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K. Schilcher

Publications and source records attributed to K. Schilcher.

At least 19 recordsLinked to original sources
arXiv2024

Estimating the strong coupling from $τ$ decay using accelerating series convergence

We apply the Euler transformation to accelerate the convergence of the QCD perturbative series with the aim to determine the strong coupling $α_s$ in terms of the total $τ$-decay rate $r_τ$. The variation of the result with the order of the QCD perturbation theory is small and comparable with the uncertainties of $r_τ$. We also present an estimate of a range of the yet unknown 5th and 6th order coefficients $k_5$ and $k_6$ of the Adler function.

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arXiv2018

Up- and down-quark masses from QCD sum rules

The QCD up- and down-quark masses are determined from an optimized QCD Finite Energy Sum Rule (FESR) involving the correlator of axial-vector current divergences. In the QCD sector this correlator is known to five loop order in perturbative QCD (PQCD), together with non-perturbative corrections from the quark and gluon condensates. This FESR is designed to reduce considerably the systematic uncertainties arising from the hadronic spectral function. The determination is done in the framework of both fixed order and contour improved perturbation theory. Results from the latter, involving far less systematic uncertainties, are: $\bar{m}_u (2\, \mbox{GeV}) = (2.6 \, \pm \, 0.4) \, {\mbox{MeV}}$, $\bar{m}_d (2\, \mbox{GeV}) = (5.3 \, \pm \, 0.4) \, {\mbox{MeV}}$, and the sum $\bar{m}_{ud} \equiv (\bar{m}_u \, + \, \bar{m}_d)/2$, is $\bar{m}_{ud}({ 2 \,\mbox{GeV}}) =( 3.9 \, \pm \, 0.3 \,) {\mbox{MeV}}$.

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arXiv2018

Non-Abelian quantum field theory of pionic strong interactions

A renormalizable non-Abelian theory of strong interactions of pions, mediated by rho-mesons, is formulated at tree- and at one-loop level in perturbation theory. Hadron masses are generated through spontaneous symmetry breaking using the Higgs mechanism. Quantization and gauge fixing is achieved using the generalized class of $R_ξ$ gauges. As an application of this theory, pion-pion scattering lengths are obtained at tree-level in good agreement with data.

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arXiv2017

Anomalous magnetic moment of the muon, a hybrid approach

A new QCD sum rule determination of the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon, $a_μ^{\rm hvp}$, is proposed. This approach combines data on $e^{+}e^{-}$ annihilation into hadrons, perturbative QCD and lattice QCD results for the first derivative of the electromagnetic current correlator at zero momentum transfer, $Π_{\rm EM}^\prime(0)$. The idea is based on the observation that, in the relevant kinematic domain, the integration kernel $K(s)$, entering the formula relating $a_μ^{\rm hvp}$ to $e^{+}e^{-}$ annihilation data, behaves like $1/s$ times a very smooth function of $s$, the squared energy. We find an expression for $a_μ$ in terms of $Π_{\rm EM}^\prime(0)$, which can be calculated in lattice QCD. Using recent lattice results we find a good approximation for $a_μ^{\rm hvp}$, but the precision is not yet sufficient to resolve the discrepancy between the $R(s)$ data-based results and the experimentally measured value.

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arXiv2017

QCD determination of the leading order hadronic contribution to the muon g-2

The leading order hadronic contribution to the muon magnetic moment anomaly, $a^{HAD}_μ$, is determined entirely in the framework of QCD. The result in the light-quark sector, in units of $10^{-10}$, is $a^{HAD}_μ|_{uds} =686 \pm 26$, and in the heavy-quark sector $a^{HAD}_μ|_{c} =14.4 \pm 0.1$, and $a^{HAD}_μ|_{b} =0.29 \pm 0.01$, resulting in $a^{HAD}_μ= 701 \pm 26$. The main uncertainty is due to the current lattice QCD value of the first and second derivative of the electromagnetic current correlator at the origin. Expected improvement in the precision of these derivatives may render this approach the most accurate and trustworthy determination of the leading order $a^{HAD}_μ$.

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arXiv2016

Tests of quark-hadron duality in tau-decays

An exhaustive number of QCD finite energy sum rules for $τ$-decay together with the latest updated ALEPH data is used to test the assumption of global duality. Typical checks are the absence of the dimension $d=2$ condensate, the equality of the gluon condensate extracted from vector or axial vector spectral functions, the Weinberg sum rules, the chiral condensates of dimensions $d=6$ and $d=8$, as well as the extraction of some low-energy parameters of chiral perturbation theory. Suitable pinched linear integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations and experimental errors. We find no compelling indications of duality violations in hadronic $τ$-decay in the kinematic region above $s\simeq2.2$ GeV$^{2}$ for these kernels.

