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

Abstract

We compute the order α 2 s QCD corrections to the b-quark forward-backward asymmetry in e + e − → bb collisions at the Z boson resonance, taking the non-zero mass of the b quark into account. We determine these corrections with respect to both the b-quark axis and the thrust axis definition of the asymmetry. We compute also the distributions of these axes with respect to the electron beam. If one neglects the flavor singlet contributions to the b-quark asymmetry, as was done in previous computations for massless b quarks, then the second-order QCD corrections for m b = 0 are smaller in magnitude than the corresponding corrections for m b = 0. Including the singlet contributions slightly increases the magnitude of the corrections. The massive α 2 s corrections to the b-quark forwardbackward asymmetry slightly diminish the well-known tension between the bare b-quark asymmetry and the standard model fit from 2.9σ to 2.6σ.

Top-quark physics: Status and prospects

“…The top-quark polarization in tt events is predicted to be very small in the SM [113]; the exact value depends on the choice of the spin quantization axis, as discussed in Section 2. to the central values and uncertainties given in table 1 and table 2. The uncertainties were assumed to be uncorrelated.…”

“…Top quarks and antiquarks produced in tt pair production show only very small polarization (approximately 1%, depending on the initial state and the choice of the quantization axes [113]); however, their spins are significantly correlated. The quantum-mechanical observable connected to a spin is its projection to a quantization axis.…”

Revisiting the bottom quark forward–backward asymmetry $$A_\mathrm{{FB}}$$ in electron–positron collisions

“…2.1 PMC scale-setting for the b quark pair production cross section in electron-positron collisions For our PMC scale-setting analysis for the b quark forwardbackward asymmetry to NNLO in QCD, we employ the computational set-up of Refs. [11,13] for massive b quark pair production in electron-positron collisions. The NNLO QCD corrections consist of three classes of contributions: (i) the two-loop and 1-loop squared corrections to the two-parton final state (bb); (ii) the one-loop corrections to the threeparton final state (bbg); (iii) the tree level processes with four-parton final states (bbgg, bbqq, bbbb).…”

“…The b quark forward-backward asymmetry was computed for m b = 0 at NNLO both for the quark axis and the thrust axis definition in Ref. [13], for conventional scale settings. It was found that this result reduces the tension between the measurements and the SM predictions but only slightly to 2.6σ .…”

Global fits of the SM parameters

“…The first measurement of APV as a function of isotope number has been achieved by the group of Dima Budker at the JGU Mainz [18] just a few months ago, where the weak charges of Ytterbium showed the expected isotope dependence. Note, that there has been a change in the sin 2 θ W extraction from the FB asymmetry for bb final states by the LEP Collaborations, as two years ago the two-loop QCD correction necessary to extract the pole asymmetry has been obtained with the finite b quark mass dependence [20], reducing the largest LEP discrepancy with the SM by about a quarter of a standard deviation. Another change affected the extraction from the APV measurement in 133 Cs [15], for which the Stark vector transition polarizability needs to be known.…”