A measurement of the forward-backward asymmetry of e+e−→bb by applying a jet charge algorithm to lifetime tagged events

The forward-backward asymmetry of <img src="/fulltext-image.asp?format=htmlnonpaginated&src=N54L454662126467_html\10052_2005_Article_BF01624580_TeX2GIFIE1.gif" border="0" alt=" $$e^ + e^ - \to Z^0 \to b\bar b$$ " /> has been measured using approximately 2.15 million hadronicZ⁰ decays collected at the LEP e⁺e⁻ collider with the OPAL detector. A lifetime tag technique was used to select an enriched <img src="/fulltext-image.asp?format=htmlnonpaginated&src=N54L454662126467_html\10052_2005_Article_BF01624580_TeX2GIFIE2.gif" border="0" alt=" $$b\bar b$$ " /> event sample. The measurement of the <img src="/fulltext-image.asp?format=htmlnonpaginated&src=N54L454662126467_html\10052_2005_Article_BF01624580_TeX2GIFIE3.gif" border="0" alt=" $$b\bar b$$ " /> asymmetry was then performed using a jet charge algorithm to determine the direction of the primary quark. Values of: $$\begin{gathered} A_{FB}^b = 0.062 \pm 0.034 \pm 0.002 - 0.082\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 89.52GeV, \hfill \\ A_{FB}^b = 0.0963 \pm 0.0067 \pm 0.0038 - 0.471\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 91.25GeV, \hfill \\ A_{FB}^b = 0.172 \pm 0.028 \pm 0.007 - 0.055\Delta (\Gamma _{b\bar b} /\Gamma _{had} ) \hfill \\ at\sqrt s = 92.94GeV, \hfill \\ \end{gathered}$$ were measured where, in each case, the first error is statistical, the second is systematic and the third term gives the variation due to a change <img src="/fulltext-image.asp?format=htmlnonpaginated&src=N54L454662126467_html\10052_2005_Article_BF01624580_TeX2GIFIE4.gif" border="0" alt=" $$\Delta (\Gamma _{b\bar b} /\Gamma _{had} )$$ " /> in the value of <img src="/fulltext-image.asp?format=htmlnonpaginated&src=N54L454662126467_html\10052_2005_Article_BF01624580_TeX2GIFIE5.gif" border="0" alt=" $$\Gamma _{b\bar b} /\Gamma _{had} = 0.216$$ " /> assumed. The dependence on the assumed charm asymmetry at the same energy is Δ(A_FB^b)≈+0.07Δ(A_FB^c). Assuming the Standard Model form for the couplings, these measurements correspond to an effective weak mixing angle of: $$\sin ^2 \theta _W^{eff,e} = 0.2313 \pm 0.0012 \pm 0.0006$$ giving M_top=196₋₃₈₋₁₉⁺³³⁺¹⁶GeV/c², where the first error is statistical and the second is systematic. The Higgs mass assumed is 300 GeV/c². A variation in the assumed mass of the Higgs boson between 60 and 1000 GeV/c² corresponds to an uncertainty in sin²θ_W^eff,e of ±0.00006 and on M_top of₋₂₆⁺²⁰GeV/c².