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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)}
\institute{UZH}
\title[Hunting for New Physics phenomena in LHCb experiment]{Hunting for New Physics phenomena in LHCb experiment}
\date{25 September 2014}
\begin{document}
\tikzstyle{every picture}+=[remember picture]
{
\setbeamertemplate{sidebar right}{\llap{\includegraphics[width=\paperwidth,height=\paperheight]{bubble2}}}
\begin{frame}[c]%{\phantom{title page}}
\begin{center}
\begin{center}
\begin{columns}
\begin{column}{0.9\textwidth}
\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Hunting for New Physics phenomena in LHCb experiment}
\end{column}
\begin{column}{0.2\textwidth}
%\includegraphics[width=\textwidth]{SHiP-2}
\end{column}
\end{columns}
\end{center}
\quad
\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em}\small \href{mailto:mchrzasz@cern.ch}{mchrzasz@cern.ch}}
\end{column}
\begin{column}{0.53\textwidth}
\includegraphics[height=1.3cm]{uzh-transp}{~}{~}
\includegraphics[height=1.1cm]{ifj.png}
\end{column}
\end{columns}
\vspace{1em}
% \footnotesize\textcolor{gray}{With N. Serra, B. Storaci\\Thanks to the theory support from M. Shaposhnikov, D. Gorbunov}\normalsize\\
\vspace{0.5em}
\textcolor{normal text.fg!50!Comment}{IFJ PAN \\November 24, 2016}
\end{center}
\end{frame}
}
\begin{frame}{Outline}
\begin{minipage}{\textwidth}
{~}\\
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% tau ->3mu
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{enumerate}
\item Why flavour is important.
\item LHCb detector.
\item Lepton Flavour Violation.
\item Dark Boson searches.
\item Electroweak penguins.
\item Measurement of Higher $\PKstar$ states in Electroweak Penguin decays.
\item Theory interpretation.
\item Disclaimers about some theory predictions.
\item Conclusions.
\end{enumerate}
\end{minipage}
\vspace*{2.cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Why flavour physics
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Why Flavour is important?
\end{Huge}
\end{center}
\end{frame}
\begin{frame}{A lesson from history - GIM mechanism}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.62\textwidth]{images/GIM2.png}
\end{center}
\begin{columns}
\column{0.7\textwidth}
\begin{itemize}
\begin{footnotesize}
\item Cabibbo angle was successful in explaining dozens of decay rates in the 1960s.
\item There was, however, one that was not observed by experiments: $\PKzero \to \Pmuon \APmuon$.
\item Glashow, Iliopoulos, Maiani (GIM) mechanism was proposed in the 1970 to fix this problem. The mechanism required the existence of a $4^{th}$ quark.
\item At that point most of the people were skeptical about that. Fortunately in 1974 the discovery of the $\PJpsi$ meson silenced the skeptics.
\end{footnotesize}
\end{itemize}
\column{0.3\textwidth}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/GIM3.png}\\
\includegraphics[width=0.7\textwidth]{images/604.jpg}\\{~}\\{~}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{A lesson from history - CKM matrix}
\begin{minipage}{\textwidth}
\begin{center}
{~}\\{~}\\
\includegraphics[width=0.5\textwidth]{images/CKMmatrix.png}
\end{center}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}
\item Similarly, CP violation was discovered in 1960s in the neutral kaons decays.
\item $2 \times 2$ Cabbibo matrix could not allow for any CP violation.
\item For CP violation to be possible one needs at least a $3 \times 3$ unitary matrix \\ $\looparrowright$ Cabibbo-Kobayashi-Maskawa matrix (1973).
\item It predicts existence of $\Pbottom$ (1977) and $\Ptop$ (1995) quarks.
\end{small}
\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.96\textwidth]{bottom.jpg}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{A lesson from history - Weak neutral current}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[height=3cm]{images/weakcurr.png}{~}
\includegraphics[height=3cm]{images/weakcurr2.png}
\end{center}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\begin{small}
\item Weak neutral currents were first introduced in 1958 by Buldman.
\item Later on they were naturally incorporated into unification of weak and electromagnetic interactions.
\item 't Hooft proved that the GWS models was renormalizable.
\item Everything was there on theory side, only missing piece was the experiment, till 1973.
\end{small}
\end{itemize}
\column{0.4\textwidth}
\begin{center}
{~}
%\includegraphics[height=2cm]{images/CP.png}\\
\includegraphics[width=0.85\textwidth]{images/bubblecern.png}
\end{center}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
LHCb detector
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% DETECTOR
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\only<1>{\frametitle{LHCb detector - tracking}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/sketch.png}
\end{columns}
\begin{itemize}
\item Excellent Impact Parameter (IP) resolution ($20~\rm \mu m$).\\
$\Rightarrow$ Identify secondary vertices from heavy flavour decays
\item Proper time resolution $\sim~40~\rm fs$.\\
$\Rightarrow$ Good separation of primary and secondary vertices.
\item Excellent momentum ($\delta p/p \sim 0.4 - 0.6\%$) and inv. mass resolution.\\
$\Rightarrow$ Low combinatorial background.
\end{itemize}
}
\only<2>{\frametitle{LHCb detector - particle identification}
\begin{columns}
\column{3in}
\includegraphics[width=0.9\textwidth]{images/1050px-Lhcbview.jpg}
\column{2in}
\includegraphics[width=0.95\textwidth]{images/cher.png}
\end{columns}
\begin{itemize}
\item Excellent Muon identification $\epsilon_{\mu \to \mu} \sim 97\%$, $\epsilon_{\pi \to \mu} \sim 1-3\%$
\item Good $\PK-\Ppi$ separation via RICH detectors, $\epsilon_{\PK \to \PK} \sim 95\%$, $\epsilon_{\Ppi \to \PK} \sim 5\%$.\\
$\Rightarrow$ Reject peaking backgrounds.
\item High trigger efficiencies, low momentum thresholds.
Muons: $p_T > 1.76 \GeV$ at L0, $p_T > 1.0 \GeV$ at HLT1,\\
$B \to \PJpsi X $: Trigger $\sim 90\%$.
\end{itemize}
}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
Lepton Flavour Violation
\end{Huge}
\end{center}
\end{frame}
\begin{frame}\frametitle{Lepton Flavour/Number Violation}
\begin{enumerate}
\item Lepton Flavour Violation (LFV) found in neutrino sector - the first phenomena outside the Standard Model.
\item The search for charged lepton flavour violation (CLFV) commenced with muon discovery (1936) and its identification as a separate particle.
\end{enumerate}
\begin{columns}
\column{3in}
\begin{itemize}
\item Expected: $B(\mu\to\Pe\gamma) \approx 10^{-4}$
\item Unless there is another $\Pnu$.
\end{itemize}
\column{2in}
{~}\includegraphics[width=0.98\textwidth]{images/rabi.png}
\end{columns}
\begin{footnotesize}
\begin{enumerate}
\setcounter{enumi}{2}
\item The observation of CLFV would be a clear signature of New Physics (NP) - paramount importance for flavour physics and the enigma of generations.
\item LFV vs LNV (Lepton Number Violation)
\end{enumerate}\end{footnotesize}
\begin{columns}
\column{3.5in}
\begin{footnotesize}
\begin{itemize}
\item Even with LFV, lepton number can be a conserved quantity.
\item Many NP models predict LNV (Majorana neutrinos)
\item LNV searched in so-called neutrinoless double $\beta$ decays.
\end{itemize}
\end{footnotesize}
\column{1.5in}
\includegraphics[width=0.65\textwidth]{images/Double_beta_decay_feynman.png}
\end{columns}
% \textref{M.Chrz\k{a}szcz 2014}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Status of searches for $ \tau \to \mu \mu \mu$}
\begin{columns}
\begin{column}{.55\textwidth}
\includegraphics[width=.90\textwidth]{feymn.png}
{{
\begin{small}
\begin{itemize}
\item Charged Lepton Flavour Violation process.
\item The Standard Model contribution: penguin diagram with neutrino oscillation.
\item Negligible SM branching fraction.
\item Large enhacement from NP models like: SUSY, Little Higgs, Fourth generation, etc.
% \item SM prediction is beyond experimental reach~$O(10^{-40})$.
\end{itemize}
\end{small}
}}
\end{column}
\begin{column}{.45\textwidth}
\begin{alertblock}{Predictions}
\begin{description}
\item[SM] $ O(10^{-40})$
\item[var.\ SUSY] $10^{-10}$
\item[non universal $\color{green}{Z'}$] $10^{-8}$
\item[mSUGRA+seesaw] $10^{-9}$
\item[and many more...]
\end{description}
\end{alertblock}
\begin{alertblock}{Current limits ($ \color{white} 90\,\%$ CL)}
\begin{description}
\item[BaBar] $3.3\times 10^{-8}$
\item[Belle] $2.1\times 10^{-8}$
\end{description}
\end{alertblock}
\includegraphics[width=.63\textwidth]{SUSY.png}
\end{column}
\end{columns}
\end{frame}
\iffalse
\begin{frame} \frametitle{Strategy}
\begin{enumerate}
\item Data sample: $1 \invfb~7~\TeV$ and $2 \invfb~8\TeV$.
\item Normalization (control) decay channel: $\PDs\to\Pphi(\Pmu\Pmu)\Ppi$.
\item Blind analysis in the region of $| m_{\mu\mu\mu} - m_{\tau} | <20~\MeV/c^2$.
\item Event selection:
\begin{itemize}
\item Preselection of three tracks that combine to give a mass close to $m_{\tau}$, with displaced vertex.
\item Selection based on three classifiers:
\begin{itemize}
\item Geometry and topology ($\mathcal{M}_{3body}$) - multivariate classifier
\item PID ($\mathcal{M}_{PID}$) - multivariate classifier
\item Three muon invariant mass ($m_{\mu\mu\mu}$)
\end{itemize}
\end{itemize}
\item Major background contributions:$\PDs \to \eta(\mu\mu\gamma) \mu \nu$ and $\PD \to \PK \Ppi \Ppi$ decays.
