Second order QCD corrections to the forward-backward asymmetry in e+e−-collisions

Abstract

We will present the result of an analytical calculation of the second order contribution to the forward-backward asymmetry A H FB and the shape constant a H for heavy flavour production in e + e − -collisions. The calculation has been carried out by assuming that the quark mass is equal to zero. This is a reasonable approximation for the exact second order correction for charm and bottom quark production at LEP energies but not for top production at future linear colliders. Our result for A H FB is a factor 2.6 (charm) and 4.7 (bottom) larger than obtained by a numerical calculation performed earlier in the literature. We study the effect of the second order corrections on the above parameters including their dependence on the renormalization scale. Further we make a comparison between the fixed pole mass and the running mass approach.

The forward-backward asymmetry for massive bottom quarks at the Z peak at next-to-next-to-leading order QCD

“…Next we compute the second-order correction to the b-quark forward-backward asymmetry for a sequence of decreasing values of m b . This allows us to compare with the results of [18,19] obtained for m b = 0. In order to conform to the calculation of [19] we neglect now, as was done in [19], the singlet and the triangle contributions.…”

“…The full next-to-next-to-leading order (NNLO) QCD corrections, i.e., the contributions of α 2 s to this asymmetry, were recently published for the top quark in tt production above the production threshold 1 in [14,15]. For b quarks, the order α 2 s corrections were calculated so far only in the limit of vanishing b-quark mass [17][18][19][20]. As pointed out in [19], the forwardbackward asymmetry for a specific massless quark flavor Q is not infrared (IR) safe if the direction that specifies the forward and backward hemisphere is defined by the direction of flight of the quark Q or by the thrust direction.…”

Heavy quark form factors at two loops

“…(3.14) is a particular case of Eq. (3.15), 6 we will consider for illustration purposes one of the integrals that require an expansion of the form (3.15). The integral K 4 ¼ Kð1; 1; 1; 1; 0; 0Þ is simple enough (it consists of a product of two one-loop integrals) to be calculated just through Feynman parameters, but precisely because of this simplicity, it allows us to describe the main features of the method without unnecessary complications or long formulas.…”

“…[3,4], the first-order QCD corrections were obtained for the vector and axial-vector form factors. A massless approximation was considered to obtain the nextto-next-to-leading-order (NNLO) QCD corrections in [5] numerically, later followed by an analytic computation in [6]. Another numerical computation was performed in [7] at NNLO using a different formalism.…”

Electroweak production of top-quark pairs ine+e−annihilation at NNLO in QCD: The vector current contributions

“…Total cross sections are known to NNLO in the threshold expansions [8][9][10][11][12] and high-energy expansions [13][14][15][16][17]. Results for the forwardbackward asymmetry are also known in the small mass approximation [18][19][20]. In the near future, the threshold cross section at NNNLO will also be available [21][22][23].…”