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csintroduction.tex
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csintroduction.tex
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\section{Introduction}
\label{sec:introduction}
A significant fraction of the production cross-section of $\jpsi$ and
$\Upsilon$ states in hadron collisions is due to feed-down from heavier
quarkonium states. A study of this effect is important for the interpretation of
onia production cross-section and polarization measurements in hadron
collisions. For P-wave quarkonia, measurements of \chic have been reported by
\cdf~\cite{Abulencia:2007bra}, HERA-B~\cite{Abt:2008ed}
and \lhcb~\cite{LHCb-PAPER-2011-019}, whereas \cdf~\cite{Affolder:1999wm} and
\atlas~\cite{Aad:2011ih} have performed measurements involving $\chi_b$ states.
\lhcb has reported~\cite{LHCb-PAPER-2012-015} a measurement of
the \chibOneP production cross-section, and subsequent decay into \OneS $\gamma$,
relative to the \OneS production. This measurement was performed on 2010 data
in a region defined by $6 \gevc < \pt^{\Y1S} < 15 \gevc$ and
$2.0 < y^{\Y1S} < 4.5$.
The corresponding integrated luminosity was $32.4\invpb$.
An update of the previous \lhcb study is part of the thesis presented here. Data collected in
2012 were also analyzed, allowing for cross-section measurements at \sqs=8\tev.
Using the full integrated luminosity allows for a measurement of the
differential cross-section in \pt and rapidity bins of the $\Upsilon(1,2,3S)$
mesons, and to study the production of $\chi_b(2P)$ and $\chi_b(3P)$ mesons. A
measurement of the $\chi_b(3P)$ mass, which was recently observed at
ATLAS~\cite{Aad:2011ih}, D0~\cite{Abazov:2012gh} and
LHCb~\cite{LHCb-CONF-2012-020} collaborations, is also performed in this study
by combining data collected in 2011 and 2012.
The analysis proceeds through the reconstruction of $\Upsilon(nS)$ candidates
via their dimuon decays, and their subsequent pairing with a photon to look for
$\chi_b(mP) \to \Upsilon(nS) \gamma$ decays. The fraction of $\Upsilon(nS)$
originating from $\chi_b(mP)$ decays can be written as:
\begin{equation}
\resizebox{.9\hsize}{!}{
$
\frac{\sigma(pp \to \chi_b (mP) X) \times Br (\chi_b (mP) \to \Upsilon(nS) \gamma)}{\sigma(pp \to \Upsilon(nS) X)} =
\frac{N_{\chi_b (mP)\to \Upsilon(nS) \gamma}}{N_{\Upsilon(nS)}} \times \frac{\epsilon_{\Upsilon(nS)}}{\epsilon_{\chi_b (mP)\to \Upsilon(nS) \gamma}} =
\frac{N_{\chi_b (mP)\to \Upsilon(nS) \gamma}}{N_{\Upsilon(nS)}} \times \frac{1}{\epsilon^{reco}_{\gamma}}
$
}
\label{eqn:master}
\end{equation}
\noindent where
${N_{\Upsilon(nS)}}$ and ${N_{\chi_b(mP)\to \Upsilon(nS) \gamma}}$ are the
$\Upsilon(nS)$ and $\chi_b(mP)$ yields, $\epsilon_{\Upsilon(nS)}$ and
$\epsilon_{\chi_b(mP)\to \Upsilon(nS) \gamma}$ are their corresponding selection
efficiencies. The latter are the product of geometric acceptance, trigger
efficiency and reconstruction efficiency. Since the selection criteria for the
two samples differ only in the reconstruction of a photon, the efficiency ratio
can be replaced by 1/$\epsilon^{reco}_{\gamma}$, the reconstruction efficiency for the
photon from the $\chi_b$ decay. Similar expressions may be used to compute
differential cross sections in $\Upsilon$ \pt bins.