\item Evaluation of the upper limit on $\mathcal{B}(\Ptau \to \Pmu \Pmu \Pmu)$ using $\rm CL_s$ method.
\end{enumerate}
\end{frame}
\fi
\begin{frame}
\frametitle{$\tau$ production at LHCb}
\begin{itemize}
\item $\Ptau$'s in LHCb come from five main sources:
\end{itemize}
\begin{center}
\begin{tabular}{| c | c | c | }
\hline
Mode & $7~\TeV$ & $8~\TeV$ \\ \hline
Prompt $\PDs\to\Ptau$ & $71.1\pm3.0\,\%$ & $72.4\pm2.7\,\%$ \\
Prompt $\PDplus\to\Ptau$ & $4.1\pm0.8\,\%$ & $4.2\pm0.7\,\%$ \\
Non-prompt $\PDs\to\Ptau$ & $9.0\pm2.0\,\%$ & $8.5\pm1.7\,\%$ \\
Non-prompt $\PDplus\to\Ptau$ & $0.18\pm0.04\,\%$ & $0.17\pm0.04\,\%$ \\
$X_{\Pbottom}\to\Ptau$ & $15.5\pm2.7\,\%$ & $14.7\pm2.3\,\%$ \\ \hline
\end{tabular}
\end{center}
\begin{columns}
\column{0.8\textwidth}
\begin{exampleblock}{$\mathcal{B}(\PDplus\to\Ptau)$}
\begin{itemize}
\item There is no measurement of $\mathcal{B}(\PDplus\to\Ptau)$.
\item One can calculate it from: $\mathcal{B}(\PDplus\to\Pmu\Pnum)$ + helicity suppression + phase space.
\item \texttt{hep-ex:0604043}.
\item $\mathcal{B}(\PDplus\to\Ptau\Pnut)=(1.0\pm0.1) \times10^{-3}$.
\end{itemize}
\end{exampleblock}
\column{0.2\textwidth}
{~}
\end{columns}
\end{frame}
\begin{frame}
\frametitle{Multivariate Analysis}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.1in}
{~}\\
\column{2.9in}
\ARROW First usage of of the blending \\technique in HEP!\\
\ARROW Each $\tau$ source has it's own ''targer'' classifier.\\
\ARROW 5 classifiers are then ''blended'' together.\\
\ARROW Gain $6\%$ on signal efficiency.\\
\begin{exampleblock}{}
Up to today the most advanced MVA used in LHCb!
\end{exampleblock}
~\\
\ARROW Calibrated on data using $\PDs \to \phi \pi$
\includegraphics[angle=-90,width=.6\textwidth]{m3body_2012.pdf}
\column{2in}
\includegraphics[width=.99\textwidth]{images/diagram.png}\\
\includegraphics[angle=-90, width=.98\textwidth]{images/mixing.pdf}
\end{columns}
\end{minipage}
\end{frame}
\iffalse
\begin{frame}
\frametitle{Optimization}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\begin{itemize}
\item Events are distributed among $\mathcal{M}_{3body}, \mathcal{M}_{PID}$ plane.
\item In 2D we collect the events in groups(bins)
\item Bins are optimised using $CL_s$ method:
\begin{equation}
CL_s = \dfrac{\prod_{i=1}^{N_{\text{chan}}}\sum_{n=0}^{n_i} \dfrac{e^{-(s_i+b_i)} (s_i+b_i)^{n}}{n!} }{\prod_{i=1}^{n_{\text{chan}}} \sum_{n=0}^{n_i} \dfrac{e^{-b_i} b_i^{n}}{n!}} \nonumber~,
\end{equation}
\end{itemize}
\end{footnotesize}
\begin{center}
\includegraphics[width=.6\textwidth]{images/rank.pdf}
\end{center}
\end{minipage}
\end{frame}
\fi
\iffalse
\begin{frame}
\frametitle{Relative normalisation}
$\boxed{\mathcal{B}(\Ptau\to\Pmu\Pmu\Pmu) = \frac{\mathcal{B}(\PDs\to\Pphi\Ppi)}{\mathcal{B}(\PDs\to\Ptau\Pnut)} \times f_{\PDs}^{\Ptau} \times \frac{\varepsilon_\text{norm} }{\varepsilon_\text{sig} } \times \frac{N_\text{sig}}{N_\text{norm}} = \alpha\times N_\text{sig}}$
\begin{itemize}
\item where $\varepsilon$ stands for trigger, reconstruction, selection efficiency.
\item $f_{\PDs}^{\Ptau}$ is the fraction of $\Ptau$ coming from $\PDs$.
\item $\text{norm}$ = normalisation channel $\PDs\to\Pphi\Ppi$
\newline i.e.\ $(83\pm3)\,\%$ for 2012 data.
\end{itemize}
\begin{columns}
\column{2.3in}
\center{2011}\\
\includegraphics[angle=-90,width=.97\textwidth]{images/Ds_data_2011.pdf}
\column{2.3in}
\center{2012}\\
\includegraphics[angle=-90,width=.97\textwidth]{images/Ds_data_2012.pdf}
\end{columns}
\end{frame}
\fi
\begin{frame}
\frametitle{Model dependence}
\begin{itemize}
\begin{small}
\item Model description in \href{http://arxiv.org/abs/0707.0988}{\color{blue}\texttt{arXiv:0707.0988}} by S.Turczyk using Effective Field Theory approach.
\item 5 relevant Dalitz distributions: 2 four-point operators, 1 radiative operator, 2 interference terms.
\item All five cases implemented in TAUOLA.
\end{small}
\end{itemize}
\only<1>{
\begin{columns}
\column{0.33\textwidth}
\includegraphics[angle=-90,width=.78\textwidth]{images/LLLL.pdf}\\
\includegraphics[angle=-90,width=.78\textwidth]{images/LLRR.pdf}\\
\column{0.33\textwidth}
\includegraphics[angle=-90,width=.78\textwidth]{images/LLLLRAD.pdf}\\
\includegraphics[angle=-90,width=.78\textwidth]{images/LLRRRAD.pdf}
\column{0.33\textwidth}
\includegraphics[angle=-90,width=.78\textwidth]{images/RAD.pdf}\\
\begin{small}
\begin{exampleblock}{}
M.Chrzaszcz, T.Przedzinski, Z.Was, J.Zareba\\ \href{https://arxiv.org/abs/1609.04617}{\color{blue}\texttt{arXiv:1609.04617 }}\\{~}\\
\end{exampleblock}
{~}\\
\end{small}
% \begin{itemize}
% \item Same models as in Z.Was \href{https://indico.cern.ch/event/300387/session/7/contribution/33}{\color{blue}talk}
% \end{itemize}
%{~}\\ {~}\\
\end{columns}
}
\end{frame}
\begin{frame}
\frametitle{Results}
\begin{center}
\includegraphics[angle=-90,width=0.65\textwidth]{banana_line.pdf}
\end{center}
\begin{columns}
\column{0.2in}{~}
\column{2in}
Limits(PHSP):\\
Observed(Expected)\\
$\color{red}4.6~(5.0)\times 10^{-8}$ at $90\%$ CL\\
$\color{pink}5.6~(6.1)\times 10^{-8}$ at $95\%$ CL\\
\column{3in}
\includegraphics[width=0.5\textwidth]{model.png}
\end{columns}
\end{frame}
\begin{frame}\frametitle{Combination of LFV UL}
\ARROW To ''squeeze'' the most of the LFV New Physics exclusions there was an idea to combine the limits for LHCb and B factories.\\
\ARROW As a result I have been enrolled as HFAG member.\\
\begin{exampleblock}{}
$\tau \to \mu \mu \mu$ is the most cited number of the HFAG report!!!\\
\end{exampleblock}
{~}\\
\includegraphics[width=0.9\textwidth]{images/TauLFV_UL_2014001_averaged.png}
\begin{exampleblock}{}
\texttt{arXiv:1412.7515}, [HFAG, M.Chrzaszcz, et. al.]
\end{exampleblock}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
Dark Boson searches
\end{Huge}
\end{center}
\end{frame}
\begin{frame}\frametitle{Generalize Higgs potential}
\begin{minipage}{\textwidth}
\begin{small}
\ARROW The model is extremely simple:
\begin{align*}
V(H,S)=V_H + V_{\rm mix} + V_S,
\end{align*}
where
\begin{columns}
\column{0.1in}
{~}\\
\column{2.9in}
\begin{align*}
V_H = -\mu^2 H^{\dag}H + \lambda_H (H^{\dag} H)^2\\
V_{\rm mix} = \frac{a_1}{2}\left(H^{\dag}H\right)S + \frac{a_2}{2}\left(H^{\dag}H\right)S^2\\
V_S = \frac{b_2}{2}S^2 + \frac{b_3}{3}S^3 + \frac{b_4}{4}S^4
\end{align*}
\column{2in}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/h.png}
\end{center}
\end{columns}
\ARROW The main advantage of this potential is that it fixes the inflation problem.\\
\ARROW Now the Lagrangian needs to be written in physical degrees of freedom\\
\ARROW Then you generate the mass is given(see backup for details):
\begin{align*}
\begin{pmatrix}
h \\
s
\end{pmatrix}=
\begin{pmatrix}
\sin \theta & \cos \theta \\
\cos \theta & \sin \theta
\end{pmatrix}
\begin{pmatrix}
s^{\prime}\\
h^{\prime}
\end{pmatrix}
\end{align*}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}\frametitle{Implications for Flavour}
\begin{minipage}{\textwidth}
\begin{small}
{~}\\
\ARROW The mixing angle between the Higgs and the Inflaton has to be small.\\
\ARROW Typically if $m_H=125~\GeV$ then $m_S \sim \mathcal{O}(1)~\GeV$.\\
\ARROW If yes we can look for this in $\PB$ decays:
\begin{columns}
\column{0.1in}
{~}\\
\column{3.4in}
\begin{equation}
{\rm Br} (\PB \to \chi X_s) ~\sim 10^{-6}\left(1-\frac{m^2_{\chi}}{m^2_b}\right) \left(\frac{\beta}{\beta_0}\right) \left(\frac{300{\rm MeV}}{m_{\chi}}\right)\nonumber
\end{equation}
\column{1.5in}
\begin{center}
\includegraphics[width=0.95\textwidth]{images/diagram.pdf}
\end{center}
\end{columns}
\ARROW The inflaton has a small width and non zero life-time. \\
\ARROW The analysis is a peak search.\\
\begin{exampleblock}{}
It has passed the collaboration review and will be shown first time by my PhD student at the Epiphany conference.
