2+1 flavour Domain Wall Fermion simulations by the RBC and UKQCD Collaborations

Abstract

We review simulations of dynamical domain wall fermions at a fixed inverse lattice spacing of 1.73GeV and with pion masses as light as 330MeV and spatial dimensions as large as 2.7fm performed by the RBC and UKQCD collaborations. These results include pseudoscalar masses and decay constants and low energy constants of the chiral effective lagrangian. We also review results for the neutral kaon mixing amplitude B K , the Kl3 form factor, pseudoscalar meson structure, and vector meson decay constants. In the baryon sector we review results for the spectrum, and nucleon form factors and structure functions. Highlights of our programme include preliminary quark masses, and determinations of V us from both f K / f π and from Kl3, and an updated result for B K. We find significant finite volume effects in the nucleon axial charge g A for our m π = 330 MeV ensemble on a (2.7fm) 3 lattice, and highlight the importance of large physical volumes for non-trivial nucleon physics.

Status of Kaon physics on the lattice

“…The blue vertical line represents Marciano's update for |V ud | from nuclear β -decays [12]. The horizontal band is the result for |V us | from RBC+UKQCD's lattice calculation of the semi-leptonic form factor [1,41,60] and the slightly tilted horizontal band represents (2.15). The solid black line represents CKM first-row unitarity (neglecting |V ub |).…”

“…The underlying assumption is that cut-off effects in the quenched and unquenched theory behave similarly. RBC+UKQCD [82,83,1] and JLQCD [85] use chiral fermions with 2+1 flavours of domain wall quarks and 2 flavours of overlap quarks, respectively. RBC+UKQCD estimate the cut-off effects from the experience with the quenched case [81,86] and both collaborations consider non-degenerate s-and d-quarks in the partially quenched framework and have renormalised the B K operator non-perturbatively in the RI-MOM scheme [87].…”

“…If used to constrain the Standard Model and also to constrain models that go beyond, consistency of the results from different discretisations will increase the reliability of the lattice output. To this end I want to draw the reader's attention to the plenary talks on recent simulations with domain wall fermions (DWF) [1], overlap fermions [2], twisted mass fermions (tmQCD) [3] and clover improved Wilson fermions [4] and also the two plenary talks by Creutz [5] and Kronfeld [6] 1 discussing different perspectives on the consistency of the staggered fermion (KS) formulation.…”

Nucleon Axial Charge in (2+1)-Flavor Dynamical-Lattice QCD with Domain-Wall Fermions

“…Our calculation is performed with a fixed lattice spacing, two space-time lattice sizes, 16 3 [17,18], were generated using the RHMC algorithm [19] with trajectories of unit length. The measurements were performed at the unitary points only, m f m val m sea .…”

On the low energy end of the QCD spectrum

“…Figure 2 compares recent lattice results for the dependence of the condensate on m s [29,30,31] with phenomenological estimates found in the literature [32,33,34,35] (the latter are calculated from the values quoted for the running coupling constant L 6 , using the relation (3) with F 0 = F π ). The errors shown exclusively account for the quoted uncertainties in the coupling constants, while 1 The contributions of O(m 2 s ) are also known explicitly, not only for F, B, Σ, but also for the coupling constants ℓ 1 , .…”