Christoph Lehner

Domain wall QCD with physical quark masses

We present results for several light hadronic quantities ( f π , f K , B K , m ud , m s , t 0 ½, w 0 ) obtained from simulations of 2+1 flavor domain wall lattice QCD with large physical volumes and nearly physical pion masses at two lattice spacings. We perform a short, O (3) %, extrapolation in pion mass to the physical values by combining our new data in a simultaneous chiral/continuum “global fit” with a number of other ensembles with heavier pion masses. We use the physical values of m π , m K and m Ω to determine the two quark masses and the scale—all other quantities are outputs from our simulations. We obtain results with subpercent statistical errors and negligible chiral and finite-volume systematics for these light hadronic quantities, including f π = 130.2(9) MeV; f K = 155.5(8) MeV; the average up/down quark mass and strange quark mass in the ‾MS scheme at 3 GeV, 2.997(49) and 81.64(1.17) MeV respectively; and the neutral kaon mixing parameter, B K , in the renormalization group invariant scheme, 0.750(15) and the ‾MS scheme at 3 GeV, 0.530(11).

Lattice determination of the K → ( π π ) I = 2 decay amplitude A 2

We describe the computation of the amplitude A2 for a kaon to decay into two pions with isospin I = 2. The results presented in the letter [1] from an analysis of 63 gluon configurations are updated to 146 configurations giving ReA2 = 1:381(46)stat(258)syst 10 8 GeV and ImA2 = 6:54(46)stat(120) syst10 13 GeV . ReA2 is in good agreement with the experimental result, whereas the value of ImA2 was hitherto unknown. We are also working towards a direct computation of the K! (pp)I=0 amplitude A0 but, within the standard model, our result for ImA2 can be combined with the experimental results for ReA0, ReA2 and e 0 =e to give ImA0=ReA0 = 1:61(28) 10 4 . Our result for ImA2 implies that the electroweak penguin

Λb → pℓ¯ν¯ℓ and Λb → Λcℓ¯ν¯ℓ form factors from lattice QCD with relativistic heavy quarks

William Detmold, Christoph Lehner, and Stefan Meinel 3, 4, ∗ Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA Department of Physics, University of Arizona, Tucson, AZ 85721, USA RIKEN BNL Research Center, Brookhaven National Laboratory, Upton, NY 11973, USA Measurements of the Λb → p `ν̄` and Λb → Λc `ν̄` decay rates can be used to determine the magnitudes of the CKM matrix elements Vub and Vcb, provided that the relevant hadronic form factors are known. Here we present a precise calculation of these form factors using lattice QCD with 2+1 flavors of dynamical domain-wall fermions. The b and c quarks are implemented with relativistic heavy-quark actions, allowing us to work directly at the physical heavy-quark masses. The lattice computation is performed for six different pion masses and two different lattice spacings, using gauge-field configurations generated by the RBC and UKQCD collaborations. The b→ u and b→ c currents are renormalized with a mostly nonperturbative method. We extrapolate the form factor results to the physical pion mass and the continuum limit, parametrizing the q-dependence using z-expansions. The form factors are presented in such a way as to enable the correlated propagation of both statistical and systematic uncertainties into derived quantities such as differential decay rates and asymmetries. Using these form factors, we present predictions for the Λb → p `ν̄` and Λb → Λc `ν̄` differential and integrated decay rates. Combined with experimental data, our results enable determinations of |Vub|, |Vcb|, and |Vub/Vcb| with theory uncertainties of 5.0%, 2.2%, and 5.3%, respectively.

Lattice Calculation of Hadronic Light-by-Light Contribution to the Muon Anomalous Magnetic Moment

The quark-connected part of the hadronic light-by-light scattering contribution to the muon’s anomalous magnetic moment is computed using lattice QCD with chiral fermions. Here we report several significant algorithmic improvements and demonstrate their effectiveness through specific calculations which show a reduction in statistical errors by more than an order of magnitude. The most realistic of these calculations is performed with a near-physical 171 MeV pion mass on a (4.6 fm)3 spatial volume using the 323×64 Iwasaki+DSDR gauge ensemble of the RBC/UKQCD Collaboration.

K to ππ decay amplitudes from lattice QCD

We report a direct lattice calculation of the K to ?? decay matrix elements for both the ?I=1/2 and 3/2 amplitudes A0 and A2 on 2+1 flavor, domain wall fermion, 163×32×16 lattices. This is a complete calculation in which all contractions for the required ten, four-quark operators are evaluated, including the disconnected graphs in which no quark line connects the initial kaon and final two-pion states. These lattice operators are nonperturbatively renormalized using the Rome-Southampton method and the quadratic divergences are studied and removed. This is an important but notoriously difficult calculation, requiring high statistics on a large volume. In this paper, we take a major step toward the computation of the physical K??? amplitudes by performing a complete calculation at unphysical kinematics with pions of mass 422 MeV at rest in the kaon rest frame. With this simplification, we are able to resolve Re(A0) from zero for the first time, with a 25% statistical error and can develop and evaluate methods for computing the complete, complex amplitude A0, a calculation central to understanding the ?=1/2 rule and testing the standard model of CP violation in the kaon system.

Covariant approximation averaging

We present a new class of statistical error reduction techniques for Monte-Carlo simulations. Using covariant symmetries, we show that correlation functions can be constructed from inexpensive approximations without introducing any systematic bias in the final result. We introduce a new class of covariant approximation averaging techniques, known as all-mode averaging (AMA), in which the approximation takes account of contributions of all eigenmodes through the inverse of the Dirac operator computed from the conjugate gradient method with a relaxed stopping condition. In this paper we compare the performance and computational cost of our new method with traditional methods using correlation functions and masses of the pion, nucleon, and vector meson in

Neutral B meson mixings and B meson decay constants with static heavy and domain-wall light quarks

N_f=2+1

Nonperturbative tuning of an improved relativistic heavy-quark action with application to bottom spectroscopy

lattice QCD using domain-wall fermions. This comparison indicates that AMA significantly reduces statistical errors in Monte-Carlo calculations over conventional methods for the same cost.

Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study

Neutral

Matching factors for Δ S = 1 four-quark operators in RI/SMOM schemes

B