arXiv subjects

Norman H. Christ

Publications and source records attributed to Norman H. Christ.

51 records · Page 3Linked to original sources

arXiv2010

Neutral B-meson mixing from unquenched lattice QCD with domain-wall light quarks and static b-quarks

We demonstrate a method for calculating the neutral B-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static b-quarks. Our computation is performed on the "2+1" flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of a approx 0.11 fm (a^-1 = 1.729 GeV) and a lattice spatial volume of approximately (1.8 fm)^3. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the b-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the B-meson decay constant to O(alpha_s p a) using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios f_{B_s}/f_{B_d} and xi = f_{B_s} sqrt{B_{B_s}}/f_{B_d} sqrt{B_{B_d}}, thereby demonstrating the viability of the method. For the ratio of decay constants, we find f_{B_s}/f_{B_d} = 1.15(12) and for the ratio of mixing matrix elements, we find xi = 1.13(12), where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected O(1/m_b) effects.

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arXiv2009

Theoretical strategies for epsilon'/epsilon

We review the current status of calculations of the two pion decays of the kaon using the first-principles methods of lattice gauge theory and the significant challenges that these calculations pose. While a calculation with controlled errors at even the 10-20% level has not yet been performed, present results suggest that such a calculation of the real and imaginary parts of the Delta I = 3/2 amplitude should be accomplished within the next two years. The more difficult Delta I = 1/2 amplitude may also be now within reach.

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arXiv2009

G parity boundary conditions and Delta I = 1/2, K to pi pi decays

The use of G-parity boundary conditions to compute Delta I = 1/2, K to pi pi decays is reviewed and a method to consistently treat both the pions and kaon in full QCD proposed. This approach creates a physical, final-state, pion momentum using a 3 fm box and avoids statistical noise coming from pions with smaller momentum.

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arXiv2008

Chiral perturbation theory, K to pi pi decays and 2+1 flavor domain wall QCD

We present a calculation of the low energy constants describing the real and imaginary parts of the $K \to ππ$ decay amplitudes $A_0$ and $A_2$. Leading and next leading order chiral perturbation theory is used and its applicability assessed. A combination of statistical and systematic errors limits the precision of the results. The apparent limitations of chiral perturbation theory raise doubts about the accuracy of a possible extrapolation to physical $K \to ππ$ kinematics.

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arXiv2007

Localization and chiral symmetry in 2+1 flavor domain wall QCD

We present results for the dependence of the residual mass of domain wall fermions (DWF) on the size of the fifth dimension and its relation to the density and localization properties of low-lying eigenvectors of the corresponding hermitian Wilson Dirac operator relevant to simulations of 2+1 flavor domain wall QCD. Using the DBW2 and Iwasaki gauge actions, we generate ensembles of configurations with a $16^3\times 32$ space-time volume and an extent of 8 in the fifth dimension for the sea quarks. We demonstrate the existence of a regime where the degree of locality, the size of chiral symmetry breaking and the rate of topology change can be acceptable for inverse lattice spacings $a^{-1} \ge 1.6$ GeV.

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arXiv2007

The Static Approximation to B Meson Mixing using Light Domain-Wall Fermions: Perturbative Renormalization and Ground State Degeneracies

We discuss the theoretical input into the current RBC-UKQCD calculation of $f_{B_{d, s}}$ and $B_{B_{d, s}}$ using a smeared static heavy quark propagator, light domain-wall quarks and the Iwasaki gauge action. We present the complete one-loop, mean-field improved matching of heavy-light current and four-fermion lattice operators onto the static continuum theory renormalized in $\bar{\text{MS}}$(NDR). The large degeneracies present in a static calculation are addressed, and a method for extracting $f_B$ and $B_B$ using only box sources is described; implications for future calculations are discussed.

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arXiv2006

Relativistic Heavy Quark Effective Action

We study the fermion action needed to accurately describe the low energy physics of systems including heavy quarks in lattice QCD even when the heavy fermion mass $m$ is on the order of, or larger than, the inverse lattice spacing: $m \ge 1/a$. We carry out an expansion through first order in $|\vec p| a$ (where $\vec p$ is the heavy quark momentum) and all orders in $ma$, refining the analysis of the Fermilab and Tsukuba groups. We demonstrate that the spectrum of heavy quark bound states can be determined accurately through $|\vec p| a$ and $(ma)^n$ for arbitrary exponent $n$ by using a lattice action containing only three unknown coefficients: $m_0$, $ζ$ and $c_P$ (a generalization of $c_{SW}$), which are functions of $ma$. In a companion paper, we show how these three coefficients can be precisely determined using non-perturbative techniques.

