  We perform a detailed, fully-correlated study of the chiral behavior of the
pion mass and decay constant, based on 2+1 flavor lattice QCD simulations.
These calculations are implemented using tree-level, O(a)-improved Wilson
fermions, at four values of the lattice spacing down to 0.054 fm and all the
way down to below the physical value of the pion mass. They allow a sharp
comparison with the predictions of SU(2) chiral perturbation theory (\chi PT)
and a determination of some of its low energy constants. In particular, we
systematically explore the range of applicability of NLO SU(2) \chi PT in two
different expansions: the first in quark mass (x-expansion), and the second in
pion mass (\xi-expansion). We find that these expansions begin showing signs of
failure around M_\pi=300 MeV for the typical percent-level precision of our
N_f=2+1 lattice results. We further determine the LO low energy constants
(LECs), F=88.0 \pm 1.3\pm 0.3 and B^\msbar(2 GeV)=2.58 \pm 0.07 \pm 0.02 GeV,
and the related quark condensate, \Sigma^\msbar(2 GeV)=(271\pm 4\pm 1 MeV)^3,
as well as the NLO ones, l_3=2.5 \pm 0.5 \pm 0.4 and l_4=3.8 \pm 0.4 \pm 0.2,
with fully controlled uncertainties. We also explore the NNLO expansions and
the values of NNLO LECs. In addition, we show that the lattice results favor
the presence of chiral logarithms. We further demonstrate how the absence of
lattice results with pion masses below 200 MeV can lead to misleading results
and conclusions. Our calculations allow a fully controlled, ab initio
determination of the pion decay constant with a total 1% error, which is in
excellent agreement with experiment.