\end{exampleblock}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}\frametitle{RIP Inflaton}
\begin{minipage}{\textwidth}
\begin{small}
\begin{center}
\includegraphics[angle=-90,width=0.9\textwidth]{{images/Inflaton_parameter_space_log}.pdf}
\end{center}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\iffalse
\begin{frame}[c]{The inflaton model, so what?}
\begin{minipage}{\textwidth}
\begin{small}
{~}\\
\ARROW Now if we look how many of the $X_s$ are $\PK$ and $\PKstar$ we define the variables:
\begin{align*}
r_K = \frac{\PB \to \PK \chi}{\PB \to X_s \chi}~~~~r_{\PKstar} = \frac{\PB \to \PKstar \chi}{\PB \to X_s \chi}
\end{align*}
\includegraphics[width=0.45\linewidth]{images/rk_graph.png}
\includegraphics[width=0.45\linewidth]{images/rkstar.png} \\
{~}\\
\ARROW So the assumption about $33~\%$ was generous assumption.
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\fi
\begin{frame}
\begin{center}
\begin{Huge}
Electroweak penguins
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Why Electroweak penguins?}
\begin{columns}
\column{4in}
\begin{itemize}
\item The SM allows only the charged interactions to change flavour.
\begin{itemize}
\item Other interactions are flavour conserving.
\end{itemize}
\item One can escape this constraint and produce $\Pbottom \to \Pstrange$ and $\Pbottom \to \Pdown$ at loop level.
\begin{itemize}
\item These kind of processes are suppressed in SM $\to$~Rare decays.
\item New Physics can enter in the loops.
\end{itemize}
\end{itemize}
\begin{center}
\includegraphics[scale=0.3]{lupa.png}
\includegraphics[scale=0.3]{example.png}
\end{center}
\column{1.5in}
\includegraphics[width=0.61\textwidth]{couplings.png}
\end{columns}
\end{frame}
\begin{frame}{Tools in rare $\PBzero$ decays}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item \textbf{Operator Product Expansion and Effective Field Theory}
\end{itemize}
\begin{columns}
\column{0.1in}{~}
\column{3.2in}
\begin{footnotesize}
\begin{align*}
H_{eff} = - \dfrac{4G_f}{\sqrt{2}} V V^{\prime \ast}\ \sum_i \left[\underbrace{C_i(\mu)O_i(\mu)}_\text{left-handed} +\
\underbrace{C'_i(\mu)O'_i(\mu)}_\text{right-handed}\right],
\end{align*}
\end{footnotesize}
\column{2in}
\begin{tiny}
\begin{description}
\item[i=1,2] Tree
\item[i=3-6,8] Gluon penguin
\item[i=7] Photon penguin
\item[i=9.10] EW penguin
\item[i=S] Scalar penguin
\item[i=P] Pseudoscalar penguin
\end{description}
\end{tiny}
\end{columns}
where $C_i$ are the Wilson coefficients and $O_i$ are the corresponding effective operators.
\begin{center}
\includegraphics[width=0.85\textwidth,height=3cm]{images/all.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\iffalse
\begin{frame}{Analysis of Rare decays}
\begin{footnotesize}
%{\Large Since a long time ago...} \\ \medskip
%\hspace*{1.4cm}$\Rightarrow$ $b \to s \gamma$ and $b \to s \ell\ell $ {\bf Flavour Changing Neutral Currents} have been used as {\bf \cred Our Portal} \\ to explore the fundamental theory beyond SM. \\
%\medskip
%\medskip
%\hfill....... with not much success till 2013.\hspace*{1cm}
%\bigskip
Analysis of FCNC in a model-independent approach, effective Hamiltonian:
\vspace*{-0.1cm}
\begin{columns}
\begin{column}{1cm}
~
\end{column}
\begin{column}{8cm}
\begin{equation*}
b\to s\gamma(^*): {\mathcal H}^{SM}_{\Delta F=1} \propto
\sum_{i=1}^{10} V_{ts}^* V_{tb} {\cgreen \C{i}} \alert{ {\cal O}_i} + \ldots
\end{equation*}
\vspace{-0.2cm}
\begin{itemize}
\item $\alert{ {\cal O}_7} = \frac{e}{16 \pi^2}m_b\,
(\bar s\sigma^{\mu\nu} P_R b) F_{\mu\nu}\,$ %\quad [real or soft photon]
\item $\alert{ {\cal O}_9}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b)\ (\bar\ell\gamma_\mu\ell)$
%\quad [$b\to s\mu\mu$ via $Z$/hard $\gamma$]
\item $\alert{ {\cal O}_{10}}=\frac{e^2}{16 \pi^2}(\bar{s}\gamma_\mu P_L b) \ (\bar\ell\gamma_\mu\gamma_5\ell)$, ...
%\quad [$b\to s\mu\mu$ via $Z$]
\end{itemize}
\end{column}
\begin{column}{5.5cm}
\includegraphics[width=3.5cm]{images/qum1.png}
%\includegraphics[width=3cm]{bsll.pdf}
\end{column}
\end{columns}
%\hspace*{5cm} with no clear success yet...
%\bigskip
%\centerline{{\bf Goal}: \underline{Decode the short distance physics to find a smoking gun of BSM}\hspace*{2cm}}
\bigskip
\hspace*{0.0cm} $\bullet$ {\bf SM} Wilson coefficients up to NNLO + e.m. corrections at $\mu_{ref}=4.8$ GeV [{\cgreen Misiak et al.}]: $${\cal C}_7^{\rm SM}=-0.29,\, {\cal C}_9^{\rm SM}=4.1,\, {\cal C}_{10}^{\rm SM}=-4.3$$
%BUT, like in the film there is always the good, the bad and the ugly.
\bigskip
$\bullet$ {\bf NP} changes short distance ${\cal C}_i-{\cal C}_i^{\rm SM}={\cal C}_i^{\rm NP}$ and induce new operators, like ${\cal O}^\prime_{7,9,10}={\cal O}_{7,9,10}\,\, (P_L \leftrightarrow P_R)$ ... also scalars, pseudoescalar, tensor operators...%\bigskip
\end{footnotesize}
\end{frame}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iffalse
%%%%%%%%%%%%%%%%%%%%5
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$, where it all begun}
{~}
\begin{minipage}{\textwidth}
\only<1>{
\begin{columns}
\column{0.6\textwidth}
August 2013:\\
\includegraphics[width=0.95\textwidth]{images/P5prime.png}
\column{0.4\textwidth}
\begin{itemize}
\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
\item It turned out that the discrepancy occurred in an observable that was not constrained.
\item $q^2$ is the dimuon invariant mass.
\end{itemize}
\end{columns}
}
\only<2>{
\begin{columns}
\column{0.6\textwidth}
August 2013:\\
\includegraphics[width=0.95\textwidth]{images/P5prime.png}
\column{0.4\textwidth}
\begin{itemize}
\item LHCb observed a deviation in $4.3-8.68~\GeV^2$ using $1~\invfb$ of data.
\item It turned out that the discrepancy occurred in an observable that was not constrained.
\end{itemize}
\end{columns}
\begin{exampleblock}{}
Now let's move back and see the theory behind the $\PBzero \to \PKstar \Pmuon \APmuon$ and $P_5^{\prime}$.
