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(/usr/share/texmf/tex/latex/tipa/t3cmr.fd File: t3cmr.fd 2001/12/31 TIPA font definitions ) -LaTeX Font Info: ... okay on input line 286. +LaTeX Font Info: ... okay on input line 316. *geometry* driver: auto-detecting *geometry* detected driver: xetex @@ -2433,7 +2433,7 @@ ABD: EveryShipout initializing macros \AtBeginShipoutBox=\box108 -Package hyperref Info: Link coloring OFF on input line 286. +Package hyperref Info: Link coloring OFF on input line 316. (/usr/share/texlive/texmf-dist/tex/latex/hyperref/nameref.sty Package: nameref 2012/10/27 v2.43 Cross-referencing by name of section @@ -2443,9 +2443,9 @@ ) \c@section@level=\count438 ) -LaTeX Info: Redefining \ref on input line 286. -LaTeX Info: Redefining \pageref on input line 286. -LaTeX Info: Redefining \nameref on input line 286. +LaTeX Info: Redefining \ref on input line 316. +LaTeX Info: Redefining \pageref on input line 316. +LaTeX Info: Redefining \nameref on input line 316. (./mchrzasz.out) (./mchrzasz.out) \@outlinefile=\write9 @@ -2476,7 +2476,7 @@ tionary/translator-theorem-dictionary-English.dict Dictionary: translator-theorem-dictionary, Language: English ) -LaTeX Info: Redefining \includegraphics on input line 286. +LaTeX Info: Redefining \includegraphics on input line 316. *** you should *not* be loading the inputenc package *** XeTeX expects the source to be in UTF8 encoding @@ -2572,8 +2572,8 @@ Package biblatex Info: Trying to load bibliographic data... Package biblatex Info: ... file 'mchrzasz.bbl' not found. No file mchrzasz.bbl. -Package biblatex Info: Reference section=0 on input line 286. -Package biblatex Info: Reference segment=0 on input line 286. +Package biblatex Info: Reference section=0 on input line 316. +Package biblatex Info: Reference segment=0 on input line 316. 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b/Seminars/Padova/mchrzasz.synctex.gz Binary files differ diff --git a/Seminars/Padova/mchrzasz.tex b/Seminars/Padova/mchrzasz.tex index 99a2830..ecb80d9 100644 --- a/Seminars/Padova/mchrzasz.tex +++ b/Seminars/Padova/mchrzasz.tex @@ -276,10 +276,40 @@ \def\BsToPhimmFULL {\decay{\Bs}{\phi(\to\!K^{+}K^{-})\mumu}} \def\BsToKKmm {\decay{\Bs}{\Kp\Km\mumu}} +\newcommand{\delC}[1]{\delta {\cal C}_{#1}} +\newcommand{\dC}[1]{{\cal C}_{#1}^{\rm NP}} +\newcommand{\dCp}[1]{{\cal C}_{#1^\prime}^{\rm NP}} + + + + +\definecolor{green}{rgb}{0.2,0.6,0.2} +\definecolor{lightgreen}{rgb}{0.4,1,0.4} +\definecolor{verylightgreen}{rgb}{0.7,1,0.7} +\def\cgreen{\color{green}} +\definecolor{brown}{rgb}{0.4,0.2,0.0} +\def\cbrown{\color{brown}} +\def\cred{\color{red}} +\definecolor{darkblue}{rgb}{0.0,0.0,1.0} +\def\cdarkblue{\color{darkblue}} +\definecolor{darkgrey}{rgb}{0.4,0.4,0.4} +\definecolor{lightgrey}{rgb}{0.7,0.7,0.7} +\definecolor{verylightblue}{rgb}{0.8,0.8,1.0} +\definecolor{lightblue}{rgb}{0.6,0.6,1.0} +\definecolor{verylightyellow}{rgb}{1.0,1.0,0.5} +\definecolor{lightyellow}{rgb}{1.0,0.7,0.3} +\definecolor{darkred}{rgb}{0.6,0.0,0.0} + +\definecolor{green}{rgb}{0.3,0.6,0.2} +\definecolor{green}{rgb}{0.3,0.7,0.4} + + + + \author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich, IFJ PAN)} \institute{UZH} -\title[Particle Phenomenology, Particle Astrophysics and Cosmology Seminar]{Particle Phenomenology, Particle Astrophysics and Cosmology Seminar} +\title[Department of Physics, University of Padova Seminar]{Department of Physics, University of Padova Seminar} \date{25 September 2014} @@ -325,14 +355,21 @@ \begin{frame}{Outline} \begin{minipage}{\textwidth} - -\fixme +{~}\\ \begin{enumerate} \item Why flavour is important. +\item LHCb detector. \item $\Pbeauty \to \Pstrange \ell \ell$ theory in a nutshell. -\item LHCb measurements of $\Pbeauty \to \Pstrange \ell \ell$. +\item LHCb measurements of $\PBd \t o\PKstar \Pmu \Pmu$ +\begin{itemize} +\item Maximum likelihood fit. +\item Method of moments. +\item Amplitudes fit. +\end{itemize} +\item Other related LHCb