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\author{ {\fontspec{Trebuchet MS}Marcin Chrz\k{a}szcz} (Universit\"{a}t Z\"{u}rich)}
\institute{UZH}
\title[Form factors for $\PLambda_b \to \PLambda_c^{\ast} \ell \nu$]{Form factors for $\PLambda_b \to \PLambda_c^{\ast} \ell \nu$}
\date{5 February 2016}


\begin{document}
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{
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\begin{center}
\begin{center}
	\begin{columns}
		\begin{column}{0.75\textwidth}
			\flushright\fontspec{Trebuchet MS}\bfseries \Huge {Form factors for $\PLambda_b \to \PLambda_c^{\ast} \ell \nu$}
		\end{column}
                \begin{column}{0.02\textwidth}
                  {~}
                  \end{column}
                \begin{column}{0.23\textwidth}
                 % \hspace*{-1.cm}
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                  \includegraphics[width=0.6\textwidth]{lhcb-logo}
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	\quad
	\vspace{3em}
\begin{columns}
\begin{column}{0.44\textwidth}
\flushright \vspace{-1.8em} {\fontspec{Trebuchet MS} \Large Marcin Chrząszcz\\\vspace{-0.1em} Nicola Serra  \\\vspace{-0.1em} Elena Graverini}

\end{column}
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\includegraphics[height=1.3cm]{uzh-transp}
\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}{$R(\Lambda_c^{\ast})$ meeting, CERN\\February 5, 2016}
\end{center}
\end{frame}
}


\begin{frame}[c]{Introduction}
\begin{minipage}{\textwidth}

The matrix elements for our $\PLambdab$ decays are depended on $F_{1,..,4}$ and $G_{1,...,4}$ form factors:



\begin{tiny}
%\scalebox{0.8}{
\begin{equation}
\langle   \Lambda_{c}^{1/2^-}(p', s') | V_{\mu}| \Lambda_{b}(p, s)\rangle =
\overline{u}(p', s')\left(F_1(q^2) \gamma_{\mu} + F_2(q^2)
\frac{ p_\mu}{m_{\Lambda_Q}} +  F_3(q^2)\frac{ p'_\mu}{m_{\Lambda_q}}
\right) u(p,s), \nonumber
\end{equation}
\begin{equation}
\langle \Lambda_{c}^{1/2^-}(p', s')| A_{\mu}| \Lambda_{b}(p, s)\rangle =
\overline{u}(p', s')\left(G_1(q^2) \gamma_{\mu} + G_2(q^2)
\frac{ p_\mu}{m_{\Lambda_Q}} +  G_3(q^2)\frac{ p'_\mu}{m_{\Lambda_q}}\right)
\gamma_{5} u(p,s), \nonumber
\end{equation}
\begin{equation}
\langle \Lambda_{c}^{3/2^-}(p', s')| V_{\mu}|  \Lambda_{b}(p, s)\rangle=
\overline{u}^\alpha(p', s')\left[
\frac{p_\alpha}{m_{\Lambda_Q}}\left(F_1\gamma_{\mu} + F_2\frac{
p_\mu}{m_{\Lambda_Q}} +  F_3\frac{ p'_\mu}{m_{\Lambda_q^{3/2}}}\right)+F_4 g_{\alpha\mu}\right]
u(p,s), \nonumber
\end{equation}
\begin{equation}
\langle \Lambda_{c}^{3/2^-}(p', s')| A_{\mu}|  \Lambda_{b}(p, s)\rangle = 
\overline{u}^\alpha(p', s')\left[
\frac{p_\alpha}{m_{\Lambda_Q}}\left(G_1 \gamma_\mu + 
G_2\frac{ p_\mu}{m_{\Lambda_Q}} +  G_3
\frac{ p'_\mu}{m_{\Lambda_q^{3/2}}}\right)+G_4 g_{\alpha\mu}\right]\gamma_{5} u(p,s). \nonumber
\end{equation}

%}
\end{tiny}


	\end{minipage}
\end{frame}




\begin{frame}[c]{What is in the simulation?}
\begin{minipage}{\textwidth}

$\Rrightarrow$ The simulation that we have uses the form factors calculated in \href{http://arxiv.org/pdf/nucl-th/0503030v1.pdf}{arXiv:nucl-th/0503030}\\
$\Rrightarrow$ In this paper the form factors are calculated in constituent quark model.\\
$\Rrightarrow$ Let me quote a theorists that wants to remain anonymous: ,,it's not even wrong''.\\
$\Rrightarrow$ Never the less this is what Syracuse is using and is now in the simulation $\rightarrow$ we will reweigh our MC.\\
$\Rrightarrow$ To do so, we firstly looked at reproducing the calculations from \texttt{EvtGen}.




