Convergence of the Chiral Expansion in Two-Flavor Lattice QCD

Abstract

We test the convergence property of the chiral perturbation theory using a lattice QCD calculation of pion mass and decay constant with two dynamical quark flavors. The lattice calculation is performed using the overlap fermion formulation, which realizes exact chiral symmetry at finite lattice spacing. By comparing various expansion prescriptions, we find that the chiral expansion is well saturated at the next-to-leading order for pions lighter than approximately 450 MeV. Better convergence behavior is found, in particular, for a resummed expansion parameter xi, with which the lattice data in the pion mass region 290-750 MeV can be fitted well with the next-to-next-to-leading order formulas. We obtain the results in two-flavor QCD for the low energy constants l[over ]_{3} and l[over ]_{4} as well as the pion decay constant, the chiral condensate, and the average up and down quark mass.

Nearly conformal gauge theories on the lattice

“…The fitted value of B is a · B = 1.76(7) in lattice units and M ρ /F = 13(1) in the chiral limit (the linear fit of M ρ = c + d · m q is used at all N f values to determine M ρ (m q = 0)). The fitted value of B/F = 53(6) indicates significant enhancement of the chiral condensate from its N f = 2 value [53,68]. In our simultaneous fits we get Λ 3 = 0.37(5) and Λ 4 = 0.51(1) which set the chiral couplings in the NLO chiral Lagrangian.…”

“…(2.8,2.9) can also have some effect on the results. On the right-hand sides of the equations, the variable pair (M, F) in the chiral logs can be replaced with the pair (M π , F π ) which is equivalent to a partial resummation [68]. This will be reported in our more detailed forthcoming journal publication [2].…”

Light meson physics from maximally twisted mass lattice QCD

“…[1,2] for recent reviews). Simulations containing the dynamics of the light-quark flavours in the sea, as well as those due to the strange quark and recently also to the charm, using pseudo scalar masses below 300 MeV, spatial lattice extents L ≥ 2 fm and lattice spacings smaller than 0.1 fm are presently being performed by several lattice groups [3][4][5][6][7][8][9][10]. Such simulations will eventually allow for an extrapolation of the lattice data to the continuum limit and to the physical point while keeping also the finite volume effects under control.…”

Determination of $\alpha_s$ in 2+1-flavor QCD through vacuum polarization function

“…Then the quark mass dependence of Π V +A | pert (Q 2 ), which consists of the third and fourth terms in (2.2), is determined by α s only, once the quark condensate is determined elsewhere. The third term is given by m r (Q 2 ) = Z m (2 GeV)m q × [m(Q 2 )/m(4 GeV 2 )] with Z m (2 GeV) 0.833 [15]. In the fourth term, quark condensate is an input parameter, qq = −[0.236(7)(+13) GeV] 3 , which is taken from N f = 2 hadron spectroscopy [15].…”

“…The third term is given by m r (Q 2 ) = Z m (2 GeV)m q × [m(Q 2 )/m(4 GeV 2 )] with Z m (2 GeV) 0.833 [15]. In the fourth term, quark condensate is an input parameter, qq = −[0.236(7)(+13) GeV] 3 , which is taken from N f = 2 hadron spectroscopy [15]. While the precise value of the quark condensate obtained in [16] has not been used here so far, this makes only a tiny difference to VPF since C V +Ā qq (Q 2 , α s ) mqq /Q 4 is relatively small.…”