measurements. \item Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements. +\item Disclaimers about some theory predictions. \item Conclusions. \end{enumerate} @@ -343,6 +380,18 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 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} @@ -453,6 +502,17 @@ \vspace*{2.1cm} \end{frame} +\begin{frame} +\begin{center} +\begin{Huge} +LHCb detector +\end{Huge} +\end{center} + + + + +\end{frame} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % DETECTOR @@ -540,9 +600,24 @@ \end{frame} \fi +\begin{frame} +\begin{center} +\begin{Huge} + $\Pbeauty \to \Pstrange \ell \ell$ theory in a nutshell. +\end{Huge} +\end{center} + + + + +\end{frame} + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}\frametitle{Why rare decays?} + \begin{columns} \column{4in} \begin{itemize} @@ -567,6 +642,8 @@ \end{frame} + + \begin{frame}{Tools in rare $\PBzero$ decays} {~} \begin{minipage}{\textwidth} @@ -614,15 +691,65 @@ + +\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} + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}\frametitle{$\PB \to \PKstar \Pmu \Pmu$ as a golden channel} - - - - - - -\end{frame} \iffalse @@ -713,7 +840,7 @@ &&\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. @@ -753,7 +880,7 @@ 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}} +\label{Js}\nonumber} }} \end{minipage} @@ -774,12 +901,12 @@ \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}} +\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. \\ \pause $\color{JungleGreen}{\Rrightarrow}$ 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)} } +\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 } @@ -787,9 +914,19 @@ \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} {~} @@ -1036,26 +1173,17 @@ \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} - -\begin{columns} - -\column{0.5\textwidth} - -\includegraphics[width=0.95\textwidth]{images/mlogjpsi.png} -\column{0.5\textwidth} -\includegraphics[width=0.95\textwidth]{images/mkpijpsi.png} - -\end{columns} - - -\includegraphics[width=0.99\textwidth]{images/angles2.png} - +\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} @@ -1067,7 +1195,10 @@ \begin{frame}{The columns of New Physics} {~} \begin{minipage}{\textwidth} -\includegraphics[width=0.95\textwidth]{images/columns.png} + \begin{center} + \includegraphics[width=0.94\textwidth]{images/columns.png} + + \end{center} \end{minipage} @@ -1106,8 +1237,10 @@ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}{Maximum likelihood fit} +\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: @@ -1116,25 +1249,39 @@ \end{align*} \ARROW Only the relative weights matters!\\ \ARROW The Procedure was commissioned with TOY MC study.\\ -\ARROW Angular background component is modelled with $2^{\rm nd }$ order Chebyshev polynomials, which was tested on the side-bands. - - +\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}{Method of moments} +\begin{frame}{Maximum likelihood fit - Results} {~} \begin{minipage}{\textwidth} -\ARROW See {\color{blue}{\href{http://arxiv.org/abs/1503.04100}{arXiv::1503.04100}}}, F.Beaujean , M.Chrzaszcz, N.Serra, D. van Dyk for details.\\ -\ARROW The idea behind Method of Moments is extremely simple: +\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} @@ -1147,29 +1294,11 @@ - - - - - - - - - - - - - - - - - - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}{Results in $\PB \to \PKstar \Pmu \Pmu$} +\begin{frame}{Maximum likelihood fit - Results} \begin{minipage}{\textwidth} \begin{center} - \includegraphics[angle=-90,width=0.65\textwidth]{images/Fig17.pdf}\\ + \includegraphics[angle=-90,width=0.65\textwidth]{images/P5pPadOverlay.pdf}\\ \end{center} \begin{itemize} @@ -1183,6 +1312,209 @@ \vspace*{2.1cm} \end{frame} + + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + + + +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\begin{frame}{Method of moments} +{~} +\begin{footnotesize} + \begin{minipage}{\textwidth} +\ARROW 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.