diff --git a/draft.tex b/draft.tex index 6cdf57d..78a9d43 100644 --- a/draft.tex +++ b/draft.tex @@ -495,34 +495,30 @@ %We acknowledge useful contributions from Gino Isidori, Danny van Dyk and Patrick Owen. -%This work is supported by the Swiss National Science Foundation (SNF) under contract - +%This work is supported by the Swiss National Science Foundation (SNF) under contract PZ00P2-174182. \bibliography{references} +\FloatBarrier -\newpage +\appendix + +%\newpage \section{Supplemental material} An extension of the physics case of the proposed method is to investigate the sensitivity to the chirality-flipped counterparts of the usual Wilson coefficients, -\textit{i.e.} $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$. -We assume the primed WCs to be fixed to the SM value for electrons mode and let free-floating the -muon channel. In the following, we consider different NP scenarios concerning the $\WC'^{(\mu)}_i$, -while $\WC^{(\mu,e)}_i$ are set as for \texttt{BMP}$_{\WC_{9,10}}$. +\textit{i.e.} $\WC^{\prime (\mu)}_9$ and $\WC^{\prime(\mu)}_{10}$. +Following the formalism discussed in this letter, the primed WCs are examined by considering in addition to the +\texttt{BMP}$_{\WC_{9,10}}$ three different modified NP scenarios for the muon only: +$\WC_{9,10}^{\prime(\mu)} = \WC^{\prime \rm{SM}}_{9,10} = 0$; +$\WC^{\prime (\mu)}_9 = \WC^{\prime (\mu)}_{10} = 0.3$; +and $\WC^{\prime (\mu)}_9 = - \WC^{\prime (\mu)}_{10} = 0.3$. +Notice that for the electron mode the $\WC_{9,10}^{\prime(e)}$ is set and fixed to the SM value $\WC^{\prime \rm{SM}}_{9,10} = 0$. -Firstly, Fig.~\ref{fig:Cp_Hz} shows the fit results for different order of the analytic expansion for -the non-local hadronic contribution for a NP scenario with $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$, -and yields corresponding to the \lhcb Run II expected statistics. -The dependency of the determination of $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$ on the -order of the expansion clearly saturates after $\mathcal{H}_\lambda[z^3]$ and allows a measurement -of the primed Wilson coefficients for the muon decay channel $B^{0} \to K^{*0} \mumu$ independent -on the theoretical hadronic uncertainty. - - -\begin{figure}[tbh] +\begin{figure}[b] \includegraphics[width=.4\textwidth]{plots/ellipses_CpMu_Hz.pdf} \caption{% Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and @@ -534,21 +530,27 @@ } \end{figure} - +Figure~\ref{fig:Cp_Hz} shows the fit results for different order of the analytic expansion for +the non-local hadronic contribution for a NP scenario with $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$, +and yields corresponding to the \lhcb Run II expected statistics. +The dependency on the determination of $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$ on the +order of the expansion clearly saturates after $\mathcal{H}_\lambda[z^3]$ and allows a measurement +of the primed Wilson coefficients for the muon decay channel $B^{0} \to K^{*0} \mumu$ independent +on the theoretical hadronic uncertainty. +% Figure~\ref{fig:Cp} shows the prospects for the sensitivity to the $\WC'^{(\mu)}_9$ and -$\WC'^{(\mu)}_{10}$ Wilson coefficients corresponding to the expected statistics at \belle II -and \lhcb upgrades [$50\,$-$\,300\,$fb$^{-1}$]. - - -\begin{figure}[tbh] +$\WC'^{(\mu)}_{10}$ Wilson coefficients corresponding to the expected statistics at +Note that only with the full capability of the LHCb experiment it is possible +to start disentangling the different NP hypotheses. +% +\begin{figure}[t] \includegraphics[width=.4\textwidth]{plots/ellipses_CpMu.pdf} \caption{% Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and $\WC'^{(\mu)}_{10}$ for three NP scenarios: (blue) $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0$, (orange) $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$ and (magenta) $\WC'^{(\mu)}_9 = - \WC'^{(\mu)}_{10} = 0.3$. - The contours correspond to $3\,\sigma$ statistical-only uncertainty bands expected for the \belle II 50~ab$^{-1}$ (dashed) - and \lhcb Upgrade $50\,$fb$^{-1}$ (dotted) and $\,300\,$fb$^{-1}$ (solid) statistics. - \textbf{Figure to be updated.} + The contours correspond to $3\,\sigma$ statistical-only uncertainty bands expected for the LHCb Upgrade (dotted) + $50\,$fb$^{-1}$ and (solid) $\,300\,$fb$^{-1}$ statistics. \label{fig:Cp} } \end{figure}