Related papers: Heavy Quark Vacuum Polarisation to Three Loops
The three-loop vacuum polarization function $\Pi(q^2)$ induced by a massive quark is calculated. A comprehensive description of the method is presented. From the imaginary part the ${\cal O}(\alpha_s^2)$ result for the production of heavy…
In this paper the three-loop polarization functions \Pi(q^2) are calculated for the cases of an external vector, axial-vector, scalar or pseudo-scalar current. Results are presented for the imaginary part which directly leads to the cross…
The heavy-quark contribution to the polarisation function $\Pi$ at higher perturbative orders is presently only known approximately. We scrutinise the accuracy of state-of-the-art approximations at three- and four-loop order. At three…
We determine the full mass and $q^2$ dependence of the heavy quark vacuum polarization function $\Pi(q^2)$ and its contribution to the total $e^+e^-$ cross section at ${\cal O}(\alpha_s^2)$ and ${\cal O}(\alpha_s^3)$ in perturbative QCD. We…
New results at four-loop order in perturbative QCD for the first two Taylor coefficients of the heavy quark vacuum polarization function are presented. They can be used to perform a precise determination of the charm- and bottom-quark mass.…
The vacuum polarization due to a virtual heavy quark pair and specifically the coefficients of its Taylor expansion in the external momentum are closely related to moments of the cross section for quark-antiquark pair production in…
Fully analytical results for the first two moments of the heavy-quark vacuum polarisation function at four loops in quantum chromo-dynamics are presented.
We compute the virtual O(\alpha_s^3 n_f^2) corrections to the heavy quark vector current correlator in terms of expansions in the external momentum and as an exact numerical solution. As a byproduct, the available high-energy expansion at…
We present analytical calculation of the first seven moments of the heavy quark vacuum polarization function in the three-loop order. The obtained results are compared against the asymptotic formulas following from the threshold…
We calculate a correction to the electromagnetic current induced by a heavy quark loop. The contribution of this correction to the vacuum polarization function appears at the O(alpha_s^3) order of perturbation theory and has a qualitatively…
The vacuum polarization functions $\Pi(q^2)$ of charged and neutral gauge bosons which arise from top and bottom quark loops lead to important shifts in relations between electroweak parameters which can be measured with ever-increasing…
Vacuum polarization mediated by quark loops is susceptible to external electromagnetic fields as well as to the QCD vacuum structure. Employing the stochastic vacuum model, we calculate the modification of the one-loop Euler-Heisenberg…
Hadronic vacuum polarization at low virtualities limits the precision of experimental tests of the standard model via important physical observables. Here we compute that effect in two-flavor chiral perturbation theory to three loops. Among…
With the increasing experimental precision available at colliders, higher-order perturbative calculations are required to reduce the theory uncertainty in order to extract crucial QCD parameters, such as the strong coupling constant, to the…
We present the first genuine QCD five-loop calculation of the vacuum polarization functions: analytical terms of order alpha_s^4 n_f^2 to the absorptive parts of vector and scalar correlators. These corrections form an important…
The three-loop QCD contributions to the vacuum polarization functions of the $Z$ and $W$ bosons at zero momentum are calculated. The top quark is considered to be massive and the other quarks massless. Using these results, we calculate the…
The static potential between an infinitely heavy quark and antiquark is derived in the framework of perturbative QCD to three loops by performing a full calculation of the two-loop diagrams and using the renormalization group. The…
The QED vacuum polarization function is calculated to O(alpha^2) (next-to-leading order) accuracy in the threshold regime by using the concept of effective field theories to resum diagrams with the instantaneous Coulomb exchange of…
We present the results for heavy quark form factors at two-loop order in perturbative QCD for different currents, namely vector, axial-vector, scalar and pseudo-scalar currents, up to second order in the dimensional regularization…
We compute the color-planar and complete light quark non-singlet contributions to the heavy quark form factors in the case of the axialvector, scalar and pseudoscalar currents at three loops in perturbative QCD. We evaluate the master…