0000000000267237
AUTHOR
S. Bodenstein
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.
Charm-quark mass from weighted finite energy QCD sum rules
The running charm-quark mass in the scheme is determined from weighted finite energy QCD sum rules 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 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 us 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 theo…
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 u…
Hadronic contribution to the muong−2factor: A theoretical determination
The leading-order hadronic contribution to the muon $g\ensuremath{-}2$, ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$, 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 ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$ with a simpler function of $s$. The integral determining ${a}_{\ensuremath{\mu}}^{\mathrm{HAD}}$ 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,…