% vim: set sts=4 et : \documentclass[reprint,preprintnumbers,prd,nofootinbib]{revtex4-1} \usepackage{amsfonts} \usepackage{amsmath} \usepackage{array} \usepackage{braket} \usepackage{epstopdf} \usepackage{graphicx} \usepackage{hepparticles} \usepackage{hepnicenames} \usepackage{hepunits} \usepackage{hyperref} \usepackage[% utf8 ]{inputenc} \usepackage{slashed} \usepackage{subfigure} \usepackage{placeins} \usepackage[% normalem ]{ulem} \usepackage[% usenames, svgnames, dvipsnames ]{xcolor} %% Shortcuts %% \newcommand{\ie}{\textit{i.e.}} \newcommand{\nuvec}{\vec{\nu}} \newcommand{\refapp}[1]{appendix~\ref{app:#1}} \newcommand{\refeq}[1]{eq.~(\ref{eq:#1})} \newcommand{\refeqs}[2]{eqs.~(\ref{eq:#1})--(\ref{eq:#2})} \newcommand{\reffig}[1]{figure~\ref{fig:#1}} \newcommand{\refsec}[1]{section~\ref{sec:#1}} \newcommand{\reftab}[1]{table~\ref{tab:#1}} %\let\oldtheta\theta %\renewcommand{\theta}{\vartheta} \newcommand{\eps}{\varepsilon} \newcommand{\para}{\parallel} \newcommand{\Gfermi}{G_F} %\newcommand{\dd}[2][]{{\mathrm{d}^{#1}}#2\,} \newcommand{\dd}{\ensuremath{\textrm{d}}} \newcommand{\order}[1]{\ensuremath{\mathcal{O}\left(#1\right)}} \DeclareMathOperator{\sign}{sgn} \DeclareMathOperator{\ReNew}{Re} \DeclareMathOperator{\ImNew}{Im} \let\Re\ReNew \let\Im\ImNew \DeclareMathOperator*{\sumint}{% \mathchoice% {\ooalign{$\displaystyle\sum$\cr\hidewidth$\displaystyle\int$\hidewidth\cr}} {\ooalign{\raisebox{.14\height}{\scalebox{.7}{$\textstyle\sum$}}\cr\hidewidth$\textstyle\int$\hidewidth\cr}} {\ooalign{\raisebox{.2\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr$\scriptstyle\int$\cr}} {\ooalign{\raisebox{.2\height}{\scalebox{.6}{$\scriptstyle\sum$}}\cr$\scriptstyle\int$\cr}} } \DeclareMathOperator*{\argmax}{arg\,max} \newcommand{\wilson}[2][]{\mathcal{C}^\text{#1}_{#2}} \newcommand{\op}[1]{\mathcal{O}_{#1}} \newcommand{\la}{\langle} \newcommand{\ra}{\rangle} \newcommand{\eqa}[1]{\begin{eqnarray} #1 \end{eqnarray}} \def\deriv {\ensuremath{\mathrm{d}}} \def\qsq {\ensuremath{q^2}\xspace} \def\PB {\ensuremath{\mathrm{B}}\xspace} \def\B {{\ensuremath{\PB}}\xspace} \def\PK {\ensuremath{\mathrm{K}}\xspace} \def\kaon {{\ensuremath{\PK}}\xspace} \def\Kstarz {{\ensuremath{\kaon^{*0}}}\xspace} \def\Bd {{\ensuremath{\B^0}}\xspace} \def\Bz {{\ensuremath{\B^0}}\xspace} %% Key decay channels \def\BdToKstmm {\decay{\Bd}{\Kstarz\mup\mun}} \def\BdbToKstmm {\decay{\Bdb}{\Kstarzb\mup\mun}} \def\BsToJPsiPhi {\decay{\Bs}{\jpsi\phi}} \def\BdToJPsiKst {\decay{\Bd}{\jpsi\Kstarz}} \def\BdbToJPsiKst {\decay{\Bdb}{\jpsi\Kstarzb}} %% Rare decays \def\BdKstee {\decay{\Bd}{\Kstarz\epem}} \def\BdbKstee {\decay{\Bdb}{\Kstarzb\epem}} \def\bsll {\decay{\bquark}{\squark \ell^+ \ell^-}} \def\lepton {{\ensuremath{\ell}}\xspace} \def\ellm {{\ensuremath{\ell^-}}\xspace} \def\ellp {{\ensuremath{\ell^+}}\xspace} \def\ellell {\ensuremath{\ell^+ \ell^-}\xspace} \def\mumu {{\ensuremath{\Pmu^+\Pmu^-}}\xspace} \def\lhcb {\mbox{LHCb}\xspace} \def\belle {\mbox{Belle}\xspace} \def\WC {\ensuremath{\mathcal{C}}\xspace} \begin{document} \allowdisplaybreaks \preprint{ZU-TH-15/18} \title{Supplemental material for ``Towards establishing Lepton Flavour Universality violation in $\bar{B}\to \bar{K}^*\ell^+\ell^-$ decays''} \author{Andrea Mauri} \email{a.mauri@cern.ch} \author{Nicola Serra} \email{nicola.serra@cern.ch} \author{Rafael Silva Coutinho} \email{rafael.silva.coutinho@cern.ch} \affiliation{Physik-Institut, Universit\"at Z\"urich, Winterthurer Strasse 190, 8057 Z\"urich, Switzerland} %\appendix %\section{Supplemental material} \maketitle 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.} $\WC^{\prime (\mu)}_9$ 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 $\WC^{\prime \rm{SM}}_{9,10} = 0$. 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 $\WC'^{(\mu)}_9 = \WC'^{(\mu)}_{10} = 0.3$ % \begin{figure}[h] \includegraphics[width=.4\textwidth]{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 99\% confidence level statistical-only uncertainty bands evaluated with the expected statistics after \lhcb Run II. \label{fig:Cp_Hz} } \end{figure} % 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 the LHCb upgrade with $50\,$fb$^{-1}$ and $\,300\,$fb$^{-1}$. Note that only with the full capability of the LHCb experiment it is possible to start disentangling the different NP hypotheses. % \begin{figure}[b] \includegraphics[width=.4\textwidth]{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 99\% confidence level statistical-only uncertainty bands expected for the LHCb Upgrade (dotted) $50\,$fb$^{-1}$ and (solid) $\,300\,$fb$^{-1}$ statistics. \label{fig:Cp} } \end{figure} %\FloatBarrier \end{document}