\end{exampleblock}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
\only<1>{
{\tiny{
\eqa{\label{dist}
\frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
\frac{3}{4} (1- F_L) \sin^2\theta_K + F_L \cos^2\theta_K \nn\\[1.5mm] &&\hspace{-2.7cm} + \left(\frac{1}{4}(1-F_L) \sin^2\theta_K - F_L \cos^2\theta_K\right) \cos 2\theta_l\nn\\[1.5mm]
&&\hspace{-2.7cm}+ S_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + S_4 \sin 2\theta_K \sin 2\theta_l \cos\phi + S_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ (S_{6s} \sin^2\theta_K + {S_{6c} \cos^2\theta_K}) \cos\theta_l
+ S_7 \sin 2\theta_K \sin\theta_l \sin\phi + S_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ S_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
\nonumber}
}}
$\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\iffalse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Transversity amplitudes }
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ One can link the angular observables to transversity amplitudes
{\tiny{
\eqa{
J_{1s} & = & \frac{(2+\beta_\ell^2)}{4} \left[|\apeL|^2 + |\apaL|^2 +|\apeR|^2 + |\apaR|^2 \right]
+ \frac{4 m_\ell^2}{q^2} \re\left(\apeL\apeR^* + \apaL\apaR^*\right)\,,\nn\\[1mm]
%
J_{1c} & = & |\azeL|^2 +|\azeR|^2 + \frac{4m_\ell^2}{q^2} \left[|A_t|^2 + 2\re(\azeL^{}\azeR^*) \right] + \beta_\ell^2\, |A_S|^2 \,,\nn\\[1mm]
%
J_{2s} & = & \frac{ \beta_\ell^2}{4}\left[ |\apeL|^2+ |\apaL|^2 + |\apeR|^2+ |\apaR|^2\right],
\hspace{0.92cm} J_{2c} = - \beta_\ell^2\left[|\azeL|^2 + |\azeR|^2 \right]\,,\nn\\[1mm]
%
J_3 & = & \frac{1}{2}\beta_\ell^2\left[ |\apeL|^2 - |\apaL|^2 + |\apeR|^2 - |\apaR|^2\right],
\qquad J_4 = \frac{1}{\sqrt{2}}\beta_\ell^2\left[\re (\azeL\apaL^* + \azeR\apaR^* )\right],\nn \\[1mm]
%
J_5 & = & \sqrt{2}\beta_\ell\,\Big[\re(\azeL\apeL^* - \azeR\apeR^* ) - \frac{m_\ell}{\sqrt{q^2}}\,
\re(\apaL A_S^*+ \apaR^* A_S) \Big]\,,\nn\\[1mm]
%
J_{6s} & = & 2\beta_\ell\left[\re (\apaL\apeL^* - \apaR\apeR^*) \right]\,,
\hspace{2.25cm} J_{6c} = 4\beta_\ell\, \frac{m_\ell}{\sqrt{q^2}}\, \re (\azeL A_S^*+ \azeR^* A_S)\,,\nn\\[1mm]
%
J_7 & = & \sqrt{2} \beta_\ell\, \Big[\im (\azeL\apaL^* - \azeR\apaR^* ) +
\frac{m_\ell}{\sqrt{q^2}}\, \im (\apeL A_S^* - \apeR^* A_S)) \Big]\,,\nn\\[1mm]
%
J_8 & = & \frac{1}{\sqrt{2}}\beta_\ell^2\left[\im(\azeL\apeL^* + \azeR\apeR^*)\right]\,,
%
\hspace{1.9cm} J_9 = \beta_\ell^2\left[\im (\apaL^{*}\apeL + \apaR^{*}\apeR)\right] \,,
\label{Js}\nonumber}
}}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Link to effective operators}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ So here is where the magic happens. At leading order the amplitudes can be written as:
{\tiny{
\eqa{
\apeLR &=&\sqrt{2} N m_B(1- \hat s)\bigg[ (\Ceff9 + \Cpeff9) \mp (\C{10} + \Cp{10})
+\frac{2\hat{m}_b}{\hat s} (\Ceff7 + \Cpeff7) \bigg]\xi_{\bot}(E_{K^*}) \nn \\[2mm]
\apaLR &=& -\sqrt{2} N m_B (1-\hat s)\bigg[(\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10})
+\frac{2\hat{m}_b}{\hat s}(\Ceff7 - \Cpeff7) \bigg] \xi_{\bot}(E_{K^*}) \nn \\[2mm]
\azeLR &=& -\frac{N m_B (1-\hat s)^2}{2 \hat{m}_{K^*} \sqrt{\hat s}} \bigg[ (\Ceff9 - \Cpeff9) \mp (\C{10} - \Cp{10}) + 2\hat{m}_b (\Ceff7 - \Cpeff7) \bigg]\xi_{\|}(E_{K^*}),
\label{LargeRecoilAs}\nonumber}
}}
where $\hat s = q^2 /m_B^2$, $\hat{m}_i = m_i/m_B$. The $\xi_{\|,\bot }$ are the form factors. \\
\only<1>{
\ARROW In practice one measures normalized $J$ by branching fractions:
\begin{equation*}
S_i/A_i = \frac{J_i \pm \overline{J}_i}{d\Gamma + d \overline{\Gamma}/dq^2}
\end{equation*}
}
\only<2>{
$\color{JungleGreen}{\Rrightarrow}$ Now we can construct observables that cancel the $\xi$ form factors at leading order:
\eq{P_5^{\prime} = \dfrac{J_5+\bar{J}_5}{2\sqrt{-(J_2^c+\bar{J}_2^c)(J_2^s+\bar{J}_2^s)} }\nonumber
}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
LHCb measurement of $\PBd \to \PKstar \Pmu \Pmu$
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{LHCbs $\PBzero \to \PKstar \Pmuon \APmuon$, Selection}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\begin{columns}
\column{0.2in}
{~}
\column{2in}
\ARROW Trigger
\begin{itemize}
\item Muon trigger.
\item Topological trigger.
\end{itemize}
\ARROW Good modelling with MC. \\
\ARROW Selection:
\begin{itemize}
\item As loose as possible.
\item Based on the $\PBzero$ vertex quality, impact parameters, loose Particle identification for the hadrons.
\item The variables were chosen in a way we are sure the are correctly modelled in MC.
\end{itemize}
\column{2.8in}
\includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_pt}.pdf}\\
\includegraphics[angle=-90,width=0.75\textwidth]{{images/tistos_L0Muon_costhetal}.pdf}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\fi
\iffalse
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Peaking backgrounds}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW A number of peaking backgrounds that can mistaken as your signal.\\
\ARROW There where a specially designed vetoes to fight each of them.
\begin{center}
\begin{tiny}
\hspace{-1cm}\begin{tabular}{ r | c c | c c }
\hline
& \multicolumn{2}{c|}{after preselection, before vetoes} & \multicolumn{2}{c }{after vetoes and selection}\\
Channel & Estimated events & \% signal & Estimated events & \% signal \\
\hline
\hline
$\PLambda_b \to \PLambda^{\ast}(1520)^{0} \mu\mu$ &$ (1.0\pm0.5)\times10^3 $&$ 19\pm8 $&$ 51\pm25 $&$ 1.0\pm0.4$\\
$\PLambda_b \to {\rm p } \PK \mu\mu$ &$ (1.0\pm0.5)\times10^2 $&$ 1.9\pm0.8 $&$ 5.7\pm2.8 $&$ 0.11\pm0.05$ \\
$\PBd \to \PKplus \mu \mu$ &$ 28\pm7 $&$ 0.55\pm0.06 $&$ 1.6\pm0.5 $&$ 0.031\pm0.006$\\
$\PBs \to \Pphi \mu \mu$ &$ (3.2\pm1.3)\times10^2 $&$ 6.2\pm2.1 $&$ 17\pm7 $&$ 0.33\pm0.12$\\
signal swaps &$ (3.6\pm0.9)\times10^2 $&$ 6.9\pm0.6 $&$ 33\pm9 $&$ 0.64\pm0.06$ \\
$\PBd \to \PKstar \PJpsi$ swaps &$ (1.3\pm0.4)\times10^2 $&$ 2.6\pm0.4 $&$ 2.7\pm2.8 $&$ 0.05\pm0.05$ \\
\hline
\end{tabular}
\end{tiny}
\includegraphics[angle=-90,width=0.49\textwidth]{{images/h_Bd_Kstmm_vetoes}.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{{h_Lb_L1520mm_vetoes}.pdf}
\end{center}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Multivariate simulation}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.5\textwidth}
\begin{itemize}
\begin{footnotesize}
\item PID, kinematics and isolation variables used in a Boosted Decision Tree (BDT) to discriminate signal and background.
\item BDT with k-Folding technique.
\item Completely data driven.
\end{footnotesize}
\end{itemize}
\begin{footnotesize}
\begin{exampleblock}{}
The k-Folding became a standard in LHCb
\end{exampleblock}
\end{footnotesize}
\begin{center}
\includegraphics[width=0.70\textwidth]{images/Chopping_Distrib.pdf}
\end{center}
\column{0.5\textwidth}
\includegraphics[angle=-90,width=0.82\textwidth]{images/Fig1.pdf} \\
\includegraphics[width=0.88\textwidth]{images/fold.png}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Multivariate simulation, efficiency}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW BDT was also checked in order not to bias our angular distribution:
\begin{center}
\includegraphics[angle=-90,width=0.8\textwidth]{images/BDT_Eff_Comp.pdf}
\end{center}
\ARROW The BDT has small impact on our angular observables. We will correct for these effects later on.
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\iffalse
\begin{frame}{Mass modelling}
{~}
\begin{minipage}{\textwidth}
\begin{tiny}
\begin{columns}
\column{0.1in}
{~}
\column{2.5in}
\ARROW The signal is modelled by a sum of two Crystal-Ball functions with common mean.\\
\ARROW The background is a single exponential.\\
\ARROW The base parameters are obtained from the proxy channel: $\PBd \to \PJpsi (\mu\mu) \PKstar$.\\
\ARROW All the parameters are fixed in the signal pdf.\\
\ARROW Scaling factors for resolution are determined from MC.\\
\ARROW In fitting the rare mode only the signal, background yield and the slope of the exponential is left floating.\\
\begin{center}
\includegraphics[angle=-90,width=0.9\textwidth]{images/msignal.pdf}\\
\end{center}
\ARROW We found $624\pm30$ candidates in the most interesting $\left[1.1,6.0\right]~\GeV^2/c^4$ region \\ and $2398 \pm 57$ in the full range $\left[ 1.1, 19.\right]~\GeV^2/c^4$.
\column{2.5in}
\includegraphics[angle=-90,width=0.95\textwidth]{{images/FitJpsiKstar_withBDT_withoutPartially}.pdf}\\
\includegraphics[angle=-90,width=0.95\textwidth]{{images/Scaling_factor}.pdf}\\
\ARROW The S-wave fraction is extracted using a \texttt{LASS} model.
\end{columns}
\end{tiny}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Monte Carlo corrections}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\ARROW No Monte Carlo simulation is perfect! One needs to correct for remaining differences.\\
\ARROW We reweighted our $\PBd \to \PKstar \mu \mu$ Monte Carlo accordingly to differences between the $\PBd \to \PKstar \PJpsi$ in data (Splot) and Monte Carlo.
\only<1>{
\begin{center}
\includegraphics[angle=-90,width=0.38\textwidth]{images/pt.pdf}
\includegraphics[angle=-90,width=0.38\textwidth]{images/vertex.pdf}\\
\includegraphics[angle=-90,width=0.38\textwidth]{images/nTracks.pdf}
\end{center}
}
\only<2>{
\begin{center}
\includegraphics[angle=-90,width=0.38\textwidth]{images/eta_logy.pdf}
\includegraphics[angle=-90,width=0.38\textwidth]{images/B0_p.pdf} \\
\includegraphics[angle=-90,width=0.38\textwidth]{{images/bdt_data_mc_nominalMkpi}.pdf}
\end{center}
}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\fi
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Detector acceptance}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\begin{columns}
\column{0.6\textwidth}
\begin{itemize}
\item Detector distorts our angular distribution.