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arXiv2016

Tau-decay hadronic spectral functions: probing quark-hadron duality

The vector and axial-vector ALEPH hadronic spectral functions from $τ$-decay are used to probe potential quark-hadron duality violations (DV). This is done in the framework of finite energy QCD sum rules (FESR). A pinched integration kernel is introduced in the FESR in order to (a) quench potential duality violations on the real axis in the complex squared energy $s$-plane, and (b) effectively extend the analysis well beyond the kinematical $τ$-decay end-point where there is no longer data, i.e.\ in the range $s = 3 - 10 \,{\mbox{GeV}}^2$. In the vector channel this procedure is supplemented with actual data from $e^+ e^-$-annihilation into hadrons, above the tau-decay kinematical end-point, with results fully supporting this extension. Very good agreement is obtained between data and two specific pinched FESR. Results from this analysis are confronted with those from a specific model of DV. As the sum rules are well satisfied in both cases within experimental errors, we conclude that possible DV must be buried under the experimental uncertainties. In other words, there seems to be no need for explicit models of DV in this case. Pinched kernels work as well, but with far less free parameters.

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arXiv2016

Quark-hadron duality: pinched kernel approch

Hadronic spectral functions measured by the ALEPH collaboration in the vector and axial-vector channels are used to study potential quark-hadron duality violations (DV). This is done entirely in the framework of pinched kernel finite energy sum rules (FESR), i.e. in a model independent fashion. The kinematical range of the ALEPH data is effectively extended up to $s = 10\; {\mbox{GeV}^2}$ by using an appropriate kernel, and assuming that in this region the spectral functions are given by perturbative QCD. Support for this assumption is obtained by using $e^+ e^-$ annihilation data in the vector channel. Results in both channels show a good saturation of the pinched FESR, without further need of explicit models of DV.

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arXiv2016

Theoretical determination of the hadronic (g-2) of the muon

An approach is discussed on the determination of the leading order hadronic contribution to the muon anomaly, $a_μ^{HAD}$, based entirely on theory. This method makes no use of $e^+ e^-$ annihilation data, a likely source of the current discrepancy between theory and experiment beyond the $3\, σ$ level. What this method requires is essentially knowledge of the first derivative of the vector current correlator at zero-momentum. In the heavy-quark sector this is obtained from the well known heavy quark expansion in perturbative QCD, leading to values of $a_μ^{HAD}$ in the charm- and bottom-quark region which were fully confirmed by later lattice QCD (LQCD) results. In the light-quark sector, using recent preliminary LQCD results for the first derivative of the vector current correlator at zero-momentum leads to the value $a_μ^{HAD} = (729 - 871)\, \times\,10^{-10}$, which is significantly larger than values obtained from using $e^+ e^-$ data. A separate approach based on the operator product expansion (OPE), and designed to quench the contribution of these data, reduces the discrepancy by at least 40\%. In addition, it exposes a tension between the OPE and $e^+ e^-$ data, thus suggesting the blame for the discrepancy on the latter.

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arXiv2015

Determination of the gluon condensate from data in the charm-quark region

The gluon condensate, $\langle \frac{α_s}π G^2 \rangle$, i.e. the leading order power correction in the operator product expansion of current correlators in QCD at short distances, is determined from $e^+ e^-$ annihilation data in the charm-quark region. This determination is based on finite energy QCD sum rules, weighted by a suitable integration kernel to (i) account for potential quark-hadron duality violations, (ii) enhance the contribution of the well known first two narrow resonances, the $J/ψ$ and the $ψ(2S)$, while quenching substantially the data region beyond, and (iii) reinforce the role of the gluon condensate in the sum rules. By using a kernel exhibiting a singularity at the origin, the gluon condensate enters the Cauchy residue at the pole through the low energy QCD expansion of the vector current correlator. These features allow for a reasonably precise determination of the condensate, i.e. $\langle \frac{α_s}π G^2 \rangle =0.037 \,\pm\, 0.015 \;{\mbox{GeV}}^4$.

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arXiv2015

Chiral sum rules and vacuum condensates from tau-lepton decay data

QCD finite energy sum rules, together with the latest updated ALEPH data on hadronic decays of the tau-lepton are used in order to determine the vacuum condensates of dimension $d=2$ and $d=4$. These data are also used to check the validity of the Weinberg sum rules, and to determine the chiral condensates of dimension $d=6$ and $d=8$, as well as the chiral correlator at zero momentum, proportional to the counter term of the ${\cal{O}}(p^4)$ Lagrangian of chiral perturbation theory, $\bar{L}_{10}$. Suitable (pinched) integration kernels are introduced in the sum rules in order to suppress potential quark-hadron duality violations. We find no compelling indications of duality violations in the kinematic region above $s \simeq 2.2$ GeV$^2$ after using pinched integration kernels.

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arXiv2014

$B$ Meson Decay Constants $f_{B_c}$, $f_{B_s}$ and $f_B$ from QCD Sum Rules

Finite energy QCD sum rules with Legendre polynomial integration kernels are used to determine the heavy meson decay constant $f_{B_c}$, and revisit $f_B$ and $f_{B_s}$. Results exhibit excellent stability in a wide range of values of the integration radius in the complex squared energy plane, and of the order of the Legendre polynomial. Results are $f_{B_c} = 528 \pm 19$ MeV, $f_B = 186 \pm 14$ MeV, and $f_{B_s} = 222 \pm 12$ MeV.

