In this Report we have summarised the achievements of the last years of the
experimental and theoretical groups working on hadronic cross section
 measurements and tau physics. In addition we  have sketched 
the prospects in this  field for the years to come.
  We have emphasised the importance of continuous
 and close collaboration between the experimental and theoretical groups
 which is crucial in the quest for precision in hadronic physics. The platform
 set to simplify this collaboration is a  
{\it Working Group on Radiative Corrections  and  Monte Carlo Generators
for Low Energies (Radio MontecarLow)}, for the better understanding of
 the needs and limitations of both experimental and theoretical communities
 and to facilitate the information flow between them. This Review is a result
 of the Working Group.

 The Report was divided
 into five  Sections covering the luminosity
 measurements at low energies (up to the energy of $B$ factories)
 (Section \ref{sec:1}),
 $R$ measurement by energy scan (Section \ref{sec:2}), $R$ measurement 
 using radiative return (Section \ref{sec:3}), tau physics (Section \ref{sec:5}), and the calculation
 of the vacuum polarisation with emphasis on the hadronic contributions
 (Section \ref{sec:4}).
  In all the Sections, with the exception of Section \ref{sec:4},
  we gave an overview of the experimental results
 and the status of the Monte Carlo event generators used in the experimental
 analyses with emphasis on their accuracy and tests.

%lumi
Concerning the work done on the topic of precision luminosity measurement
(Section \ref{sec:1}),
 a particular effort was paid to arrive at an up-to-date estimate
 of the accuracy of the most precise MC tools used by the experimentalists. 
Several tuned comparisons between the predictions of independent
 generators were presented, considering the large-angle Bhabha 
process with realistic event selection criteria and at different
 c.m. energies. It turned out that the three most precise luminosity tools,
 i.e. the programs BabaYaga@NLO, BHWIDE and MCGPJ, agree within 0.1\% for the
 integrated cross sections and within less than 1\% for the differential 
distributions. 
Therefore the main conclusion of the work on tuned comparisons is
 that the technical precision of MC programs is well under control,
 the (minor) discrepancies still observed being due to slightly
 different 
details in the treatment of radiative corrections 
and their implementation. 
 The theoretical accuracy of the generators with regard to  radiative corrections
not fully taken into account was assessed 
by performing detailed comparisons between the results of the generators
 and those of exact perturbative calculations. In particular, explicit
 cross-checks with the predictions of available NNLO QED calculations
 and with new exact results for lepton and hadron pair corrections led
 to the conclusion that the total theoretical uncertainty is at the one
 per mill level for the large-angle Bhabha process at different c.m.
 energies. Albeit this error estimate could be put on firmer grounds
 thanks to further work in progress, it appears to be already quite
 robust and sufficient for a precise determination of the luminosity.
%lumi
%scan

In Section  \ref{sec:2} 
we presented the current status of the studies of $e^+e^-$ annihilation 
into hadrons and muons at the energies up to a  few GeV.  Accurate 
measurements of the ratio $R$, {\it i.e.} the ratio of the cross sections
of hadron and muon channels, are crucial 
for the evaluation of the hadronic contribution to vacuum polarisation and
subsequently for various precision tests of the Standard Model.
Results of several experimental collaborations have been reviewed for the most
important processes with the final states $\mu^+\mu^-$, $\pi^+\pi^-$, 
$\pi^+\pi^-\pi^0$, $\pi^+\pi^-2\pi^0$, $\pi^+2\pi^-$, two kaons and 
heavier mesons.
In particular, $R$ scans at the experiments CMD-2, SND, CLEO and BES experiments have been
 discussed.
Analytic expressions for the Born level cross sections of the main processes 
have been presented.
 First-order QED radiative corrections have been given explicitly 
for the case of muon, pion and kaon pair production.
The two latter cases are computed using scalar QED to describe interactions 
of pseudoscalar mesons with photons in the final state.
Matching with higher-order QED corrections evaluated in the leading logarithmic 
approximation have been discussed. Good agreement between 
different Monte Carlo codes for the muon channel has been shown.
The theoretical uncertainty in the description of these processes has been
 evaluated.
For the two main channels, $e^+e^-\to\mu^+\mu^-$ and $e^+e^-\to\pi^+\pi^-$, 
this uncertainty has been estimated to be of the order of $0.2\%$.
%scan