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arXiv2005

Non-perturbatively determined relativistic heavy quark action

Preliminary results are presented in a step scaling determination of the coefficients in the relativistic heavy quark action. By matching finite volume, heavy-heavy and heavy-light meson masses, we attempt to determine the four parameters ($m$, $ζ$, $c_B$ and $c_E$) in the on-shell-improved, heavy quark action. In this report we carry out one step in this program by matching two physically equivalent systems. The first is a fully relativistic calculation using a $24^3\times 48$, $1/a=5.4$ GeV lattice with both the heavy and light quarks treated as domain wall fermions. The second calculation uses at $16^3\times 32$, $1/a=3.6$ GeV lattice, a domain-wall light quark and a heavy quark computed with the relativistic heavy quark action. The four parameters in this heavy quark effective action are then varied to reproduce the mass spectrum from the first calculation. These calculations are carried out in the quenched approximation for a heavy quark mass approximately that of the charmed quark.

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arXiv2005

Finite Volume Corrections to the Two-Particle Decay of States with Non-Zero Momentum

We study the effects of finite volume on the two-particle decay rate of an unstable state with non-zero momentum. First Luscher's field-theoretic relation between the infinite volume scattering phase shifts and the quantized energy levels of a finite volume, two-particle system is generalized to the case of non-zero total momentum and compared with the earlier results of Rummukainen and Gottlieb. We then use this result and the method of Lellouch and Luscher to determine the corrections needed for a finite-volume calculation of a two-particle decay amplitude when the decaying particle has non-vanishing center-of-mass momentum.

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arXiv2002

K \to ππdecay amplitudes from the lattice

In order to directly compute physical two-pion K-decay amplitudes using lattice methods we must prepare a two-pion state with non-zero relative momentum. Building upon a proposal of Lellouch and Lüscher, we describe a finite-volume method to realize such a state as the lowest energy state of two pions.

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arXiv1999

Computers for Lattice QCD

The architecture and capabilities of the computers currently in use for large-scale lattice QCD calculations are described and compared. Based on this present experience, possible future directions are discussed.

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arXiv1998

The domain wall fermion chiral condensate in quenched QCD

We examine the chiral limit of domain wall fermions in quenched QCD. One expects that in a quenched simulation, exact fermion zero modes will give a divergent, 1/m behavior in the chiral condensate for sufficiently small valence quark masses. Unlike other fermion formulations, domain wall fermions clearly demonstrate this behavior.

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arXiv1998

Status of the QCDSP project

We describe the completed 8,192-node, 0.4Tflops machine at Columbia as well as the 12,288-node, 0.6Tflops machine assembled at the RIKEN Brookhaven Research Center. Present performance as well as our experience in commissioning these large machines is presented. We outline our on-going physics program and explain how the configuration of the machine is varied to support a wide range of lattice QCD problems, requiring a variety of machine sizes. Finally a brief discussion is given of future prospects for large-scale lattice QCD machines.

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arXiv1997

QCDSP - A status report

The QCDSP machine at Columbia University has grown to 2,048 nodes achieving a peak speed of 100 Gigaflops. Software for quenched and Hybrid Monte Carlo (HMC) evolution schemes has been developed for staggered fermions, with support for Wilson and clover fermions under development. We provide an overview of the runtime environment, the current status of the QCDSP construction program and preliminary results not presented elsewhere in these proceedings.

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arXiv1992

Lattice QCD with 8 Light Quark Flavors

QCD with eight flavors is studied on $16^3\times N_t$ lattices with $N_t=4$, 6, 8, 16 and 32, a dynamical quark mass $ma=0.015$ and lattice coupling $β=6/g^2$ between 4.5 and 5.0. For $N_t=16$ and 32, hadron masses and screening lengths are computed for a variety of valence quark masses. The previously observed, strong, first-order transition for $N_t=4$, 6 and 8 is seen, for $N_t=16$, to become a $β$-independent, zero-temperature transition characterized by a factor of $\approx 3$ change in lattice scale. This strong, first-order transition restores chiral symmetry, at least for $N_t=4$, 6 and 8, producing a chirally symmetric, weak-coupling phase. However, as $N_t$ increases to 16, the chiral symmetry properties of the weak-coupling side of the zero-temperature transition are unclear and offer a hint of a normal, finite-temperature, chiral symmetry breaking transition in the weak-coupling phase.

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