Two-Loop QCD Corrections to the Heavy Quark Form Factors: Axial Vector Contributions

We consider the Z Q Qbar vertex to second order in the QCD coupling for an on-shell massive quark-antiquark pair and for arbitrary momentum transfer of the Z boson. We present closed analytic expressions for the two parity-violating form factors of that vertex at the two-loop level in QCD, excluding the contributions from triangle diagrams. These form factors are expressed in terms of 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 57 pages, 5 figures. All the results in Section 6 of the paper are available in an electronic form in the file formulas.in

Differential equations and massive two-loop Bhabha scattering: the B5l2m3 case

The two-loop box contributions to massive Bhabha scattering may be reduced to two-loop box master integrals (MIs) with five, six, and seven internal lines, plus vertices and self energies. The self-energy and vertex MIs may be solved analytically by the differential equations (DE) method. This is true for only few of the box masters. Here we describe some details of the analytical determination, including constant terms in ep=(4-d)/2, of the complicated topology B5l2m3 (with 5 lines, 2 of them being massive). With the DE approach, three of the four coupled masters have been solved in terms of (generalized) standard Harmonic Polylogarithms.Comment: 5 pages, 2 figures, contribution to RADCOR 2005, Oct 2-7, 2005, Shonan Village, Japan, to appear in Nucl. B (Proc. Suppl.

Two-Loop QCD Corrections to the Heavy Quark Form Factors: Anomaly Contributions

We present closed analytic expressions for the order $\alpha_s^2$ triangle diagram contributions to the matrix elements of the singlet and non-singlet axial vector currents between the vacuum and a quark-antiquark state. We have calculated these vertex functions for arbitrary momentum transfer and for four different sets of internal and external quark masses. We show that both the singlet and non-singlet vertex functions satisfy the correct chiral Ward identities. Using the exact expressions for the finite axial vector form factors, we check the quality and the convergence of expansions at production threshold and for asymptotic energies.Comment: 24 pages, 6 figure

Reduze - Feynman Integral Reduction in C++

Reduze is a computer program for reducing Feynman Integrals to master integrals employing a Laporta algorithm. The program is written in C++ and uses classes provided by the GiNaC library to perform the simplifications of the algebraic prefactors in the system of equations. Reduze offers the possibility to run reductions in parallel.Comment: 18 pages, 2 figure

Two-Loop N_F =1 QED Bhabha Scattering: Soft Emission and Numerical Evaluation of the Differential Cross-section

Recently, we evaluated the virtual cross-section for Bhabha scattering in pure QED, up to corrections of order alpha^4 (N_F =1). This calculation is valid for arbitrary values of the squared center of mass energy s and momentum transfer t; the electron and positron mass m was considered a finite, non vanishing quantity. In the present work, we supplement the previous calculation by considering the contribution of the soft photon emission diagrams to the differential cross-section, up to and including terms of order alpha^4 (N_F=1). Adding the contribution of the real corrections to the renormalized virtual ones, we obtain an UV and IR finite differential cross-section; we evaluate this quantity numerically for a significant set of values of the squared center of mass energy s.Comment: 24 pages, 15 figures. Formulas in Appendix B corrected, changes in Section 3, references adde

Electroweak top-quark pair production at the LHC with Z′Z' bosons to NLO QCD in POWHEG

We present the calculation of the NLO QCD corrections to the electroweak production of top-antitop pairs at the CERN LHC in the presence of a new neutral gauge boson. The corrections are implemented in the parton shower Monte Carlo program POWHEG. Standard Model (SM) and new physics interference effects are properly taken into account. QED singularities, first appearing at this order, are consistently subtracted. Numerical results are presented for SM and $Z'$ total cross sections and distributions in invariant mass, transverse momentum, azimuthal angle and rapidity of the top-quark pair. The remaining theoretical uncertainty from scale and PDF variations is estimated, and the potential of the charge asymmetry to distinguish between new physics models is investigated for the Sequential SM and a leptophobic topcolor model.Comment: 33 pages, 15 figures, 1 table. Discussion added on uncertainties from parton showers and NLL contribution

Two-Loop Corrections to Top-Antitop Production at Hadron Colliders

The status of the theoretical predictions for the top-anti top production in hadronic collisions is shortly reviewed, paying a articular attention to the analytic calculation of the two-loop QCD corrections to the parton-level matrix elements.Comment: Talk presented at the 35th International Conference of High Energy Physics - ICHEP2010, July 22-28, 2010, Paris Franc

Master Integrals for the 2-loop QCD virtual corrections to the Forward-Backward Asymmetry

We present the Master Integrals needed for the calculation of the two-loop QCD corrections to the forward-backward asymmetry of a quark-antiquark pair produced in electron-positron annihilation events. The abelian diagrams entering in the evaluation of the vector form factors were calculated in a previous paper. We consider here the non-abelian diagrams and the diagrams entering in the computation of the axial form factors, for arbitrary space-like momentum transfer Q^2 and finite heavy quark mass m. Both the UV and IR divergences are regularized in the continuous D-dimensional scheme. The Master Integrals are Laurent-expanded around D=4 and evaluated by the differential equation method; the coefficients of the expansions are expressed as 1-dimensional harmonic polylogarithms of maximum weight 4.Comment: 38 pages, 6 figures, typos corrected, version accepted by Nucl. Phys.

Heavy-Quark Form Factors and Threshold Cross Section at O(\alpha_S^2)

During the last year, analytic expressions for the two-loop QCD corrections to the form factors for the vector, axial-vector, scalar and pseudo-scalar vertices involving a pair of heavy quarks, $Q \bar{Q}$, were calculated. The results are valid for arbitrary momentum transfer and mass of the heavy quarks. These form factors have a number of applications, including anomalous couplings, the $e^{+}e^{-} \to Q \bar Q$ cross section, and the forward-backward asymmetry of heavy quarks. Here the $Q {\bar Q}$ threshold cross section is presented with some new second order axial vector contributions.Comment: 5 pages. Presented at the International Europhysics Conference on High Energy Physics (HEP2005), July 21-27 2005, Lisboa, Portuga

Two-Loop QCD Corrections to the Heavy-to-Light Quark Decay

We present an analytic expression for the two-loop QCD corrections to the decay process b -> u W^*, where b and u are a massive and massless quark, respectively, while W^* is an off-shell charged weak boson. Since the W-boson can subsequently decay in a lepton anti-neutrino pair, the results of this paper are a first step towards a fully analytic computation of differential distributions for the semileptonic decay of a b-quark. The latter partonic process plays a crucial role in the study of inclusive semileptonic charmless decays of B-mesons. The three independent form factors characterizing the b W u vertex are provided in form of a Laurent series in (d-4), where d is the space-time dimension. The coefficients in the series are expressed in terms of Harmonic Polylogarithms of maximal weight 4, and are functions of the invariant mass of the leptonic decay products of the W-boson.Comment: 27 pages, 3 figures, References added, version published on JHE