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arXiv2013

Hadronic Contribution to the muon $g-2$ factor

The lowest order hadronic contribution to the $g-2$ factor of the muon is analyzed in the framework of the operator product expansion at short distances, and a QCD finite energy sum rule designed to quench the role of the $e^+ e^-$ data. This procedure reduces the discrepancy between experiment and theory, $Δa_μ\equiv a^{EXP}_μ- a^{SM}_μ$, from $Δa_μ= 28.7 (8.0) \times 10^{-10}$ to $Δa_μ= 19.2 (8.0) \times 10^{-10}$, i.e. without changing the uncertainty.

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arXiv2012

Hadronic contribution to the QED running coupling $α(M_{Z}^2)$

We introduce a model independent method for the determination of the hadronic contribution to the QED running coupling, $Δα_{\text{HAD}}(M_{Z}^{2})$, requiring no $e^+e^-$ annihilation data as input. This is achieved by calculating the heavy-quark contributions entirely in perturbative QCD, whilst the light-quark resonance piece is determined using available lattice QCD results. Future reduction in the current uncertainties in the latter shall turn this method into a valuable alternative to the standard approach. Subsequently, we find that the precision of current determinations of $Δα_{\text{HAD}}(M_{Z}^{2})$ can be improved by some 20% by computing the heavy-quark pieces in PQCD, whilst using $e^+e^-$ data only for the low-energy light-quark sector. We obtain in this case $Δα_{\text{HAD}}(M_{Z}^{2})=275.7(0.8) \times 10^{-4}$, which currently is the most precise value of $Δα_{\text{HAD}}(M_{Z}^{2})$.

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arXiv2012

Corrections to the ${\bf SU(3)\times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$

Next to leading order corrections to the $SU(3) \times SU(3)$ Gell-Mann-Oakes-Renner relation (GMOR) are obtained using weighted QCD Finite Energy Sum Rules (FESR) involving the pseudoscalar current correlator. Two types of integration kernels in the FESR are used to suppress the contribution of the kaon radial excitations to the hadronic spectral function, one with local and the other with global constraints. The result for the pseudoscalar current correlator at zero momentum is $ψ_5(0) = (2.8 \pm 0.3) \times 10^{-3} GeV^{4}$, leading to the chiral corrections to GMOR: $δ_K = (55 \pm 5)%$. The resulting uncertainties are mostly due to variations in the upper limit of integration in the FESR, within the stability regions, and to a much lesser extent due to the uncertainties in the strong coupling and the strange quark mass. Higher order quark mass corrections, vacuum condensates, and the hadronic resonance sector play a negligible role in this determination. These results confirm an independent determination from chiral perturbation theory giving also very large corrections, i.e. roughly an order of magnitude larger than the corresponding corrections in chiral $SU(2) \times SU(2)$. Combining these results with our previous determination of the corrections to GMOR in chiral $SU(2) \times SU(2)$, $δ_π$, we are able to determine two low energy constants of chiral perturbation theory, i.e. $L^r_8 = (1.0 \pm 0.3) \times 10^{-3}$, and $H^r_2 = - (4.7 \pm 0.6) \times 10^{-3}$, both at the scale of the $ρ$-meson mass.

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arXiv2012

Bottom-quark mass from finite energy QCD sum rules

Finite energy QCD sum rules involving both inverse and positive moment integration kernels are employed to determine the bottom quark mass. The result obtained in the $\bar{\text {MS}}$ scheme at a reference scale of $10\, {GeV}$ is $\bar{m}_b(10\,\text{GeV})= 3623(9)\,\text{MeV}$. This value translates into a scale invariant mass $\bar{m}_b(\bar{m}_b) = 4171 (9)\, {MeV}$. This result has the lowest total uncertainty of any method, and is less sensitive to a number of systematic uncertainties that affect other QCD sum rule determinations.

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arXiv2011

Confronting electron-positron annihilation into hadrons with QCD: an operator product expansion analysis

Experimental data on the total cross section of $e^+ e^-$ annihilation into hadrons are confronted with QCD and the operator product expansion using finite energy sum rules. Specifically, the power corrections in the operator product expansion, i.e. the vacuum condensates, of dimension $d = 2$, 4 and 6 are determined using recent isospin $I=0+1$ data sets. Reasonably stable results are obtained which are compatible within errors with values from $τ$-decay. However, the rather large data uncertainties, together with the current value of the strong coupling constant, lead to very large errors in the condensates. It also appears that the separation into isovector and isoscalar pieces introduces additional uncertainties and errors. In contrast, the high precision $τ$-decay data of the ALEPH collaboration in the vector channel allows for a more precise determination of the condensates. This is in spite of QCD asymptotics not quite been reached at the end of the $τ$ spectrum. We point out that isospin violation is negligible in the integrated cross sections, unlike the case of individual channels.

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