arXiv subjects

Robert D. Mawhinney

Publications and source records attributed to Robert D. Mawhinney.

At least 19 recordsLinked to original sources

arXiv2020

Direct CP violation and the $ΔI=1/2$ rule in $K\toππ$ decay from the Standard Model

We present a lattice QCD calculation of the $ΔI=1/2$, $K\toππ$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\toππ$ decay, improving our 2015 calculation of these quantities. Both calculations were performed with physical kinematics on a $32^3\times 64$ lattice with an inverse lattice spacing of $a^{-1}=1.3784(68)$ GeV. However, the current calculation includes nearly four times the statistics and numerous technical improvements allowing us to more reliably isolate the $ππ$ ground-state and more accurately relate the lattice operators to those defined in the Standard Model. We find ${\rm Re}(A_0)=2.99(0.32)(0.59)\times 10^{-7}$ GeV and ${\rm Im}(A_0)=-6.98(0.62)(1.44)\times 10^{-11}$ GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result ${\rm Re}(A_0)=3.3201(18)\times 10^{-7}$ GeV. These results for $A_0$ can be combined with our earlier lattice calculation of $A_2$ to obtain ${\rm Re}(\varepsilon'/\varepsilon)=21.7(2.6)(6.2)(5.0) \times 10^{-4}$, where the third error represents omitted isospin breaking effects, and Re$(A_0)$/Re$(A_2) = 19.9(2.3)(4.4)$. The first agrees well with the experimental result of ${\rm Re}(\varepsilon'/\varepsilon)=16.6(2.3)\times 10^{-4}$. A comparison of the second with the observed ratio Re$(A_0)/$Re$(A_2) = 22.45(6)$, demonstrates the Standard Model origin of this "$ΔI = 1/2$ rule" enhancement.

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arXiv2019

2+1 Flavor Domain Wall Fermion QCD Lattices: Ensemble Production and (some) Properties

The RBC and UKQCD Collaborations continue to produce 2+1 flavor domain wall fermion ensembles, currently focusing on an ensemble with a $96^3 \times 192$ volume on SUMMIT at ORNL with $1/a \approx 2.8$ GeV, and smaller ensembles at stronger couplings. The $1/a \approx 2.8$ GeV ensemble uses the Exact One Flavor Algorithm for the strange quark, along with the Multisplitting Preconditioned Conjugate Gradient for solving the Dirac equation. We report on our progress and experience to date with the evolution of this ensemble.

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arXiv2015

The kaon semileptonic form factor in Nf=2+1 domain wall lattice QCD with physical light quark masses

We present the first calculation of the kaon semileptonic form factor with sea and valence quark masses tuned to their physical values in the continuum limit of 2+1 flavour domain wall lattice QCD. We analyse a comprehensive set of simulations at the phenomenologically convenient point of zero momentum transfer in large physical volumes and for two different values of the lattice spacing. Our prediction for the form factor is f+(0)=0.9685(34)(14) where the first error is statistical and the second error systematic. This result can be combined with experimental measurements of K->pi decays for a determination of the CKM-matrix element for which we predict |Vus|=0.2233(5)(9) where the first error is from experiment and the second error from the lattice computation.

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arXiv2014

Diffusion of topological charge in lattice QCD simulations

We study the autocorrelations of observables constructed from the topological charge density, such as the topological charge on a time slice or in a subvolume, using a series of hybrid Monte Carlo simulations of pure SU(3) gauge theory with both periodic and open boundary conditions. We show that the autocorrelation functions of these observables obey a simple diffusion equation and we measure the diffusion coefficient, finding that it scales like the square of the lattice spacing. We use this result and measurements of the rate of tunneling between topological charge sectors to calculate the scaling behavior of the autocorrelation times of these observables on periodic and open lattices. There is a characteristic lattice spacing at which open boundary conditions become worthwhile for reducing autocorrelations and we show how this lattice spacing is related to the diffusion coefficient, the tunneling rate, and the lattice Euclidean time extent.

