2005

B and B_s decay constants from QCD Duality at three loops

Using special linear combinations of finite energy sum rules which minimize the contribution of the unknown continuum spectral function, we compute the decay constants of the pseudoscalar mesons B and B_s. In the computation, we employ the recent three loop calculation of the pseudoscalar two-point function expanded in powers of the running bottom quark mass. The sum rules show remarkable stability over a wide range of the upper limit of the finite energy integration. We obtain the following results for the pseudoscalar decay constants: f_B=178 \pm 14 MeV and f_{B_s}=200 \pm 14 MeV. The results are somewhat lower than recent predictions based on Borel transform, lattice computations or HQET. Our sum rule approach of exploiting QCD quark hadron duality differs significantly from the usual ones, and we believe that the errors due to theoretical uncertainties are smaller.

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arXiv2004

QCD condensates from tau-decay data: A functional approach

We study a functional method to extract the V-A condensate of dimension 6 from a comparison of tau-decay data with the asymptotic space-like QCD prediction. Our result is in agreement within errors with that from conventional analyses based on finite energy sum rules.

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arXiv2003

Finite energy chiral sum rules in QCD

The saturation of QCD chiral sum rules of the Weinberg-type is analyzed using ALEPH and OPAL experimental data on the difference between vector and axial-vector correlators (V-A). The sum rules exhibit poor saturation up to current energies below the tau-lepton mass. A remarkable improvement is achieved by introducing integral kernels that vanish at the upper limit of integration. The method is used to determine the value of the finite remainder of the (V-A) correlator, and its first derivative, at zero momentum: $\barΠ(0) = - 4 \bar{L}_{10} = 0.0257 \pm 0.0003 ,$ and $\barΠ^{\prime}(0) = 0.065 \pm 0.007 {GeV}^{-2}$. The dimension $d=6$ and $d=8$ vacuum condensates in the Operator Product Expansion are also determined: $<{\cal {O}}_{6}> = -(0.004 \pm 0.001) {GeV}^6,$ and $<{\cal {O}}_{8}> = -(0.001 \pm 0.006) {GeV}^8.$

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arXiv2003

Bottom quark mass and QCD duality

The mass of the bottom quark is analyzed in the context of QCD finite energy sum rules. In contrast to the conventional approach, we use a large momentum expansion of the QCD correlator including terms to order α_{s}^{2}(m_{b}^{2}/q^{2})^{6} with the upsilon resonances from e^{+}e^{-} annihilation data as main input. A stable result m_{b}(m_{b})=4.19\pm 0.05 GeV} for the bottom quark mass is obtained. This result agrees with the independent calculations based on the inverse moment analysis.

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arXiv2002

Charged pion pair production by two photons from a chiral sum rule

The cross-section for a charged pion pair production by two photons is evaluated by using the low energy expression previously obtained from current algebra and PCAC which involves an integral over a vector and axial-vector spectral functions. Data on the latter obtained from tau-decay as measured by the ALEPH collaboration is then inserted in the integral which is appropriately modified in order to eliminate contributions near the cut in the duality contour integral. The experimental behavior of the cross-section for gamma-gamma into pi (+)-pi(-) is well reproduced at low energies.

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arXiv2002

K_l3 form factors at order p^6 in chiral perturbation theory

This paper describes the calculation of the semileptonic K_l3 decay form factor at order p^6 of chiral perturbation theory which is the next-to-leading order correction to the well-known p^4 result achieved by Gasser and Leutwyler. At order p^6 the chiral expansion contains 1- and 2-loop diagrams which are discussed in detail. The irreducible 2-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian L^6 produces direct couplings with the W-bosons. Due to these unknown couplings, one can always add linear terms in q^2 to the predictions of the form factor f_-(q^2). For the form factor f_+(q^2), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q^4 counter term, the q^4-ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q^2 our calculation shows that chiral perturbation theory converges very well in this application, as the O(p^6) corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f_+(q^2) is well described by a linear fit, but that the slope lambda_+ is smaller by about 2 standard deviations than the O(p^4) prediction. The unavoidable q^2 counter term of the O(p^6) corrections allows to bring the predictions of chiral perturbation theory into perfect agreement with experiment.

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