Peter Marquard

Charm and Bottom Quark Masses: An Update

Using new four-loop results for the heavy quark vacuum polarization and new data for bottom quark production in electron-positron annihilation, an update on the determination of charm- and bottom-quark masses through sum rules has been performed. The previous result for the charm-quark mass,

Quark Mass Relations to Four-Loop Order in Perturbative QCD

{m}_{c}(3\text{ }\text{ }\mathrm{GeV})=0.986(13)\text{ }\text{ }\mathrm{GeV}

Hadronic contribution to the muon anomalous magnetic moment to next-to-next-to-leading order

, based on the lowest moment, is supported by the new results from higher moments which lead to consistent values with comparable errors. The new value for the bottom quark,

Reconstruction of heavy quark current correlators at O(\alpha_s^3)

{m}_{b}(10\text{ }\text{ }\mathrm{GeV})=3.610(16)\text{ }\text{ }\mathrm{GeV}

Reconstruction of heavy quark current correlators at O(αs3)

, corresponding to

The second physical moment of the heavy quark vector correlator at O(αs3)

{m}_{b}({m}_{b})=4.163(16)\text{ }\text{ }\mathrm{GeV}

Low-energy moments of heavy quark current correlators at four loops

, makes use of both the new data and the new perturbative results and is consistent with the earlier determination.

Next-to-Next-to-Next-to-Leading Order QCD Prediction for the Top Antitop S-Wave Pair Production Cross Section Near Threshold in e + e − Annihilation

We present results for the relation between a heavy quark mass defined in the on-shell and minimal subtraction (MS[over ¯]) scheme to four-loop order. The method to compute the four-loop on-shell integral is briefly described and the new results are used to establish relations between various short-distance masses and the MS[over ¯] quark mass to next-to-next-to-next-to-leading order accuracy. These relations play an important role in the accurate determination of the MS[over ¯] heavy quark masses.

Precise charm- and bottom-quark masses: Theoretical and experimental uncertainties

Abstract We compute the next-to-next-to-leading order hadronic contribution to the muon anomalous magnetic moment originating from the photon vacuum polarization. The corresponding three-loop kernel functions are calculated using asymptotic expansion techniques which lead to analytic expressions. Our final result, a μ had , NNLO = 1.24 ± 0.01 × 10 − 10 , has the same order of magnitude as the current uncertainty of the leading order hadronic contribution and should thus be included in future analyses.

Three Loop Cusp Anomalous Dimension in QCD

We construct approximate formulas for the O(αs3) QCD contributions to vector, axial-vector, scalar and pseudo-scalar quark current correlators, which are valid for arbitrary values of momenta and masses. The derivation is based on conformal mapping and the Pade approximation procedure and incorporates known expansions in the low energy, threshold and high energy regions. We use our results to estimate additional terms in these expansions.