Measuring $$A_\textrm{FB}^b$$ and $$R_b$$ with exclusive b-hadron decays at the FCC-ee

Abstract This paper presents a novel tagging technique to measure the beauty-quark partial decay-width ratio $$R_b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>R</mml:mi> <mml:mi>b</mml:mi> </mml:msub> </mml:math> and its forward–backward asymmetry $$A_{\textrm{FB}}^b$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>A</mml:mi> <mml:mrow> <mml:mtext>FB</mml:mtext> </mml:mrow> <mml:mi>b</mml:mi> </mml:msubsup> </mml:math> at the FCC-ee, using $$\mathcal {O}(10^{12})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>O</mml:mi> <mml:mo>(</mml:mo> <mml:msup> <mml:mn>10</mml:mn> <mml:mn>12</mml:mn> </mml:msup> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> Z -boson decays. The method is based on the exclusive reconstruction of a selected list of b -hadron decay modes in $$Z\rightarrow b\bar{b}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Z</mml:mi> <mml:mo>→</mml:mo> <mml:mi>b</mml:mi> <mml:mover> <mml:mrow> <mml:mi>b</mml:mi> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> </mml:mrow> </mml:math> events at the Z pole, which can provide the flavour and possibly the charge of the hemisphere. This approach effectively eliminates the contamination from light-quark physics events and reduces the leading systematic uncertainties arising from background contamination, tagging-efficiency correlations, and gluon-radiation corrections by exploiting the geometric and kinematic properties of beauty hadrons. This results in a total relative uncertainty of the order of 0.01 % for both observables. Furthermore, this precision allows to obtain a commensurate precision on the weak mixing angle $$\sin ^2(\theta _\text {W}^{\text {eff}})$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mo>sin</mml:mo> <mml:mn>2</mml:mn> </mml:msup> <mml:mrow> <mml:mo>(</mml:mo> <mml:msubsup> <mml:mi>θ</mml:mi> <mml:mtext>W</mml:mtext> <mml:mtext>eff</mml:mtext> </mml:msubsup> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> compared to the muon forward–backward asymmetry on the order of 0.002 %.