  We study theoretically the effects of finite volume for pipi scattering in
order to extract physical observables for infinite volume from lattice QCD. We
compare three different approaches for pipi scattering (lowest order
Bethe-Salpeter approach, N/D and inverse amplitude methods) with the aim to
study the effects of the finite size of the box in the potential of the
different theories, specially the left-hand cut contribution through loops in
the crossed t,u-channels. We quantify the error made by neglecting these
effects in usual extractions of physical observables from lattice QCD spectra.
We conclude that for pipi phase-shifts in the scalar-isoscalar channel up to
800 MeV this effect is negligible for box sizes bigger than 2.5m_pi^-1 and of
the order of 5% at around 1.5-2m_pi^-1. For isospin 2 the finite size effects
can reach up to 10% for that energy. We also quantify the error made when using
the standard Luscher method to extract physical observables from lattice QCD,
which is widely used in the literature but is an approximation of the one used
in the present work.
