Chiral Limit and Light Quark Masses in 2+1 Flavor Domain Wall QCD

Abstract

We present results for meson masses and decay constants measured on 24 3 × 64 lattices using the domain wall fermion formulation with an extension of the fifth dimension of L s = 16 for N f = 2 + 1 dynamical quark flavors. The lightest dynamical meson mass in our set-up is around 331 MeV, while partially quenched mesons reach masses as low as 250 MeV. The applicability of SU(3) × SU(3) and SU(2) × SU(2) (partially quenched) chiral perturbation theory will be compared and we quote values for the low-energy constants from both approaches. We will extract the average light quark and strange quark masses and use a non-perturbative renormalization technique (RI/MOM) to quote their physical values. The pion and kaon decay constants are determined at those values from our chiral fits and their ratio is used to obtain the CKM-matrix element |V us |. The results presented here include statistical errors only.Lattice QCD allows us to study QCD phenomenology from first principles by using Monte Carlo techniques. Recent developments in both the computer technology and numerical algorithms have made possible lattice simulations with the correct number of fermion flavors in the vacuum polarization, which are essential for establishing direct connections between lattice simulations and the underlying low-energy QCD. However, the computational cost increases dramatically as one decreases the quark masses in the simulations towards the chiral limit. As such, current lattice simulations still work with quark masses heavier than their physical values, and extrapolations are necessary to obtain meaningful physical results from the simulations with heavy quark masses.Chiral perturbation theory (χPT) is a low-energy effective theory which connects physical observables to quark masses in explicit functional forms, and is a useful tool to guide the extrapolations for the lattice QCD simulations. Since it is based on the approximate chiral symmetry of QCD, it is important to have a chiral fermion formulation on the lattice in order to make direct use of the continuum χPT for the sake of the extrapolations. The domain wall fermion (DWF) formulation is well-suited in this regard, since it preserves exact flavor symmetry, and chiral symmetry is only mildly broken. Its chiral symmetry breaking effect can be quantitatively described by a small additive mass shift called the residual mass, m res . Recent work has shown [1, 2] that, to do chiral extrapolations for domain wall fermions, the only modification to the continuum χPT is to replace the input quark mass by the sum of the input quark mass and m res , leaving the number of low energy constants unchanged, at least up to terms of O(ma) which can be viewed as next-to-next-to-leading order (NNLO). This is in contrast to the cases of Wilson fermions or staggered fermions, where, at next-to-leading order, a few new low-energy constants need to be introduced to account for the chiral symmetry (Wilson) or flavor symmetry (staggered) breaking effects.One of the challenges of chiral extrapolations...

The kaon B-parameter from 2+1-flavor Domain-Wall-Fermion lattices

“…We use data from the large volume to set the scale. We use the mass of the Ω − baryon, linearly extrapolated to m l = (m u + m d )/2, and M K and M π treated in SU(2) × SU(2) chiral perturbation theory to determine a −1 = 1.73(3) GeV [6]. For the physical quark masses we find The physical strange quark mass turns out to miss our sea input (0.04 + am res ) = 0.0432 by around 15%; since the kaon bag parameter is quite sensitive to the valence strange mass, we will need to interpolate between am y = 0.03 and 0.04 determine the value at the physical point.…”

“…We discuss the setting of the lattice scale and present the values for the physical light and strange quark masses. These were calculated in [5] and [6] on the 16 3 and 24 3 volumes respectively.…”

Lattice Results for Vector Meson Couplings and Parton Distribution Amplitudes

“…We use the collaborations' two principal ensembles, generated with the Iwasaki gauge action and domain wall fermions with an inverse lattice spacing of about 1.73 GeV. The two lattices have 24 3 × 64 × 16 points (corresponding to a physical volume of L 2.7 fm) and 16 3 × 32 × 16 points (physical volume, L 1.8 fm). The properties of the 16 3 (spatial) lattice have been presented in detail in ref.…”

“…On the 24 3 where a is the lattice spacing. On the 16 3 lattice results were obtained with ma = 0.03, 0.02 and 0.01.…”

“…On the 16 3 lattice it was found that a −1 = 1.62(4) GeV and m s a = 0.04 [1]. With the new data on the 24 3 lattice it is possible to reach lower masses and perform a more detailed investigation of the chiral behaviour [2,3]. The conclusion is that a −1 = 1.73(3) GeV and m s a 0.0344(16) and below I will discuss the corresponding corrections to the results obtained directly with m s a = 0.04.…”