\item We need to model this effect.
\item 4D function is used:
\begin{align*}
\epsilon (\cos \thetal, \cos \thetak, \phi, q^2) = \\\sum_{ijkl} P_i(\cos \thetal) P_j(\cos \thetak ) P_k(\phi) P_l(q^2),
\end{align*}
where $P_i$ is the Legendre polynomial of order $i$.
\item We use up to $4^{th}, 5^{th}, 6^{th}, 5^{th}$ order for the $\cos \thetal, \cos \thetak, \phi, q^2$.
\item The coefficients were determined using Method of Moments, with a huge simulation sample.
\item The simulation was done assuming a flat phase space and reweighing the $q^2$ distribution to make is flat.
\item To make this work the $q^2$ distribution needs to be reweighted to be flat.
\end{itemize}
%\includegraphics[width=0.75\textwidth]{images/q2PHSP.png}
\column{0.4\textwidth}
%\only<1>{
%\includegraphics[width=0.99\textwidth]{images/q2PHSP.png}\\
%\includegraphics[width=0.99\textwidth]{images/q2PHSPw.png}
%}
\only<1>{
\includegraphics[width=0.99\textwidth]{images/det.png}
}
\end{columns}
\end{footnotesize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Control channel}
{~}
\begin{minipage}{\textwidth}
\begin{footnotesize}
\begin{itemize}
\item We tested our unfolding procedure on $\PB \to \PJpsi \PKstar$.
\item The result is in perfect agreement with other experiments and our different analysis of this decay.
\end{itemize}
\end{footnotesize}
\begin{center}
\includegraphics[angle=-90,width=0.4\textwidth]{images/mlogjpsi.pdf}
\includegraphics[angle=-90,width=0.4\textwidth]{images/mkpijpsi.pdf}\\
\includegraphics[width=0.99\textwidth]{images/angles3.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The columns of New Physics}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.94\textwidth]{images/columns.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{The columns of New Physics}
{~}
\begin{minipage}{\textwidth}
\begin{enumerate}
\item Maximum likelihood fit:
\begin{itemize}
\item The most standard way of obtaining the parameters.
\item Suffers from convergence problems, under coverages, etc. in low statistics.
\end{itemize}
\item Method of moments:
\begin{itemize}
\item Less precise then the likelihood estimator ($10-15\%$ larger uncertainties).
\item Does not suffer from the problems of likelihood fit.
\end{itemize}
\item Amplitude fit:
\begin{itemize}
\item Incorporates all the physical symmetries inside the amplitudes! The most precise estimator.
\item Has theoretical assumptions inside!
\end{itemize}
\end{enumerate}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - Results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW In the maximum likelihood fit one could weight the events accordingly to the $\dfrac{1}{\varepsilon(\cos \thetal, \cos \thetak, \phi, q^2)}$\\
\ARROW Better alternative is to put the efficiency into the maximum likelihood fit itself:
\begin{align*}
\mathcal{L}=\prod_{i=1}^N \epsilon_i(\Omega_i, q_i^2) \mathcal{P}(\Omega_i, q_i^2) / \int \epsilon(\Omega, q^2) \mathcal{P}(\Omega, q^2) d\Omega dq^2
\end{align*}
\ARROW Only the relative weights matters!\\
\ARROW The Procedure was commissioned with TOY MC study.\\
\ARROW Use Feldmann-Cousins to determine the uncertainties. \\
\ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands.\\
\ARROW S-wave component treated as nuisance parameter.\\
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_Afb3}.pdf}
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P11}.pdf}
\includegraphics[angle=-90,width=0.33\textwidth]{{images/FC_P57}.pdf}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - Results}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\only<1>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/FLPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/S3Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/S4Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/S5Pad.pdf}
}
\only<2>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/AFBPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/S7Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/S8Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/S9Pad.pdf}
}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Maximum likelihood fit - Results}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[angle=-90,width=0.65\textwidth]{images/P5pPadOverlay.pdf}\\
\end{center}
\begin{itemize}
\item Tension with $3~\invfb$ gets confirmed!
\item two bins both deviate by $2.8~\sigma$ from SM prediction.
\item Result compatible with previous result.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Method of moments}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\begin{exampleblock}{}
See {\color{blue}{\href{http://arxiv.org/abs/1503.04100}{Phys.Rev.D91(2015)114012}}}, F.Beaujean , M.Chrzaszcz, N.Serra, D. van Dyk for details.\\
\end{exampleblock}
\ARROW The idea behind Method of Moments is simple: Use orthogonality of spherical harmonics, $f_j(\overrightarrow{\Omega})$ to solve for coefficients within a $q^2$ bin:
\begin{align*}
\int f_i(\overrightarrow{\Omega}) f_j(\overrightarrow{\Omega}) = \delta_{ij}
\end{align*}
\begin{align*}
M_i = \int \left( \dfrac{1}{d(\Gamma+ \bar{\Gamma})/dq^2} \right) \dfrac{d^3(\Gamma+\bar{\Gamma})}{d \overrightarrow{\Omega}} f_i(\overrightarrow{\Omega})d \Omega
\end{align*}
\ARROW Don’t have true angular distribution but we ''sample'' it with our data.\\
\ARROW Therefore: $\int \to \sum$ and $M_i \to \widehat{M}_i$
\begin{align*}
\hat{M}_i=\dfrac{1}{\sum_e \omega_e} \sum_e \omega_e f_i(\overrightarrow{\Omega}_e)
\end{align*}
\ARROW The weight $\omega$ accounts for the efficiency. Again the normalization of weights does not matter.
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Method of moments - results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\only<3>
{
\begin{exampleblock}{}
Method of Moments allowed us to measure for the first time a new observable:
\end{exampleblock}
}
\begin{center}
\only<1>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_FLPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S3Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S4Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S5Pad.pdf}
}
\only<2>{
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_AFBPad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S7Pad.pdf}\\
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S8Pad.pdf}
\includegraphics[angle=-90,width=0.49\textwidth]{images/compare_S9Pad.pdf}
}
\only<3>{
\includegraphics[angle=-90,width=0.75\textwidth]{images/S6cPad.pdf}
}
\end{center}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Amplitudes method}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\ARROW Fit for amplitudes as (continuous) functions of $q^2$ in the region: $q^2 \in \left[ 1.1. 6.0 \right]~\GeV^2/c^4$.\\
\ARROW Needs some Ansatz:
\begin{align*}
A(q^2) = \alpha + \beta q^2+ \dfrac{\gamma}{q^2}
\end{align*}
\ARROW The assumption is tested extensively with toys.\\
\ARROW Set of 3 complex parameters $ \alpha, \beta, \gamma $ per vector amplitude:\begin{itemize}
\item {\color{Magenta}{$L, ~R$}}, {\color{Cerulean}{$0 ,~\| ,~\bot$}}, {\color{PineGreen}{$\Re ,~\Im$}} $\rightarrowtail$~~ $3 \times {\color{PineGreen}{2}} \times {\color{Cerulean}{3}} \times {\color{Magenta}{2}} = 36$ DoF.
\item Scalar amplitudes: $+4$ DoF.
\item Symmetries of the amplitudes reduces the total budget to: $28$.
\end{itemize}
\ARROW The technique is described in \href{http://arxiv.org/pdf/1504.00574v2.pdf}{\color{blue}{JHEP06(2015)084}}.\\
\ARROW Allows to build the observables as continuous functions of $q^2$:
\begin{itemize}
\item At current point the method is limited by statistics.
\item In the future the power of this method will increase.
\end{itemize}
\ARROW Allows to measure the zero-crossing points for free and with smaller errors than previous methods.
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Amplitudes - results}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\begin{center}
\begin{columns}
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_AFBOverlay}.pdf}\\
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S4Overlay}.pdf}
\column{0.45\textwidth}
\includegraphics[angle=-90,width=0.95\textwidth]{{images/amplitudes_S5Overlay}.pdf}\\
{~}\\{~}\\{~}\\{~}\\
\begin{large}
Zero crossing points:
\end{large}
\begin{align*}
q_0(S_4) & <2.65 & {\rm{~at~}} & 95\% ~CL \\
q_0(S_5) & \in \left[ 2.49,3.95 \right] & {\rm{~at~}} & 68\% ~CL \\
q_0(A_{FB}) & \in \left[ 3.40, 4.87 \right] & {\rm{~at~}} & 68\% ~CL
\end{align*}
\end{columns}
\end{center}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Compatibility with SM}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{0.1in}
{~}
\column{2in}
\ARROW Use \texttt{EOS} software package to test compatibility with SM.\\
\ARROW Perform the $\chi^2$ fit to the measured:
\begin{center}
\begin{align*}
F_L, A_{FB}, S_{3,..., 9} .
\end{align*}
\end{center}
\ARROW Float a vector coupling: $\Re(C_9)$.\\
\ARROW Best fit is found to be $3.4~\sigma$ away from the SM.
\column{3in}
\begin{align*}
\Delta \Re (C_9) \equiv \Re(C_9)^{{\rm fit}} - \Re(C_9)^{{\rm SM}} = -1.03
\end{align*}
\includegraphics[angle=-90,width=0.95\textwidth]{images/wilsonchi2.pdf}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}
\begin{center}
\begin{huge}
Measurement of Higher $\PKstar$ states\\ in Electroweak Penguin decays
\end{huge}
\end{center}
\end{frame}
\begin{frame}\frametitle{$\PB \to \PKstar(1430) \Pmu \Pmu$}
\begin{minipage}{\textwidth}
{~}\\
\ARROW If the NP effects the present in the $\PB \to \PKstar \Pmu \Pmu$ there is no reason why this should not appear in the higher resonances.\\
\ARROW One the $m_{\PK \Ppi}$ spectrum: $1330 < m_{\PK \Ppi} < 1530~\MeV/c^2$.\\
\ARROW Variety of states in that region: $\PKstar(1410)$, $\PKstar_0(1430)$, $\PKstar_2(1430)$.\\
%\ARROW D-wave needs to be included in the moments analysis.\\
\ARROW
{~}\\
\includegraphics[width=0.45\textwidth]{images/mkpi.png}
\includegraphics[width=0.5\textwidth]{images/brk1430.png}
\begin{exampleblock}{}
First observation of this decay!
