The Differential equation method: calculation of vertex-type diagrams with one non-zero mass

The differential equation method is applied to evaluate analytically two-loop vertex Feynman diagrams. Three on-shell infrared divergent planar two-loop diagrams with zero thresholds contributing to the processes Z --> bb bar (for zero b mass) and/or H --> gg are calculated in order to demonstrate a new application of this method.Comment: 12 pages, LATEX, uses axodray.st

Three-loop massive tadpoles and polylogarithms through weight six

We evaluate the three-loop massive vacuum bubble diagrams in terms of polylogarithms up to weight six. We also construct the basis of irrational constants being harmonic polylgarithms of arguments $e^{k i \pi/3}$.Comment: 26 pages, 4 ancillary files, v3: version published in JHEP: minor additions, file with results for massive three-loop form-factor integrals adde

The γ∗γ∗→ηc\gamma^* \gamma^*\to\eta_c transition form factor

We study the $\gamma^* \gamma^*\to\eta_c$ transition form factor, $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2),$ with the local-duality (LD) version of QCD sum rules. We analyse the extraction of this quantity from two different correlators, and $,$ with $P,$ $A,$ and $V$ being the pseudoscalar, axial-vector, and vector currents, respectively. The QCD factorization theorem for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2)$ allows us to fix the effective continuum thresholds for the and $$ correlators at large values of $Q^2=Q_2^2$ and some fixed value of $\beta\equiv Q_1^2/Q_2^2$. We give arguments that, in the region $Q^2\ge10$--$15 GeV^2$, the effective threshold should be close to its asymptotic value such that the LD sum rule provides reliable predictions for $F_{\eta_c\gamma\gamma}(Q_1^2,Q_2^2).$ We show that, for the experimentally relevant kinematics of one real and one virtual photon, the result of the LD sum rule for $F_{\eta_c\gamma}(Q^2)\equiv F_{\eta_c\gamma\gamma}(0,Q^2)$ may be well approximated by the simple monopole formula $F_{\eta_c\gamma}(Q^2)={2e_c^2N_cf_P}(M_V^2+Q^2)^{-1},$ where $f_P$ is the $\eta_c$ decay constant, $e^2_c$ is the $c$-quark charge, and the parameter $M_V$ lies in the mass range of the lowest $\bar cc$ vector states.Comment: 9 page

Electroweak corrections to ZZ-boson hadroproduction at finite transverse momentum

We calculate the full one-loop electroweak radiative corrections, of ${\cal O}(\alpha^2\alpha_s)$, to the cross section of single $Z$-boson inclusive hadroproduction at finite transverse momentum ($p_T$). This includes the ${\cal O}(\alpha)$ corrections to $Z+j$ production, the ${\cal O}(\alpha_s)$ corrections to $Z+\gamma$ production, and certain QCD-electroweak interference contributions involving a single quark trace. We recover the QCD and purely weak corrections and study the QED corrections and the QCD-electroweak interference contributions for the first time. We also consider direct and resolved photoproduction in elastic and inelastic scattering. We present $p_T$ and rapidity distributions for the experimental conditions at the Fermilab Tevatron and the CERN LHC and assess the significance of the various contributions.Comment: 31 pages, 11 figures; discussion enhanced, figures added, references added and updated; accepted for publication in Nucl. Phys.

On the bb-quark running mass in QCD and the SM

We consider electroweak corrections to the relation between the running $\overline{\mathrm{MS}}$ mass $m_b$ of the $b$ quark in the five-flavor QCD$\times$QED effective theory and its counterpart in the Standard Model (SM). As a bridge between the two parameters, we use the pole mass $M_b$ of the $b$ quark, which can be calculated in both models. The running mass is not a fundamental parameter of the SM Lagrangian, but the product of the running Yukawa coupling $y_b$ and the Higgs vacuum expectation value. Since there exist different prescriptions to define the latter, the relations considered in the paper involve a certain amount of freedom. All the definitions can be related to each other in perturbation theory. Nevertheless, we argue in favor of a certain gauge-independent prescription and provide a relation which can be directly used to deduce the value of the Yukawa coupling of the $b$ quark at the electroweak scale from its effective QCD running mass. This approach allows one to resum large logarithms $\ln(m_b/M_t)$ systematically. Numerical analysis shows that, indeed, the corrections to the proposed relation are much smaller than those between $y_b$ and $M_b$.Comment: 19 pages, 4 figures, misprints corrected (thanks to S. Martin), results not affecte