diff --git a/draft.tex b/draft.tex index 334d934..f074f28 100644 --- a/draft.tex +++ b/draft.tex @@ -361,20 +361,20 @@ the determination of $\WC_{10}^{(\mu,e)}$ is insensitive to the lack of knowledge on the non-local hadronic effects and thus independent of any model assumption. % -\begin{figure*}[bth!] -\begin{center} -\includegraphics[width=.4\textwidth]{plots/ellipses_DeltaC9C10_a.pdf}\quad\quad\quad\quad +\begin{figure}[bth!] +%\begin{center} +\includegraphics[width=.4\textwidth]{plots/ellipses_DeltaC9C10_a.pdf}\\%\quad\quad\quad\quad \includegraphics[width=.4\textwidth]{plots/ellipses_DeltaC9C10_b.pdf} \caption{% Two-dimensional sensitivity scans for the proposed observables $\Delta\WC_9$ and $\Delta\WC_{10}$ for different non-local hadronic parametrisation models - evaluated at (left) \texttt{BMP}$_{\WC_9}$ and (right) \texttt{BMP}$_{\WC_{9,10}}$, + evaluated at (top) \texttt{BMP}$_{\WC_9}$ and (bottom) \texttt{BMP}$_{\WC_{9,10}}$, and with the expected statistics after \lhcb Run II. The contours correspond to $3\,\sigma$ statistical-only uncertainty bands. \label{fig:DeltaC9C10} } -\end{center} -\end{figure*} +%\end{center} +\end{figure} The sensitivity to the two NP scenarios previously discussed using the proposed observables $\Delta \WC_i$ is shown in Fig.~\ref{fig:DeltaC9C10}. @@ -386,7 +386,7 @@ $9.0(9.6)\,\sigma$ for the \lhcb 50~fb$^{-1}$ Upgrade for the \texttt{BMP}$_{\WC_9}$ (\texttt{BMP}$_{\WC_9-\WC_{10}}$) scenario respectively. {\color{red} The two-dimensional sensitivity pull expected for the \belle II and -\lhcb Upgrades is shown in Fig.~\ref{fig:DeltaC9C10_Nev}. +\lhcb Upgrades is shown in Fig.~\ref{fig:DeltaC9C10_Upgrade}. We note that the proposed method can provide a first observation of LFU breaking in a single measurement with LHCb Run-II dataset, while for a precise determination of the nature of NP the expected statistics of future upgrades of \lhcb and \belle II is required.} @@ -400,7 +400,7 @@ for the two considered NP scenarios: (green) \texttt{BMP}$_{\WC_9}$ and (red) \texttt{BMP}$_{\WC_{9,10}}$. 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.} - \label{fig:DeltaC9C10_Nev} + \label{fig:DeltaC9C10_Upgrade} } \end{figure} @@ -454,9 +454,9 @@ would provide an historical comprehension of the underling physics. Secondly, the parameter space of the investigated WCs can naturally be broadened to incorporate direct measurement of the right-handed $\WC_i'$, currently only weakly -determined~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}, -and of possible phases in the WCs - appearing as $\Im \WC_i$ - as predicted by some -models[Ref.]. +determined by global fits~\cite{Capdevila:2017bsm,Altmannshofer:2017yso,Hurth:2017hxg}, +and of possible phases in the WCs - appearing as $\Im \WC_i$ - by mean of a separate +analysis of the two opposite charge-conjugated modes. } @@ -485,21 +485,49 @@ \section{Supplemental material} -In this supplemental material we show an extension of the physics case of the proposed method. +In this supplemental material we show an extension of the physics case of the proposed method +and investigate the sensitivity to the right-handed Wilson coefficients $\WC'^{(\mu)}_9$ and +$\WC'^{(\mu)}_{10}$. +We assume the primed WCs to be fixed at 0 (SM) for the electron 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}$_{\WC_{9,10}}$. + +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] \includegraphics[width=.4\textwidth]{plots/ellipses_CpMu_Hz.pdf} \caption{% - . + Two-dimensional sensitivity scans for the pair of Wilson coefficients $\WC'^{(\mu)}_9$ and + $\WC'^{(\mu)}_{10}$ for different non-local hadronic parametrisation models for a NP scenario + with $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$. + The contours correspond to $3\,\sigma$ statistical-only uncertainty bands evaluated with + the expected statistics after \lhcb Run II. \label{fig:Cp_Hz} } \end{figure} +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] \includegraphics[width=.4\textwidth]{plots/ellipses_CpMu.pdf} \caption{% - Figure to be updated.... + 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.} \label{fig:Cp} } \end{figure} diff --git a/plots/ellipses_CpMu.pdf b/plots/ellipses_CpMu.pdf new file mode 100644 index 0000000..a47f6ac --- /dev/null +++ b/plots/ellipses_CpMu.pdf Binary files differ diff --git a/plots/ellipses_CpMu_Hz.pdf b/plots/ellipses_CpMu_Hz.pdf new file mode 100644 index 0000000..8a034e5 --- /dev/null +++ b/plots/ellipses_CpMu_Hz.pdf Binary files differ