\end{exampleblock}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}\frametitle{$\PB \to \PKstar(1430) \Pmu \Pmu$}
\begin{minipage}{\textwidth}
{~}\\
\ARROW D-wave needs to be included in the moments analysis.\\
\ARROW You end up with 42 angular coefficients...\\
\ARROW With current statistics only Method of Moments can handle this.\\
{~}\\
\includegraphics[width=0.45\textwidth]{images/Fig6a.png}
\includegraphics[width=0.5\textwidth]{images/Fig6b.png}
\begin{exampleblock}{}
First angular analysis!\\
Theory predictions in behind.
\end{exampleblock}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Link the observables}
\begin{footnotesize}
\ARROW Fits prepare by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, \href{http://arxiv.org/abs/1510.04239}{\color{blue}{arXiv::1510.04239}}
\begin{itemize}
\item Inclusive
\begin{itemize}
\item $B\to X_s\gamma$ {\color{gray}($BR$)
.......................................................... } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\item $B\to X_s\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
............................................ } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\end{itemize}
\item Exclusive leptonic
\begin{itemize}
\item $B_s\to \ell^+\ell^-$ {\color{gray}($BR$)
........................................................ } {\color{red} $\C{10}^{(\prime)}$}
\end{itemize}
\item Exclusive radiative/semileptonic
\begin{itemize}
\item $B\to K^*\gamma$ {\color{gray}($BR$, $S$, $A_I$)
................................................ } {\color{red} $\C7^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\item $B\to K\ell^+\ell^-$ {\color{gray}($dBR/dq^2$)
.............................................. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\item $\bf \color{Red} B\to K^*\ell^+\ell^-$ {\color{gray}($dBR/dq^2$, {\bf Optimized Angular Obs.})
.. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\item $B_s\to \phi \ell^+\ell^-$ {\color{gray}($dBR/dq^2$, Angular Observables)
.............. } {\color{red} $\C7^{(\prime)}$, $\C9^{(\prime)}$, $\C{10}^{(\prime)}$}%, {\color{brown} $\C{\rm had}$}
\item $\Lambda_b\to \Lambda\ell^+\ell^-$ {\color{gray}(None so far)}
\item etc.
\end{itemize}
\end{itemize}
\end{footnotesize}
\end{frame}
\frame{ \frametitle{Statistic details}
\begin{footnotesize}
\ARROW Frequentist approach:
\medskip
$$\chi^2(C_i) = [O_\text{exp}- O_\text{th}(C_i)]_j \, [Cov^{-1}]_{jk}\, [O_\text{exp}- O_\text{th}(C_i)]_k$$
\begin{itemize}
\item $\bf Cov = Cov^\text{exp} + Cov^\text{th}$. We have $Cov^\text{exp}$ for the first time
\item Calculate $Cov^\text{th}$: correlated multigaussian scan over all nuisance parameters
\item $Cov^\text{th}$ depends on $C_i$: Must check this dependence\\[5mm]
\end{itemize}
For the Fit:
\begin{itemize}
\item Minimise $\chi^2 \to \chi^2_\text{min} = \chi^2(C_i^0)\quad$ (Best Fit Point = $C_i^0$)
\item Confidence level regions: $\chi^2(C_i) - \chi^2_\text{min} < \Delta\chi_{\sigma,n}$
%\item Compute pulls by inversion of the above formula
\end{itemize}
\medskip
\ARROW The results from 1D scans:{~}\\{~}\\
\begin{tiny}
\begin{tabular}{crccc}
%\toprule[1.6pt]
Coefficient ${\cal C}_i^{NP}={\cal C}_i-{\cal C}_i^{SM}$ & Best fit & 1$\sigma$ & 3$\sigma$ & Pull$_{\rm SM}$ \\ \hspace{10mm} \\[5mm]
% \midrule
$\bf\cred\C9^{\rm NP}$ & $ -1.09 $ & $ [-1.29,-0.87] $ & $ [-1.67,-0.39] $ & $\,\,\,\,\,\,\bf 4.5
\cred \Leftarrow$ \hspace{5mm} \\[3mm]
$\C9^{\rm NP}=-\C{10}^{\rm NP}$ & $ -0.68 $ & $ [-0.85,-0.50] $ & $ [-1.22,-0.18] $ & \bf \quad 4.2
$\cred\Leftarrow$ \hspace{5mm} \\[3mm]
$\C9^{\rm NP}=-\C{9'}^{\rm NP}$ & $ -1.06 $ & $ [-1.25,-0.86] $ & $ [-1.60,-0.40] $ & \quad \quad \quad \,\,\quad 4.8
$\cred\Leftarrow$ (no $R_K$)\hspace{5mm} \\[3mm]
\hspace{5mm} \\[3mm]
% \bottomrule[1.6pt]
\end{tabular}
\end{tiny}
\end{footnotesize}
}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Theory implications}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item The data can be explained by modifying the $C_9$ Wilson coefficient.
\item Overall there is around $4.5~\sigma$ discrepancy wrt. SM.
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/C9.png}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{2D scans}
{~}
\begin{footnotesize}
\begin{minipage}{\textwidth}
\begin{columns}
\begin{column}{0.5cm}
\end{column}
\begin{column}{17cm}
\renewcommand{\arraystretch}{1.4}
\setlength{\tabcolsep}{13pt}
\begin{tabular}{cccr}
\hline
Coefficient & Best Fit Point & Pull$_{\rm SM}$ \\ \hline
$(\C7^{\rm NP},\C9^{\rm NP})$ & $(-0.00,-1.07)$ & {\bf 4.1} \hspace{5mm} \\
$(\C9^{\rm NP},\C{10}^{\rm NP})$ & $(-1.08,0.33)$ & {\bf 4.3} \hspace{5mm} \\
$(\C9^{\rm NP},\C{7'}^{\rm NP})$ & $(-1.09,0.02)$ & {\bf 4.2} \hspace{5mm} \\
$(\C9^{\rm NP},\C{9'}^{\rm NP})$ & $(-1.12,0.77)$ & {\bf 4.5} \hspace{5mm} \\
$(\C9^{\rm NP},\C{10'}^{\rm NP})$ & $(-1.17,-0.35)$ & {\bf 4.5} \hspace{5mm} \\
$(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-1.15,0.34)$ & \!\!\!\!\!\!\!\!\!\!\! {\bf 4.7} \\
$(\C{9}^{\rm NP}=-\C{9'}^{\rm NP},\C{10}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-1.06,0.06)$ & {\bf 4.4} \hspace{5mm} \\
$(\C{9}^{\rm NP}=\C{9'}^{\rm NP},\C{10}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.64,-0.21)$ & 3.9 \hspace{5mm} \\
$(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=\C{10'}^{\rm NP})$ & $(-0.72,0.29)$ & 3.8 \hspace{5mm} \\
% $(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.66,0.03)$ & 2.0 & 23.0
%$(\C{9}^{\rm NP}=-\C{10}^{\rm NP},\C{9'}^{\rm NP}=-\C{10'}^{\rm NP})$ & $(-0.69,0.05)$ & 1.9 & 22.0 \hspace{5mm} \\
\end{tabular}
\end{column}
\end{columns}
\medskip
\begin{itemize}
\item $C_9^{NP}$ always play a dominant role
\item All 2D scenarios above 4$\sigma$ are quite indistinguishable. We have done a systematic study to check
what are the most relevant Wilson Coefficients to explain all deviations, by allowing progressively different WC to get NP contributions and comparing the pulls.
\end{itemize}
\end{minipage}
\end{footnotesize}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{If not NP?}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item We are not there yet!
\item There might be something not taken into account in the theory.
\item Resonances ($\PJpsi$, $\Ppsi(2S)$) tails can mimic NP effects.
\item There might be some non factorizable QCD corrections.\\
'' However, the central value of this effect would have to be significantly larger than expected on the basis of existing estimates'' \texttt{D.Straub, 1503.06199}
.
\end{itemize}
\only<1>{
\begin{center}
\includegraphics[width=0.9\textwidth]{images/QCDSHIT.png}
\end{center}
}
\only<2>{
\begin{center}
\includegraphics[width=0.6\textwidth]{images/charmloop2.png}
\end{center}
}
\only<3>{
\begin{center}
\includegraphics[width=0.6\textwidth]{images/charmloop3.png}
\end{center}
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% Why flavour physics
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Disclaimers about some theory predictions
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Disclaimer 1 }
{~}
\begin{minipage}{\textwidth}
\ARROW \href{http://arxiv.org/abs/1512.07157}{\color{blue}{arXiv:1512.07157}}, Ciuchini, Fedele, Franco, Mishima, Paul, Silvestrini, Valli\\
\begin{itemize}
\item Introduce a fully arbitrary parametrization for non-factorizable power correction:
\begin{align*}
\H_\lambda \to H_\lambda + h_\lambda \,\, {\rm where} \,\, h_{\lambda}=h_{\lambda}^{(0)}+h_{\lambda}^{(1)} q^2 + h_{\lambda}^{(2)} q^4 \quad {\rm and} \\ \quad h_{\lambda}^{(0)}\to C_7^{NP}, h_{\lambda}^{(1)}\to C_9^{\rm NP}
\end{align*}
with ($\lambda=0,\pm$)\hfill(copied from JC'14).\\
{\bf Complications:} complete lack of theory input/output $\Rightarrow$ {\bf no predictivity} with 18 free parameters (any shape). Specific problems...
