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%% for NNLO
\newcommand{\be}{\begin{equation}}
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
The present Section addresses the most important experimental and theoretical issues
involved in the precision determination of the luminosity at meson factories. The luminosity
is the key ingredient underlying all the measurements and studies of the physics processes
discussed in the other Sections. Particular emphasis is put on the theoretical accuracy 
inherent to the event generators used in the experimental analyses, in comparison with the
most advanced perturbative calculations %available in the literature 
and experimental 
precision requirements. The effort done during the activity of the 
working group to perform tuned comparisons
between the predictions of the most accurate programs is described in detail. 
New calculations, leading to an update of the theoretical error associated with the 
prediction of the luminosity cross section, are also presented. 
The aim of the Section is to provide a self-contained and up-to-date description of the 
progress occurred during the last few years towards high-precision luminosity monitoring 
at flavour factories, as well as of the still open issues necessary for future advances. 

The structure of the Section is as follows. After an introduction on the motivation 
for precision luminosity measurements at meson factories 
(Section \ref{MOTIVATION}), the  leading-order (LO)
cross sections of the two QED processes of major interest, i.e. Bhabha scattering and 
photon pair production, are presented in Section 
\ref{LONLO}, together with the formulae for the
next-to-leading-order (NLO) 
photonic corrections to the above processes. The remarkable progress 
on the calculation of next-to-next-leading-order (NNLO) QED corrections to the Bhabha cross section, 
as occurred in the last few years, is reviewed in Section 
\ref{NNLO}. In particular, this Section 
presents new exact results on lepton and hadron pair corrections, 
taking into account realistic 
event selection criteria. Section \ref{MP} is devoted to the description 
of the theoretical methods used in the Monte Carlo (MC) generators for the simulation of 
multiple photon radiation. The matching of such contributions with NLO corrections is also described 
in Section \ref{MP}. The main features of the MC programs used by the experimental collaborations 
are summarised in Section 
\ref{MC}. Numerical results for %various sources of 
the radiative corrections implemented into the MC generators 
are shown in Section \ref{NUMERICS} for both the Bhabha process and two-photon production. Tuned 
comparisons between the predictions of the most precise generators are presented and 
discussed in detail in 
Section \ref{TUNED}, considering the Bhabha process at different 
centre-of-mass (c.m.) energies and 
with realistic experimental cuts. The theoretical accuracy presently reached by the luminosity 
tools is addressed in Section \ref{TH}, where the most important sources of uncertainty are discussed
quantitatively. The estimate of the total error affecting the calculation
of the Bhabha cross section is given, as the main conclusion of the present work, 
in Section \ref{CONCLUSIONS}, updating and improving the robustness of
results available in the literature. 
Some remaining open issues are discussed in Section \ref{CONCLUSIONS} as well.
 
 \input{lumi-INTRO}
 
 \input{lumi-LO-NLO}
 
 \input{lumi-NNLO}
 
 \input{lumi-MP-MATCHING}
 
 \input{lumi-MC}
 
  \input{lumi-NUMERICS}
 
 \input{lumi-TUNED}
   
 \input{lumi-TH}
 
 \input{lumi-CONCLUSIONS}

%%\input{lumi0}