	\end{minipage}
		\vspace*{2.cm}
\end{frame}


\begin{frame}[c]{Form factor calculus}
\begin{minipage}{\textwidth}
$\Rrightarrow$ So in \texttt{EvtGen} the calculations of From Factors are done only in the harmonic oscillator basis.\\{~}\\
\begin{tiny}

\begin{tabular}{|l|cccccccc|}
\hline
 model & $m_\sigma$ (GeV)& $m_s$ (GeV) & $m_c$ (GeV) & $m_b$ (GeV) & $b$ (GeV$^2$) 
 & $\alpha_{\rm Coul}$ \,\,\,\,\,\,&
$\alpha_{\rm hyp}$ & $C_{qqq}$ (GeV) \\\hline
 HONR & 0.40& 0.65& 1.89 & 5.28 & 0.14 &0.45 & 0.81 & -1.20 \\
 HOSR & 0.38& 0.59& 1.83 & 5.17 & 0.17 &0.09 & 0.26 & -1.45 \\
 STNR & 0.40& 0.64& 1.87 & 5.28 & 0.13 &0.35 & 0.31 & -1.22 \\
 STSR & 0.34& 0.57& 1.78 & 5.22 & 0.15 &0.19 & 0.11 & -1.23  \\ \hline
\end{tabular}
\end{tiny}
$\Rrightarrow$ On top of this you also have the wave size:
\begin{tiny}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{tabular}{|l|l|cccc|}
\hline
$J^P$ &  model & $\Lambda_b$ & $\Lambda_c$ & $\Lambda$ & $N$  \\ 
&  & $\left(\alpha_\lambda,\,\,\,\,\alpha_\rho\right)$ &
$\left(\alpha_\lambda,\,\,\,\,\alpha_\rho\right)$ &
$\left(\alpha_\lambda,\,\,\,\,\alpha_\rho\right)$ &
$\left(\alpha_\lambda,\,\,\,\,\alpha_\rho\right)$  \\ \hline
$1/2^+$ &HONR &  (0.59, 0.61)& (0.55, 0.58) & (0.49, 0.53) & 0.48\\
$1/2^+$ &HOSR & (0.68, 0.68)& (0.60, 0.61) & (0.52, 0.57)& 0.54\\
$1/2^+$ & STNR &  (0.44, 0.66)& (0.41, 0.69) & (0.35, 0.75)&- \\
$1/2^+$ & STSR &  (0.46, 0.64)& (0.43, 0.67) & (0.38, 0.72) &-\\ \hline
$1/2^-$ & HONR &  -& (0.47, 0.49) & (0.40, 0.47) &0.37\\
$1/2^-$ & HOSR &  -& (0.55, 0.59) & (0.48, 0.54) &0.46 \\
$1/2^-$ &STNR & -& (0.60, 0.50) & (0.55, 0.54) &- \\
$1/2^-$ &STSR & -& (0.61, 0.49) & (0.58, 0.51) &-\\ \hline
$3/2^+$ &HONR & -& - & - & 0.35\\
$3/2^+$ &HOSR & -& -& -& 0.44\\\hline
$5/2^+$ &HONR & -& - & - & 0.35\\
$5/2^+$ &HOSR & -& -& -& 0.46\\\hline
\end{tabular}


\end{tiny}
	\end{minipage}
		\vspace*{2.cm}
\end{frame}

\begin{frame}[c]{Form factor results (example $\PLambda_c^{1/2+}$)}
\begin{minipage}{\textwidth}
\begin{columns}
\column{2.5in}
\includegraphics[width=0.95\textwidth]{images/FF_paper.png}


\column{2.5in}

\includegraphics[angle=-90,width=0.95\textwidth]{images/FF.pdf}

\end{columns}
$\Rrightarrow$ So I check each of the three Form factors with calculations from \texttt{EvtGen} and they are in perfect agreement.\\
$\Rrightarrow$ Wrote all the bispinor algebra routines, gamma matrices, etc.\\
$\Rrightarrow$ Didn't finish writing the matrix element calculus, once this is done we have a reweighing routine with all the form factors inside that is plug and play!\\



\end{minipage}
		\vspace*{2.cm}
\end{frame}




\begin{frame}[c]{Summary}
\begin{minipage}{\textwidth}
\begin{itemize}
\item Form factors implemented with all the algebraic structure of $V-A$ currents.
\item Working on matrix element computations.
\item Reweighing should follow.
\item Once that is ready we will test with of the discriminating variables are less form factor independent so they can be used in the selection.


\end{itemize}


\end{minipage}
		\vspace*{2.cm}
\end{frame}




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