TY - JOUR
T1 - Lattice QCD at the physical point meets S U (2 ) chiral perturbation theory
AU - Dürr, Stephan
AU - Fodor, Zoltán
AU - Hoelbling, Christian
AU - Krieg, Stefan
AU - Kurth, Thorsten
AU - Lellouch, Laurent
AU - Lippert, Thomas
AU - Malak, Rehan
AU - Métivet, Thibaut
AU - Portelli, Antonin
AU - Sastre, Alfonso
AU - Szabó, Kálmán
AU - Budapest-Marseille-Wuppertal Collaboration, null
PY - 2014/12/1
Y1 - 2014/12/1
N2 - 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 S U (2 )
chiral perturbation theory (χ PT ) and a determination of some of
its low energy constants. In particular, we systematically explore the
range of applicability of next-to-leading order (NLO) S U (2 ) χ PT
in two different expansions: the first in quark mass (x expansion), and
the second in pion mass (ξ expansion). We find that these expansions
begin showing signs of failure for Mπ≳300 MeV , for
the typical percent-level precision of our Nf=2 +1 lattice
results. We further determine the LO low energy constants (LECs), F
=88.0 ±1.3 ±0.2 and BMS ¯(2 GeV )=2.61 (6
)(1 ) GeV , and the related quark condensate, ΣMS
¯(2 GeV )=(272 ±4 ±1 MeV )3 , as
well as the NLO ones, ℓ¯3=2.6 (5 )(3 ) and
ℓ¯4=3.7 (4 )(2 ), with fully controlled
uncertainties. We also explore the next-to-next-to-leading order (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.
AB - 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 S U (2 )
chiral perturbation theory (χ PT ) and a determination of some of
its low energy constants. In particular, we systematically explore the
range of applicability of next-to-leading order (NLO) S U (2 ) χ PT
in two different expansions: the first in quark mass (x expansion), and
the second in pion mass (ξ expansion). We find that these expansions
begin showing signs of failure for Mπ≳300 MeV , for
the typical percent-level precision of our Nf=2 +1 lattice
results. We further determine the LO low energy constants (LECs), F
=88.0 ±1.3 ±0.2 and BMS ¯(2 GeV )=2.61 (6
)(1 ) GeV , and the related quark condensate, ΣMS
¯(2 GeV )=(272 ±4 ±1 MeV )3 , as
well as the NLO ones, ℓ¯3=2.6 (5 )(3 ) and
ℓ¯4=3.7 (4 )(2 ), with fully controlled
uncertainties. We also explore the next-to-next-to-leading order (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.
KW - Lattice QCD calculations
U2 - 10.1103/PhysRevD.90.114504
DO - 10.1103/PhysRevD.90.114504
M3 - Article
SN - 0556-2821
VL - 90
SP - 114504
JO - Physical Review D, particles, fields, gravitation, and cosmology
JF - Physical Review D, particles, fields, gravitation, and cosmology
IS - 11
ER -