\\ +\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 do not matter. + + +\end{minipage} +\end{footnotesize} + \vspace*{2.1cm} +\end{frame} + + + +\begin{frame}{Method of moments - results} +{~} +\begin{footnotesize} + \begin{minipage}{\textwidth} + +\only<3> +{ +\ARROW Method of Moments allowed us to measure for the first time a new observable: +} + +\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 (continues)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 test 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 then 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} +Other related LHCb measurements. + +\end{Huge} +\end{center} + + + + +\end{frame} + + + + + + + + + + + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Branching fraction measurements of $\PB \to \PKstar^{\pm} \Pmu \Pmu$} {~} @@ -1345,7 +1677,7 @@ \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} +\end{split}\nonumber \end{equation} \end{minipage} @@ -1367,42 +1699,121 @@ \vspace*{2.1cm} \end{frame} - - -%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\begin{frame}{Theory implications} -{~} - \begin{minipage}{\textwidth} -\pause -\begin{itemize} -\item A preliminary fit prepared by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, presented at \href{http://arxiv.org/abs/1510.04239}{\color{blue}{1510.04239}} -\item Took into the fit: -\begin{itemize} -\item $\mathcal{B} ( \PB \to X_s \Pphoton) = (3.36 \pm 0.23) \times 10^{-4} $, Misiak et. al. 2015. -\item $\mathcal{B} ( \PB \to\Pmu \Pmu)$, theory: Bobeth et al 2013, experiment: LHCb+CMS average (2015) -\item $\mathcal{B} ( \PB \to X_s \Pmu \Pmu$), Huber et al 2015 -\item $\mathcal{B} ( \PB \to \PK \Pmu \Pmu$),Bouchard et al 2013, 2015 -\item $PB_{(s)} \to \PKstar(\Pphi) \Pmu \Pmu$, Horgan et al 2013 -\item $\PB \to \PK \Pe \Pe$, $\PB \to \PKstar \Pe \Pe$ and $R_k$. -\end{itemize} -\item Overall there is around $4.5~\sigma$ discrepancy wrt. SM. -\end{itemize} +\begin{frame} +\begin{center} +\begin{Huge} +Global fit to $\Pbeauty \to \Pstrange \ell \ell$ measurements +\end{Huge} +\end{center} - -\end{minipage} - \vspace*{2.1cm} \end{frame} + + +\begin{frame}{Link the observables} +\begin{footnotesize} + +\ARROW Fit 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 A preliminary fit prepared by \texttt{S. Descotes-Genon, L. Hofer, J. Matias, J. Virto}, presented at \href{http://arxiv.org/abs/1510.04239}{\color{blue}{1510.04239}} \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} @@ -1417,17 +1828,60 @@ -\begin{frame}{Theory implications} +\begin{frame}{2D scans} {~} - \begin{minipage}{\textwidth} +\begin{footnotesize} -\includegraphics[height=0.9\textheight]{images/table.png} + \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 work to check + what are the most relevant Wilson Coefficients to explain all deviations, by allowing progressively different WC to get NP contributions and compare the pulls. + + +\end{itemize} + \end{minipage} - \vspace*{2.1cm} + +\end{footnotesize} + \vspace*{2.1cm} \end{frame} +%%%%%%%%%%%%%%%%% + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{If not NP?} {~} @@ -1441,14 +1895,21 @@ . \end{itemize} \only<1>{ -\includegraphics[width=0.9\textwidth]{images/charmloop.png} +\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} @@ -1490,6 +1951,62 @@ \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}{There is more!