% rr:
In Section  \ref{sec:3} 
we have given an overview of experimental measurements via radiative
return and described the Monte Carlo generators used in the
analyses. Special emphasis has been put on the modelling of the meson-photon 
interaction, crucial for reaching an accuracy below  1\%.
Radiative return has been applied successfully at the 
experiments KLOE in Frascati, BaBar in Stanford and 
Belle in Tsu\-ku\-ba, obtaining important results for the 
measurement 
of precise hadronic cross sections as well as in the field of hadron 
spectroscopy. In all three experiments, the ISR physics 
programme is still going on. New experiments like the BES-III detector at 
BEPC-II in Beijing and the experiments at the VEPP-2000 machine in Novosibirsk 
will use radiative return 
to complement their standard physics programme of energy scanning
in the regions of  2 -- 4.6 GeV (BEPC-II) and 1 -- 2 GeV (VEPP-2000). 
The success of this programme was possible only through close collaboration
between experimental and theoretical groups. Dedicated Monte Carlo
generators (PHOKHARA, EKHARA, FEVA, FASTERD) were developed to
make
the experimental analyses possible. 
The physics programme allowed for better modelling
of the photon-meson interaction which is crucial for a precise determination of the pion form factor. The measurements
 of the hadronic cross sections by means of radiative return 
 allowed to reduce the error of the  hadronic
 contribution to the anomalous magnetic moment of the muon and to the
 running of the fine structure constant.
 Ongoing and forthcoming
 measurements will aim at an even better modelling of the hadron-photon
 interaction and the inclusion of those QED radiative corrections not yet
 accounted for in the Monte Carlo generators. 
 This ongoing physics programme will lead
 to further improvements in the precision of the calculation of the hadronic
 contribution to the anomalous magnetic moment of the muon and to the
 running of the fine structure constant, which in turn
 is crucial for tests of the Standard Model and searches for New
 Physics.

% rr
In Section  \ref{sec:5} we described the 
present status of the simulation programs for the
production and decay of $\tau$ leptons. The available programs
have been discussed in the context of the required accuracy to match 
current high-statistics experimental data. After a review of the
existing programs used in the data analysis we have emphasised the
topics which will require particular attention in the future.
We have elaborated on the efforts which are going on at present
 and focused on the necessary
improvements. The techniques for fitting $\tau$ decay
currents require particular attention.
The observed spectra and angular distributions are a convolution of
theoretical predictions with experimental effects which should
be taken into account in the fitting procedures.
Background contributions also play an important role 
if high precision is requested. 
We have also commented on the impact of these efforts for forthcoming high
energy experiments (like at LHC), where $\tau$ decays are used to
constrain hard processes rather than  to measure properties of $\tau$
decays. 

%vp
 In Section \ref{sec:4}
the different vacuum polarisation (VP) contributions have been discussed, and available
parametrisations have been compared.
VP forms a universal part of radiative
corrections and as such is an important ingredient in Monte Carlo
programs. In addition, to evaluate the hadronic contributions to the muon $g-2$
and $\Delta\alpha(q^2)$ via dispersion relations, one has to use the 
`undressed' hadronic cross section, {\it i.e.} data with the VP effects
removed. 
Therefore the precise knowledge of VP is required. While in the space-like region
the VP is a smooth function and the parametrisations are in excellent
agreement, in the time-like region the VP is a fast varying function
and differences exist between different parametrisations, especially
around resonances. However, the accuracy which is typically of the
order of or below a few per mill and the agreement of the more
recent compilations indicate that the current precision of VP is
sufficient for the envisaged applications. In the future better
hadronic cross section data will lead to further improved accuracy.
%vp
% tau


% tau

 
 