\item Because of the polynomial parametrization this is completely unphysical as it will never reproduce the amplitudes that where measured at the $B \to K^{\ast} \PJpsi$.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}{Disclaimer 1 }
{~}
\begin{minipage}{\textwidth}
\ARROW If one put some physics in their complete random parametrization.\\
\ARROW For example at the $m_{\PJpsi}$ and $m_{\Ppsi(2S)}$ it has to reproduce the Babar, Belle, LHCb.\\
\begin{exampleblock}{}
\texttt{arXiv:1512.XXXX}, C.Bobeth, M.Chrzaszcz, D. van Dyk, J.Virto
\end{exampleblock}
\begin{center}
\includegraphics[width=0.65\textwidth]{{images/fig-btokstarll-p5prime}.pdf}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Disclaimer 2}
\ARROW arXiv::1603.04355
\begin{center}
\includegraphics[width=0.9\textwidth]{images/NP.png}
\end{center}
\only<2>{
\includegraphics[width=0.55\textwidth]{images/rahul.png}
}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}\frametitle{Disclaimer 2}
\ARROW arXiv::1603.04355
\begin{columns}
\column{0.1in}
{~}
\column{3in}
\ARROW ''{\it The relation in Eq. (24) between form factors is expected to be satisfied in the large $q^2$ region. Eq. (24) is naturally satisfied if it is valid at each order in the Taylor expansion of the form factors}''\\
\ARROW They need Eq. 24 to be valid with at least leading order at the Taylor expansion.\\
\ARROW But this is not guaranteed as a resonant contribution can violate this expression.\\
\ARROW Futhermore the width of the of the $\PKstar$ screws up totally the end-points relations.
\column{2in}
\includegraphics[width=0.9\textwidth]{images/mist.png}\\
\includegraphics[width=0.9\textwidth]{images/reson.png}\\
\end{columns}
\includegraphics[angle=-90,width=0.4\textwidth]{{images/ForTom_Q2_FLATQ2_Kmumu}.pdf}
\includegraphics[angle=-90,width=0.4\textwidth]{{images/ForTom_Q2_FLATQ2}.pdf}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Conclusions}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item Enormous NP program searched performed!
\item Clear tensions wrt. SM predictions!
\item Measurements cluster in the same direction.
\item We are not opening the champagne yet!
\item Still need improvement both on theory and experimental side.
\item Time will tell if this is QCD+fluctuations or new Physics:
\end{itemize}
\pause
... when you have eliminated all the\\
Standard Model explanations, whatever remains,\\
however improbable, must be New Physics.\\
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\begin{LARGE}
Thank you for the attention!
\end{LARGE}
\includegraphics[width=0.8\textwidth]{images/Joke.jpg}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\backupbegin
\begin{frame}\frametitle{Backup}
\end{frame}
\begin{frame}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/criv.png}
\end{center}
\ARROW Stolen from A.Crivelin
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\begin{center}
\begin{Huge}
Other related LHCb measurements.
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$}
{~}
\includegraphics[width=0.5\textwidth]{images/ksmumu_BF.png}
\includegraphics[width=0.5\textwidth]{images/kmumu_BF.png}
\begin{center}
\begin{columns}
\column{0.4\textwidth}
\begin{itemize}
\item Despite large theoretical errors the results are consistently smaller than SM prediction.
\end{itemize}
\column{0.6\textwidth}
\includegraphics[width=0.87\textwidth]{images/bukst_BF.png}
\end{columns}
\end{center}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PBs \to \Pphi \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[width=0.65\textwidth]{images/bs2phipi.png}\\
\end{center}
\begin{itemize}
\item Recent LHCb measurement [JHEPP09 (2015) 179].
\item Suppressed by $\frac{f_s}{f_d}$.
\item Cleaner because of narrow $\Pphi$ resonance.
\item $3.3~\sigma$ deviation in SM in the $1-6\GeV^2$ bin.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Branching fraction measurements of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{center}
\only<1>{
\includegraphics[width=0.65\textwidth]{images/Lb_BR.png}
}
\only<2>{
\includegraphics[width=0.45\textwidth]{images/Lblow.png}
\includegraphics[width=0.45\textwidth]{images/Lbhigh.png}
}
\end{center}
\begin{itemize}
\item This years LHCb measurement [JHEP 06 (2015) 115]].
\item In total $\sim 300$ candidates in data set.
\item Decay not present in the low $q^2$.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Angular analysis of $\PLambdab \to \PLambda \Pmu \Pmu$}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item For the bins in which we have $>3~\sigma$ significance the forward backward asymmetry for the hadronic and leptonic system.
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{{images/AFB_Lb}.png}
\end{center}
\begin{itemize}
\item $A_{FB}^H$ is in good agreement with SM.
\item $A_{FB}^{\ell}$ always in above SM prediction.
\end{itemize}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Lepton universality test}
{~}
\begin{minipage}{\textwidth}
\begin{columns}
\column{3.0in}
\begin{itemize}
\item If $\PZprime$ is responsible for the $P'_5$ anomaly, does it couple equally to all flavours?
\includegraphics[width=0.9\textwidth]{images/uni2.png}
\item Challenging analysis due to bremsstrahlung.
\item Migration of events modeled by MC.
\item Correct for bremsstrahlung.
\item Take double ratio with $\PBplus \to \PJpsi \PKplus$ to cancel systematics.
\item In $3\invfb$, LHCb measures $R_K=0.745^{+0.090}_{-0.074}(stat.)^{+0.036}_{-0.036}(syst.)$
\item Consistent with SM at $2.6\sigma$.
\end{itemize}
\column{2.0in}
\includegraphics[width=0.99\textwidth]{images/RK.png}\\
\begin{itemize}
\item \href{http://arxiv.org/abs/1406.6482}{Phys. Rev. Lett. 113, 151601 (2014)}
\end{itemize}
\end{columns}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Angular analysis of $\PBzero \to \PKstar \Pe \Pe$}
{~}
\only<1>{
\begin{minipage}{\textwidth}
\begin{itemize}
\item With the full data set ($3\invfb$) we performed angular analysis in $0.0004 < q^2 <1~\GeV^2$.
\item Electrons channels are extremely challenging experimentally:
\begin{itemize}
\item Bremsstrahlung.
\item Trigger efficiencies.
\end{itemize}
\item Determine the angular observables: $\FL$, $\ATD$, $\ATRe$, $\ATIm$:
\end{itemize}
\begin{equation}
\label{eq:physPars}
\begin{split}
\FL &=\frac{|A_0|^2}{|A_0|^2+|A_{||}|^2 + |A_\perp|^2}\\
\ATD &= \frac{|A_\perp|^2-|A_{||}|^2}{|A_\perp|^2+|A_{||}|^2}\\
\ATRe &= \frac{2\Real(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2}\\
\ATIm &= \frac{2\Imag(A_{||L}A^*_{\perp L} + A_{||R}A^*_{\perp R})}{|A_{||}|^2 + |A_\perp|^2},
\end{split}\nonumber
\end{equation}
\end{minipage}
}
\only<2>{
\begin{center}
\includegraphics[width=0.5\textwidth]{images/Kstee.png}\\
\end{center}
\begin{itemize}
\item Results in full agreement with the SM.
\item Similar strength on $C_7$ Wilson coefficient as from $\Pbeauty \to \Pstrange \Pphoton$ decays.
\end{itemize}
\begin{center}
\includegraphics[width=0.9\textwidth]{images/Kstee2.png}
\end{center}
}
\vspace*{2.1cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{There is more!}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item There is one other LUV decay recently measured by LHCb.
\item $R(\PDstar)=\dfrac{\mathcal{B}(\PB \to \PDstar \Ptau \Pnu)}{\mathcal{B}(\PB \to \PDstar \Pmu \Pnu)}$
\item Clean SM prediction: $R(\PDstar)=0.252(3)$, PRD 85 094025 (2012)
\item LHCb result: $R(\PDstar)= 0.336 \pm 0.027 \pm 0.030$, HFAG average: $R(\PDstar)=0.322 \pm 0.022$
\item $3.9~\sigma$ discrepancy wrt. SM prediction
\end{itemize}
\begin{center}
\includegraphics[width=0.52\textwidth]{images/RDstar.png}
\end{center}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}
\begin{center}
\begin{Huge}
Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements
\end{Huge}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{$\PBzero \to \PKstar \Pmuon \APmuon$ kinematics}
{~}
\begin{minipage}{\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ The kinematics of $\PBzero \to \PKstar \Pmuon \APmuon$ decay is described by three angles $\thetal$, $\thetak$, $\phi$ and invariant mass of the dimuon system ($q^2)$.
\only<1>{
\begin{columns}
\column{0.5\textwidth}
$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetak$: the angle between the direction of the kaon in the $\PKstar$ ($\overline{\PKstar}$) rest frame and the direction of the $\PKstar$ ($\overline{\PKstar}$) in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\cos \thetal$: the angle between the direction of the $\Pmuon$ ($\APmuon$) in the dimuon rest frame and the direction of the dimuon in the $\PBzero$ ($\APBzero$) rest frame.\\
$\color{JungleGreen}{\Rrightarrow}$ $\phi$: the angle between the plane containing the $\Pmuon$ and $\APmuon$ and the plane containing the kaon and pion from the $\PKstar$.
