More visualisation of decay-time-dependent asymmetries in multibody B-meson decays

Abstract Methods have been proposed recently to weight data in order to allow visualisation of $$C\!P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mspace/> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -violation effects in transitions of neutral B mesons to multibody final states that are not $$C\!P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mspace/> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -eigenstates. These are useful since integration of the unweighted data over the phase space would otherwise wash out the effects of interest. A similar method, elaborated upon here, with a different weighting function can also be used to visualise $$C\!P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mspace/> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -conserving $${{{B}} _{({{s}})}^0} \text {--}{{\hspace{0.0pt}\overline{\hspace{0.0pt}{B}}} _{({{s}})}^0} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mi>B</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mtext>--</mml:mtext> <mml:msubsup> <mml:mrow> <mml:mover> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mo>¯</mml:mo> </mml:mover> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>s</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> <mml:mn>0</mml:mn> </mml:msubsup> </mml:mrow> </mml:math> oscillations, rather than the $$C\!P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mspace/> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -violating asymmetries. Together with the other weighting functions, this new method could be useful, for example, to demonstrate the accuracy of the calibration of the flavour tagging algorithms that are crucial for analyses such as the measurement of the $$C\!P$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>C</mml:mi> <mml:mspace/> <mml:mi>P</mml:mi> </mml:mrow> </mml:math> -violating phase in $${{{B}} ^0_{{s}}} \rightarrow {{{J} \hspace{-1.66656pt}/\hspace{-1.111pt}\psi }} \phi $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>B</mml:mi> </mml:mrow> <mml:mi>s</mml:mi> <mml:mn>0</mml:mn> </mml:msubsup> <mml:mo>→</mml:mo> <mml:mrow> <mml:mi>J</mml:mi> <mml:mspace/> <mml:mo>/</mml:mo> <mml:mspace/> <mml:mi>ψ</mml:mi> </mml:mrow> <mml:mi>ϕ</mml:mi> </mml:mrow> </mml:math> decays. Their application to the formalism in common use for such decays is explicitly demonstrated.