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\begin{document}

\Title{Measurement of the Polarization Amplitudes and 
Triple Product Asymmetries in the $\ensuremath{B^0_s}\xspace \to \phi \phi$ Decay at LHCb}

\bigskip\bigskip

%+\addtocontents{toc}{{\it D. Reggiano}}
%+\label{ReggianoStart}

\begin{raggedright}  

{\it Sean Benson\index{Benson, S.} on behalf of LHCb collaboration\\
Department of Physics and Astronomy\\
University of Edinburgh\\
EH9 3JZ, United Kingdom}
\bigskip\bigskip
\end{raggedright}

The \ensuremath{B^0_s \to \phi \phi}\xspace decay is an example of a flavour changing
neutral current (FCNC) interaction and as such, may only proceed via penguin diagrams in the Standard Model.
\ensuremath{C\!P}\xspace violation in the \ensuremath{B^0_s \to \phi \phi}\xspace decay\index{Penguin decays}\index{$B_s^0 \to \phi \phi$} may be accessed with a time-integrated untagged method using $T$\xspace-violating triple
product asymmetries (further information on this rich subject may be found in \cite{Valencia:195789,Bensalem:2002pz,
Gronau:2011cf,Datta:2012ky}). The rest of this document details the study of the triple product asymmetries (\ensuremath{A_U}\xspace and \ensuremath{A_V}\xspace),
polarization amplitudes (\ensuremath{|A_0|^2}\xspace, \ensuremath{|A_\parallel|^2}\xspace and \ensuremath{|A_\perp|^2}\xspace) and strong phase difference in the $\ensuremath{B^0_s}\xspace \to (\phi \to KK) \; (\phi \to KK)$ decay using 1.0~\ensuremath{\mbox{\,fb}^{-1}}\xspace of proton-proton collision 
data collected at centre-of-mass (COM) energy $\sqrt{s}=7$~TeV with the LHCb detector.

\section{Experimental Method and Results}
\label{sec:phiphi}

A total of $801\pm29$ signal candidates are observed through a cut based selection optimized with the use
of the $_s\mathcal{P}lot$ method~\cite{Pivk:2004ty} to distinguish signal from background. 

The measurement of the polarization amplitudes (\ensuremath{|A_0|^2}\xspace, \ensuremath{|A_\parallel|^2}\xspace, \ensuremath{|A_\perp|^2}\xspace) and strong phase
difference (\ensuremath{\cos\delta_\parallel}\xspace) is performed using a time-integrated, untagged probability density function (PDF) under the assumption
that the time acceptance is uniform and that the \ensuremath{C\!P}\xspace-violating weak phase is zero.
A maximum log-likelihood fit is then performed to the three helicity angles (see Reference~\cite{Aaij:2012ud}
for more information). The lifetimes of the heavy and light \ensuremath{B^0_s}\xspace mass eigenstates are constrained to be within the errors of the
LHCb measured values~\cite{LHCb:2012ad} taking in to account correlations. S-wave contributions are ignored in the
fit. Data-driven methods indicate the S-wave contribution to be $(1\pm1)\%$, therefore systematic
uncertainties are based on a 2\% S-wave contribution. The angular acceptance is determined from
simulated events. The limited number of simulated events determines the systematic uncertainty due to the angular
acceptance. The time acceptance is understood from Monte Carlo events and simplified simulations
are used to assign a systematic uncertainty from the assumption that it is uniform. 
The polarization amplitudes and strong phase difference are measured to be
\begin{center}
\begin{tabular}{l@{$~=~$}r@{$\,\pm\,$}l@{$\,$(stat) 
      $\pm\,$}l@{$\,$(syst)}l@{\,}l}
$|A_0|^2$ & 0.365 & 0.022 & 0.012  & $\, ,$ \\
$|A_\perp|^2$  & 0.291 & 0.024 & 0.010 & $\, ,$  \\
$|A_\parallel|^2 $ & 0.344 & 0.024 & 0.014& $\, ,$ \\
$\cos(\delta_\parallel)$ &  $-$0.844 &  0.068 & 0.029 & $\, .$
\end{tabular}
\end{center}

Triple product asymmetries are based on $T$\xspace-odd observables U and V (defined in Reference~\cite{Aaij:2012ud}).
Events are separated in to datasets
according to whether $U(V)>0$ and a simutlaneous fit is then performed to the obtain the asymmetries (\ensuremath{A_U}\xspace,\ensuremath{A_V}\xspace)
using the $KKKK$ invariant mass as the discriminating observable.

The main systematic uncertainties arise from the choice of signal and background model;
the effect of ignoring the time acceptance and the angular acceptance of the \ensuremath{B^0_s \to \phi \phi}\xspace decay.
The systematic uncertainties on the triple product asymmetries due to acceptance effects 
are estimated using simplified MC studies.

Simultaneous fits to the U(V) datasets yield triple product asymmetries of
\begin{center}
\begin{tabular}{l@{$~=~$}r@{$\,\pm\,$}l@{$\,$(stat)
      $\pm\,$}l@{$\,$(syst)}l@{\,}l}
$A_U$ & $-$0.055 & 0.036 & 0.018 & $\, ,$ \\
$A_V$ & 0.010 & 0.036 & 0.018 & $\, .$
\end{tabular}
\end{center}

\section{Summary}
\label{sec:summary}

We provide the most accurate measurements of the physics parameters in the 
\ensuremath{B^0_s \to \phi \phi}\xspace penguin decay, which are in agreement with those reported from QCD factorization
methods~\cite{beneke,PhysRevD.80.114026}. The most precise measurements of \ensuremath{C\!P}\xspace violation 
in the \ensuremath{B^0_s \to \phi \phi}\xspace decay through triple product asymmetries are reported and are found to be in agreement
with SM expectations of \ensuremath{C\!P}\xspace conservation in the \ensuremath{B^0_s \to \phi \phi}\xspace decay. 

\begin{thebibliography}{10}

\bibitem{Valencia:195789}
G.~Valencia.
\newblock Phys. Rev. D39:3339--3345 (1988).

\bibitem{Bensalem:2002pz}
W. Bensalem, A. Datta, and D. London.
\newblock Phys. Lett. B538:309--320 (2002).

\bibitem{Gronau:2011cf}
M. Gronau and J.~L. Rosner.
\newblock Phys. Rev. D84:096013 (2011).

\bibitem{Datta:2012ky}
A. Datta, M. Duraisamy, and D. London.
\newblock arXiv:1207.4495 (2012).

\bibitem{Pivk:2004ty}
M. Pivk and F.~R. Le~Diberder.
\newblock Nucl. Instrum. Meth. A555:356--369 (2005).

\bibitem{Aaij:2012ud}
LHCb~collaboration
\newblock Phys. Lett. B713:369--377 (2012).

\bibitem{LHCb:2012ad}
LHCb~collaboration
\newblock Phys. Lett. B713:378--386 (2012).

\bibitem{beneke}
M.~Beneke, J.~Rohrer, and D.~Yang.
\newblock Nucl. Phys. B774:64--101 (2007).

\bibitem{PhysRevD.80.114026}
H. Cheng and C. Chua.
\newblock Phys. Rev. D80:114026 (2009).

\end{thebibliography}

\end{document}