\column{0.5\textwidth}
\includegraphics[width=0.95\textwidth]{images/angles.png}
\end{columns}
}
\only<2>{
{\tiny{
\eqa{\label{dist}
\frac{d^4\Gamma}{dq^2\,d\!\cos\theta_K\,d\!\cos\theta_l\,d\phi}&=&\frac9{32\pi} \bigg[
J_{1s} \sin^2\theta_K + J_{1c} \cos^2\theta_K + (J_{2s} \sin^2\theta_K + J_{2c} \cos^2\theta_K) \cos 2\theta_l\nn\\[1.5mm]
&&\hspace{-2.7cm}+ J_3 \sin^2\theta_K \sin^2\theta_l \cos 2\phi + J_4 \sin 2\theta_K \sin 2\theta_l \cos\phi + J_5 \sin 2\theta_K \sin\theta_l \cos\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ (J_{6s} \sin^2\theta_K + {J_{6c} \cos^2\theta_K}) \cos\theta_l
+ J_7 \sin 2\theta_K \sin\theta_l \sin\phi + J_8 \sin 2\theta_K \sin 2\theta_l \sin\phi \nn\\[1.5mm]
&&\hspace{-2.7cm}+ J_9 \sin^2\theta_K \sin^2\theta_l \sin 2\phi \bigg]\,,
\nonumber}
}}
$\color{JungleGreen}{\Rrightarrow}$ This is the most general expression of this kind of decay.
}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\begin{frame}\frametitle{Backup}
\ARROW ves:
\begin{align*}
\langle H \rangle = \frac{1}{\sqrt{2}}\begin{pmatrix}
0\\
\nu
\end{pmatrix}\\
\langle S \rangle = x.
\end{align*}
\ARROW Minimalization:
\begin{align*}
0 = -\mu^2 + \lambda_H \nu^2 + a_1 x^2 + \frac{1}{2} x^2\\
0 = b_2 + b_3 x+ b_4 x^2 + \frac{a_1\nu^2}{4 x_0} + \frac{a_2 \nu_0^2}{2}
\end{align*}
\end{frame}
\begin{frame}\frametitle{Backup}
\ARROW generate the mass:
\begin{align*}
\mathcal{L}_{mass}=-\frac{1}{2}
\begin{pmatrix}
h \\
s
\end{pmatrix}^T
\begin{pmatrix}
A & C \\
C & B
\end{pmatrix}
\begin{pmatrix}
s^{\prime}\\
h^{\prime}
\end{pmatrix}
\end{align*}
\begin{align*}
\cos \theta = 2(1+y^{-2}(1-\sqrt{1+y^2}))^{-0.5}\\
\sin \theta = 2(1+y^{-2}(1+\sqrt{1+y^2}))^{-0.5}\\
y=\frac{2C}{A-B}
\end{align*}
\ARROW Mass eigenvalues:
\begin{align*}
m^2_{h^{\prime}/s^{\prime}} = \frac{1}{2}\left[A + B \pm (A-B)\sqrt{1+y^2}\right]
\end{align*}
\end{frame}
\begin{frame}\frametitle{Naturalnes}
\ARROW If the $\sin \theta \ll 1$
\begin{align*}
m^2_{h^{\prime}} \sim 2 \lambda_H \nu^2\\
m^2_{s^{\prime}} \sim b_3 x + 2b_4 x^2 -\frac{a_1\nu^2}{4 x}
\end{align*}
\ARROW Since Higgs is $125\GeV$ then $m_S \sim \mathcal{O}(1)$
\end{frame}
\begin{frame}[c]{The inflaton model}
\begin{minipage}{\textwidth}
\begin{small}
\ARROW The model is extremely simple:
\begin{align*}
V(H,S)=V_H + V_{\rm mix} + V_S,
\end{align*}
where
\begin{align*}
V_H = -\mu^2 H^{\dag}H + \lambda_H (H^{\dag} H)^2\\
V_{\rm mix} = \frac{a_1}{2}\left(H^{\dag}H\right)S + \frac{a_2}{2}\left(H^{\dag}H\right)S^2\\
V_S = \frac{b_2}{2}S^2 + \frac{b_3}{3}S^3 + \frac{b_4}{4}S^4
\end{align*}
\ARROW Now the Lagrangian needs to be written in physical degrees of freedom:
\begin{itemize}
\item You start by minimizing the scalar potential.
\item Then you expand the group states (linear terms in h, s expansion vanish).
\item Then you generate the mass is given(see backup for details):
\end{itemize}
\begin{align*}
\mathcal{L}_{mass}=-\frac{1}{2}
\begin{pmatrix}
h \\
s
\end{pmatrix}^T
\begin{pmatrix}
A & C \\
C & B
\end{pmatrix}
\begin{pmatrix}
s^{\prime}\\
h^{\prime}
\end{pmatrix}
\end{align*}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}[c]{The inflaton model}
\begin{minipage}{\textwidth}{~}\\
\begin{small}
\ARROW You can diagonalize the matrix by orthogonal transformation:
\begin{align*}
\begin{pmatrix}
h \\
s
\end{pmatrix}=
\begin{pmatrix}
\sin \theta & \cos \theta \\
\cos \theta & \sin \theta
\end{pmatrix}
\begin{pmatrix}
s^{\prime}\\
h^{\prime}
\end{pmatrix}
\end{align*}
where
\begin{align*}
\cos \theta = 1 +\mathcal{O}(y^2),~~
\sin \theta = y + \mathcal{O}(y^3)~~
y = \frac{2C}{A-B}
\end{align*}
\ARROW For small mixing:
\begin{align*}
m^2_{S^{\prime}} \sim B - \frac{1}{4}(A-B)y^2
\end{align*}
\ARROW So now comes something that is the most important; all the interaction with the SM is done just by assuming it's Higgs and inserting: $h \to \sin \theta s$
\ARROW For example:
\begin{align*}
\mathcal{L}_Y = - m_f h \bar{\psi}_f \psi_f + {\rm h.c.}~~~~~\mapsto \mathcal{L}_{S^{\prime}ff}= - m_f \sin \theta s \bar{\psi}_f \psi_f + {\rm h.c.}
\end{align*}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}[c]{The inflaton model, so what?}
\begin{minipage}{\textwidth}
\begin{small}
\ARROW For a given mixing angle $\sin \theta$ and the inflaton mass we can calculate it's width:
\begin{align*}
\Gamma_{\ell \ell} = \frac{\sin^2 \theta}{8 \pi \nu^2}m_{\ell}^2 m_S \left(1-\frac{4m^2_{\ell}}{m^2_S} \right)^{\frac{3}{2}}\\
c \tau_S \approx 60 \times \left(\frac{0.01}{\sin \theta}\right)^2 \left(\frac{500}{m_S}\right)^3 \rm [mm]
\end{align*}
\ARROW Since in experiment we set limits in 2D space: $(m_S, c \tau_S)$ we can map it to: $(m_S, \sin \theta)$.\\
\ARROW Now the misunderstanding started with ''Light inflaton Hunter's Guide'' D. Gorbunov:
\begin{equation}
{\rm Br} (\PB \to \chi X_s) ~\sim 10^{-6}\left(1-\frac{m^2_{\chi}}{m^2_b}\right) \left(\frac{\beta}{\beta_0}\right) \left(\frac{300{\rm MeV}}{m_{\chi}}\right)
\end{equation}
and:
''where Xs stands for strange meson channel mostly saturated by a sum of pseudoscalar and vector kaons.''
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}[c]{The inflaton model, so what?}
\begin{minipage}{\textwidth}
\begin{small}
\ARROW In the interpretation of the $\PB \to \PKstar \xi$ they followed Gorbunov and assumed that the $33\%$ of $X_s$ are a $\PKstar$ and used the above formula.\\
\ARROW We followed a different approach and calculated the exclusive widths:
\begin{align*}
\mathcal{M}=-\frac{1}{2}c_h \theta \langle K \vert \bar{s}b \vert B \rangle = -\frac{1}{2} c_h \theta \frac{M_B^2-M_K^2}{m_b-m_s} f_0(m_s^2)
\end{align*}
\begin{align*}
\Gamma_{\PB \to \PKstar \chi} = \frac{c_h \theta^2}{64 \pi} \lambda^{1/2}(1,\frac{M_K^2}{M_B^2}, \frac{M_S^2}{M_B^2})f_0(m_S^2) \frac{(M_B^2 - M_K^2)}{M_B(m_b- m_s)^2}
\end{align*}
\ARROW Now after we calculate this our self we found the solution in the literature \href{http://journals.aps.org/prd/pdf/10.1103/PhysRevD.83.054005}{ B.Batel et. al}
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}[c]{The inflaton model, so what?}
\begin{minipage}{\textwidth}
\begin{small}
{~}\\
\ARROW Now if we look how many of the $X_s$ are $\PK$ and $\PKstar$ we define the variables:
\begin{align*}
r_K = \frac{\PB \to \PK \chi}{\PB \to X_s \chi}~~~~r_{\PKstar} = \frac{\PB \to \PKstar \chi}{\PB \to X_s \chi}
\end{align*}
\includegraphics[width=0.45\linewidth]{images/rk_graph.png}
\includegraphics[width=0.45\linewidth]{images/rkstar.png} \\
{~}\\
\ARROW So the assumption about $33~\%$ was generous assumption.
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}[c]{Cross check of the calculations}
\begin{minipage}{\textwidth}
\begin{small}
{~}\\
\ARROW So we have cross-checked this calculations with old Higgs papers. \\
\ARROW In the 80s they thought that Higgs might he light enough that it can be produced in $\PB$ decays.\\
\ARROW From Haber, et al.:
\begin{center}
\includegraphics[width=0.45\textwidth]{images/higgs.png}
\end{center}
\ARROW So everything is consistent.
\end{small}
\end{minipage}
\vspace*{2.cm}
\end{frame}
\begin{frame}{The result}
\begin{minipage}{\textwidth}
\begin{center}
\includegraphics[angle=-90,width=0.9\textwidth]{{images/Inflaton_parameter_space_log}.pdf}
\end{center}
\end{minipage}
\vspace*{2.cm}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{If not NP?}
{~}
\begin{minipage}{\textwidth}
\begin{itemize}
\item How about our clean $P_i$ observables?
\item The QCD cancel as mentioned only at leading order.
\item Comparison to normal observables with the optimised ones.
\end{itemize}
\includegraphics[width=0.9\textwidth]{images/C9_S_P.png}
\end{minipage}
\vspace*{2.1cm}
\end{frame}
\backupend
\end{document}
mchrzasz