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arXiv2013

Scaling, topological tunneling and actions for weak coupling DWF calculations

We present results from a 2+1 flavor DWF calculation at 1/a = 3 GeV and discuss strategies for similar calculations at finer lattice spacings which will target charm physics. At weak coupling the autocorrelation time of the global topological charge becomes very long because the HMC algorithm has trouble moving between topological sectors. We report the results of simulations that test two ideas for reducing the autocorrelation time of topological charge. In weak coupling quenched simulations we find that the open boundary conditions suggested by Lüscher and Schaefer do not prevent the appearance of extremely long autocorrelation times for topological observables. We discuss the idea of a "dislocation-enhancing determinant" and show that it can produce an increase in topological tunneling.

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arXiv2013

Lattice QCD with 12 Quark Flavors: A Careful Scrutiny

With a substantial amount of simulations, we have explored the system across a wide range of lattice scales. We have located a lattice artifact, first order bulk transition, have studied its properties, and found that the flavor-singlet scalar meson mass vanishes at the critical endpoint. We will discuss the lattice phase diagrams and the continuum limits for both a spontaneous chiral symmetry breaking phase and an infrared conformal phase, and compare results with other groups.

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arXiv2012

Lattice QCD with 12 Degenerate Quark Flavors

We report on new data from additional zero temperature simulations of QCD with 12 flavors. This is a continuation of previous studies using the DBW2 gauge action and naive staggered fermions. With the use of the force gradient integrator and a multiple-quark-mass preconditioned HMC, we have done simulations with input quark masses from $m_q=0.003$ to $m_q=0.008$. We have observed a metastable, first order, bulk transition that occurs at small input quark masses. As the quark mass increases, this first order bulk transition ends at a second order critical point, and, for still heavier quark masses, becomes the cross-over we have previously reported. We present measurements of hadron masses, decay constants and other low energy observables in the small quark mass region on the weak coupling side of the bulk transition. Our results show that the behavior of the system is still consistent with spontaneously broken chiral symmetry. We also discuss a preliminary investigation into the behavior of the bulk transition itself. We have found that, as the system approaches the second order critical end point, the scalar singlet meson becomes lighter. Thus it appears that the critical endpoint corresponds to a continuum limit theory only involving scalars and, following known triviality arguments, this is likely a free field theory. The presence of this critical endpoint could influence scaling of lattice observables in the conventional continuum limit.

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arXiv2011

Improving DWF Simulations: the Force Gradient Integrator and the Möbius Accelerated DWF Solver

We have implemented a variant of the force gradient integrator proposed by Kennedy et.al. and are using it in our production 2+1 flavor DWF simulations with pion masses of 180 MeV in (4.5fm)3 volumes. We find modest speed-ups (\sim 20%) from using the force gradient integrator, compared to our previously used Omelyan integrator. On other ensembles, primarily finite temperature 2+1 flavor DWF QCD, we have extensively tuned the Hasenbusch preconditioning masses and achieved speed-ups of 2-3x. Here we have also switched to the force gradient integrator, but this change has not had any impact on the speed. We also report on an improved solver for DWF, which uses Möbius fermions, with a smaller fifth dimension than the original DWF fermions, as an intermediate step in the generation of solutions of the Dirac equation. This approach cuts the number of effective Dirac applications by approximately a factor of 2 when the conjugate gradient iteration count is large.

