Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD

Chetyrkin, K.G.; Kühn, Johann H.; Sturm, Christian

doi:10.1140/epjc/s2006-02610-y

Cited by 161 publications

(243 citation statements)

References 35 publications

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“…Applying four-loop running and matching [38,39,40,41] to (19) we arrive at This is one of the most precise and presently only result in order α 4 s . We thank G. Quast for useful discussions and M. Steinhauser for reading the manuscript and good advice.…”

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confidence: 81%

Orderαs4QCD Corrections toZandτDecays

2008

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Using recently developed methods for the evaluation of five-loop amplitudes in perturbative QCD, corrections of order α 4 s for the non-singlet part of the cross section for electron-positron annihilation into hadrons and for the decay rates of the Z-boson and the τ -lepton into hadrons are evaluated. The new terms lead to a significant stabilization of the perturbative series, to a reduction of the theory uncertainly in the strong coupling constant αs, as extracted from these measurements, and to a small shift of the central value, moving the two central values closer together. The agreement between two values of αs measured at vastly different energies constitutes a striking test of asymptotic freedom. Combining the results from Z and τ decays we find αs(MZ) = 0.1198 ± 0.0015 as one of the most precise and presently only result for the strong coupling constant in order α 4 s . The strong coupling constant α s is one of the three fundamental gauge couplings constants of the Standard Model (SM) of particle physics. Its precise determination is one of the most important aims of particle physics. Experiments at different energies allow to test the predictions for its energy dependence based on the renormalization group equations, the comparison of the results obtained from different processes leads to critical tests of the theory and potentially to the discovery of physics beyond the Standard Model. Last but not least, the convergence of the three gauge coupling constants related by SU(3)xSU(2)xU(1) to a common value, after evolving them to high energies, allows us to draw conclusions about the possibility of embedding the SM in the framework of a Grand Unified Theory.One of the most precise and theoretically safe determination of α s is based on measurements of the cross section for electron-positron annihilation into hadrons. These have been performed in the low-energy region between 2 GeV and 10 GeV and, in particular, at and around the Z resonance at 91.2 GeV. Conceptually closely related is the measurement of the semileptonic decay rate of the τ -lepton, leading to a determination of α s at a scale below 2 GeV.From the theoretical side, in the framework of perturbative QCD, these rates and cross sections are evaluated as inclusive rates into massless quarks and gluons [1,2]. (Power suppressed mass effects are well under control for e + e − -annihilation, both at low energies and around the Z resonance, and for τ decays [3,4,5,6,7,8], and the same applies to mixed QCD and electroweak corrections [9,10]).The ratio R(s) ≡ σ(e + e − → hadrons)/σ(e + e − → µ + µ − ) is expressed through the absorptive part of the correlator of the electromagnetic current j µ :with Q 2 = −q 2 . It is also convenient to introduce the Adler function asWe define the perturbative expansionswhere a s ≡ α s /π and the normalization scale is set to µ 2 = Q 2 or to µ 2 = s for the Euclidian and Minkowskian functions respectively. The results for generic values of µ can be easily recovered with standard RG techniques. Note that the first th...

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confidence: 81%

Orderαs4QCD Corrections toZandτDecays

2008

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“…In particular, the master integrals in Fig. 5 enter the basis intensively used in modern QCD calculations [20,21,22,23].…”

Section: Methods Of Calculationmentioning

confidence: 99%

order of the polarization operator in Coulomb field at low energy

Kirilin

Lee

2009

Nuclear Physics B

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“…At O(α 3 s ), however, only the first physical moment proportional to (q 2 ) 1 for axial-vector and scalar correlators [10] and the first and second moment for the pseudo-scalar and vector correlators [10,11,12,13] have been available until recently. The third moment for all four current correlators and the fourth moment for the pseudo-scalar correlator are computed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Reconstruction of heavy quark current correlators at

et al. 2009

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We construct approximate formulas for the O(α 3 s ) 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 Padé 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.

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Four-loop moments of the heavy quark vacuum polarization function in perturbative QCD

Cited by 161 publications

References 35 publications

Orderαs4QCD Corrections toZandτDecays

Orderαs4QCD Corrections toZandτDecays

order of the polarization operator in Coulomb field at low energy

Reconstruction of heavy quark current correlators at

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