} +{~} +\begin{footnotesize} + + + + \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: + +$$H_\lambda \to H_\lambda + h_\lambda \,\, {\rm where} \,\, h_{\lambda}=h_{\lambda}^{(0)}+h_{\lambda}^{(1)} q^2 + h_{\lambda}^{(2)} q^4 \quad {\rm and} \quad h_{\lambda}^{(0)}\to C_7^{NP}, h_{\lambda}^{(1)}\to C_9^{\rm NP}$$ 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 "{\it No deviation is present once all the theoretical uncertainties are taken into account}". + + + + \end{itemize} + \end{minipage}\end{footnotesize} + \vspace*{2.1cm} +\end{frame} + + + + + + + + + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \begin{frame}{Conclusions} {~} @@ -1540,225 +2057,6 @@ \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 the $4^{th}$ 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 the 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}{Recent measurements} -{~} -\only<1>{ - - \begin{minipage}{\textwidth} - - -\begin{columns} - -\column{0.5\textwidth} -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}} -\begin{description} -\item [$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$] {~}{~}LHCb, Mar 14 -\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15 -\item [$\PBs \to \Pphi \Pmuon \APmuon$] {~}{~}{~}LHCb, Jun 15 -\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15 -\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15 -\item [$\PB \to\Pmuon \APmuon$] {~}{~}{~}{~}{~}CMS+LHCb, Jun 15 -\end{description} - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}} -\begin{description} -\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15 -\end{description} - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}} -\begin{description} -\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14 -\end{description} - - -\column{0.5\textwidth} -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}} -\begin{description} -\item [$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$] {~}{~}LHCb, Jun 14 -\end{description} - - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}} -\begin{description} -\item [$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$] {~}{~}{~}LHCb, Jan 15 -\item [$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$] BaBar, Aug 15 -\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15 -\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}LHCb, Mar 15 -\end{description} - - - - - -\end{columns} - -\end{minipage} -} -\only<2>{ - - \begin{minipage}{\textwidth} - - -\begin{columns} - -\column{0.5\textwidth} -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Branching fractions:}} -\begin{description} -\item [{\color{red}{$\PB^{0,\pm} \to \PK^{0,\pm} \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 14}} -\item [$\PB^{0} \to \PKstar \Pmuon \APmuon$] {~}{~}CMS, Jul 15 -\item [{\color{red}{$\PBs \to \Pphi \Pmuon \APmuon$}}] {~}{~}{~}{\color{red}{LHCb, Jun 15}} -\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}LHCb, Sep 15 -\item [$\PLambdab \to \PLambda \Pmuon \APmuon$] {~}{~}{~}{~}LHCb, Mar 15 -\item [{\color{red}{$\PB \to\Pmuon \APmuon$}}] {~}{~}{~}{~}{~}{\color{red}{CMS+LHCb, Jun 15}} -\end{description} - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{CP asymmetry:}} -\begin{description} -\item [$\PB^{\pm} \to \Ppi^{\pm} \Pmuon \APmuon$] {~}{~}LHCb, Sep 15 -\end{description} - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Isospin asymmetry:}} -\begin{description} -\item [$\PB \to \PK \Pmuon \APmuon$] {~}{~}{~}{~}{~}LHCb, Mar 14 -\end{description} - - -\column{0.5\textwidth} -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Lepton Universality:}} -\begin{description} -\item [{\color{red}{$\PB^{\pm} \to \PK^{\pm} \Plepton \APlepton$}}] {~}{~}{\color{red}{LHCb, Jun 14}} -\end{description} - - -$\color{JungleGreen}{\Rrightarrow}$ {\color{WildStrawberry}{Angular:}} -\begin{description} -\item [{\color{red}{$\PB^{0} \to \PK^{\ast} \Plepton \APlepton$}}] {~}{~}{~}LHCb, Jan 15 -\item [{\color{red}{$\PB^{\pm} \to \PK^{\ast,\pm} \Plepton \APlepton$}}] {\color{red}{BaBar, Aug 15}} -\item [$\PBs \to \Pphi \Plepton \APlepton$] {~}{~}{~}LHCb, Jun 15 -\item [{\color{red}{$\PLambdab \to \PLambda \Pmuon \APmuon$}}] {~}{~}{\color{red}{LHCb, Mar 15}} -\end{description} - -\begin{alertblock}{} -$>2~\sigma$ deviations from SM - -\end{alertblock} - -\end{columns} - -\end{minipage} -} - - \vspace*{2.1cm} -\end{frame} \backupend diff --git a/Seminars/Padova/pt.pdf b/Seminars/Padova/pt.pdf new file mode 100644 index 0000000..9d347bf --- /dev/null +++ b/Seminars/Padova/pt.pdf Binary files differ