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arXiv2010

Evidence for a First Order, Finite Temperature Phase Transition in 8 Flavor QCD

As part of our ongoing investigations of QCD with many flavors of quarks, here we report on studies of the finite temperature phase transition for eight-flavor QCD with the DBW2 gauge action and naïve staggered fermions. We find a clear first order phase transition between the chirally asymmetric phase at zero temperature and the chirally symmetric phase at finite temperature, signaled by a two-state signal for $\langle\barψψ\rangle$ at a non-zero temperature. We see this signal at a gauge coupling of $β=0.54$, where, to set the scale, the zero temperature value for $f_π$, in the chiral limit, is 0.06661(92). This strong, first-order signal is seen for two different values of the quark mass, $m_q=0.007$ and 0.0195, at $N_τ=8$ and 6 respectively. Using $f_π(m_q)$ as the scale, the critical temperature is measured to be $T_c/f_π=1.638(93)$ at $m_π/f_π=3.329(30)$ for $m_q=0.007$, and $T_c/f_π=1.779(27)$ at $m_π/f_π=4.093(15)$ for $m_q=0.0195$. At a weaker coupling $β=0.56$, where at zero temperature and in the chiral limit we find $f_π=0.0312(10)$, the first order signal becomes numerically invisible to us for the $N_τ\leq 14$ lattices we have investigated so far.

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arXiv2009

Lattice QCD with 8 and 12 degenerate quark flavors

We compare extensive simulations of QCD with 8 and 12 flavors of degenerate quarks, using the DBW2 gauge action, naive staggered fermions, and the rational hybrid Monte Carlo algorithm. A variety of values of the coupling constant, quark mass, and lattice size have been used. Our data suggests that, as the bare coupling is decreased, a rapid cross-over, which dramatically changes the lattice scale, exists with both 8 and 12 flavors. The scale change across this cross-over is much larger with 12 flavors than it is with 8 flavors. All of the observables we have measured, in both the zero and finite temperature systems, are consistent with a chiral symmetry breaking phase for the zero temperature theory on the weak coupling side of the rapid cross-over.

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arXiv2008

Lattice QCD with Eight Degenerate Quark Flavors

We report on simulations of QCD with many flavors of degenerate quarks, the DBW2 gauge action and naive staggered fermions, using the rational hybrid Monte Carlo algorithm. We primarily focus on eight degenerate quark flavors where a variety of values of the coupling constant and quark mass have been used in the simulations. The scaling behavior of the hadron spectrum and the string tension of the heavy quark potential is studied, to probe whether the zero temperature, continuum limit of the theory breaks chiral symmetry.

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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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arXiv2000

$K \to ππ$ Decays with Domain Wall Fermions: Towards Physical Results

We are using domain wall fermions to study $K \to ππ$ matrix elements by measuring $K \to π$ and $K \to 0$ matrix elements on the lattice and employing chiral perturbation theory to relate these to the desired physical result. The residual chiral symmetry breaking of domain wall fermions with a finite extent in the fifth dimension impacts these measurements. Using the Ward-Takahashi identities, we investigate residual chiral symmetry breaking effects for divergent quantities and study pathologies of the quenched approximation for small quark mass. We then discuss the $ΔS = 1$ operator $O_2$, where chiral symmetry is vital for the subtraction of unphysical effects.

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arXiv2000

The 1 Teraflops QCDSP computer

The QCDSP computer (Quantum Chromodynamics on Digital Signal Processors) is an inexpensive, massively parallel computer intended primarily for simulations in lattice gauge theory. Currently, two large QCDSP machines are in full-time use: an 8,192 processor, 0.4 Teraflops machine at Columbia University and an 12,288 processor, 0.6 Teraflops machine at the RIKEN-BNL Research Center at Brookhaven National Laboratory. We describe the design process, architecture, software and current physics projects of these computers.

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arXiv2000

Review of Unquenched Results

One of the major frontiers of lattice field theory is the inclusion of light fermions in simulations, particularly in pursuit of accurate, first principles predictions from lattice QCD. With dedicated Teraflops-scale computers currently simulating QCD, another step towards precision full QCD simulations is underway. In addition to ongoing staggered and Wilson fermion simulations, first results from full QCD with domain wall fermions are available. After some discussion of work toward better algorithms, simulations completed to date will be 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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