Status of and performance estimates for QCDOC

QCDOC is a supercomputer designed for high scalability at a low cost per node. We discuss the status of the project and provide performance estimates for large machines obtained from cycle accurate simulation of the QCDOC ASIC.Comment: 3 pages 1 figure. Lattice2002(machines

Chirality Correlation within Dirac Eigenvectors from Domain Wall Fermions

In the dilute instanton gas model of the QCD vacuum, one expects a strong spatial correlation between chirality and the maxima of the Dirac eigenvectors with small eigenvalues. Following Horvath, {\it et al.} we examine this question using lattice gauge theory within the quenched approximation. We extend the work of those authors by using weaker coupling, $\beta=6.0$, larger lattices, $16^4$, and an improved fermion formulation, domain wall fermions. In contrast with this earlier work, we find a striking correlation between the magnitude of the chirality density, $|\psi^\dagger(x)\gamma^5\psi(x)|$, and the normal density, $\psi^\dagger(x)\psi(x)$, for the low-lying Dirac eigenvectors.Comment: latex, 25 pages including 12 eps figure

Nonperturbative bound on high multiplicity cross sections in phi^4_3 from lattice simulation

We have looked for evidence of large cross sections at large multiplicities in weakly coupled scalar field theory in three dimensions. We use spectral function sum rules to derive bounds on total cross sections where the sum can be expresed in terms of a quantity which can be measured by Monte Carlo simulation in Euclidean space. We find that high multiplicity cross sections remain small for energies and multiplicities for which large effects had been suggested.Comment: 23 pages, revtex, seven eps figures revised version: typos corrected, some rewriting of discusion, same resul

Hardware and software status of QCDOC

QCDOC is a massively parallel supercomputer whose processing nodes are based on an application-specific integrated circuit (ASIC). This ASIC was custom-designed so that crucial lattice QCD kernels achieve an overall sustained performance of 50% on machines with several 10,000 nodes. This strong scalability, together with low power consumption and a price/performance ratio of $1 per sustained MFlops, enable QCDOC to attack the most demanding lattice QCD problems. The first ASICs became available in June of 2003, and the testing performed so far has shown all systems functioning according to specification. We review the hardware and software status of QCDOC and present performance figures obtained in real hardware as well as in simulation.Comment: Lattice2003(machine), 6 pages, 5 figure

Direct CP violation and the ΔI=1/2 rule in K→ππ decay from the standard model

We present a lattice QCD calculation of the ΔI=1/2, K→ππ decay amplitude A0 and ϵ′, the measure of direct CP violation in K→ππ decay, improving our 2015 calculation [1] of these quantities. Both calculations were performed with physical kinematics on a 323×64 lattice with an inverse lattice spacing of a-1=1.3784(68)  GeV. However, the current calculation includes nearly 4 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 Re(A0)=2.99(0.32)(0.59)×10-7  GeV and Im(A0)=-6.98(0.62)(1.44)×10-11  GeV, where the errors are statistical and systematic, respectively. The former agrees well with the experimental result Re(A0)=3.3201(18)×10-7  GeV. These results for A0 can be combined with our earlier lattice calculation of A2 [2] to obtain Re(ϵ′/ϵ)=21.7(2.6)(6.2)(5.0)×10-4, where the third error represents omitted isospin breaking effects, and Re(A0)/Re(A2)=19.9(2.3)(4.4). The first agrees well with the experimental result of Re(ϵ′/ϵ)=16.6(2.3)×10-4. A comparison of the second with the observed ratio Re(A0)/Re(A2)=22.45(6), demonstrates the standard model origin of this “ΔI=1/2 rule” enhancement.We present a lattice QCD calculation of the $\Delta I=1/2$, $K\to\pi\pi$ decay amplitude $A_0$ and $\varepsilon'$, the measure of direct CP-violation in $K\to\pi\pi$ 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 $\pi\pi$ 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 "$\Delta I = 1/2$ rule" enhancement

Quenched Lattice QCD with Domain Wall Fermions and the Chiral Limit

Quenched QCD simulations on three volumes, $8^3 \times$, $12^3 \times$ and $16^3 \times 32$ and three couplings, $\beta=5.7$, 5.85 and 6.0 using domain wall fermions provide a consistent picture of quenched QCD. We demonstrate that the small induced effects of chiral symmetry breaking inherent in this formulation can be described by a residual mass (\mres) whose size decreases as the separation between the domain walls ($L_s$) is increased. However, at stronger couplings much larger values of $L_s$ are required to achieve a given physical value of \mres. For $\beta=6.0$ and $L_s=16$, we find \mres/m_s=0.033(3), while for $\beta=5.7$, and $L_s=48$, \mres/m_s=0.074(5), where $m_s$ is the strange quark mass. These values are significantly smaller than those obtained from a more naive determination in our earlier studies. Important effects of topological near zero modes which should afflict an accurate quenched calculation are easily visible in both the chiral condensate and the pion propagator. These effects can be controlled by working at an appropriately large volume. A non-linear behavior of $m_\pi^2$ in the limit of small quark mass suggests the presence of additional infrared subtlety in the quenched approximation. Good scaling is seen both in masses and in $f_\pi$ over our entire range, with inverse lattice spacing varying between 1 and 2 GeV.Comment: 91 pages, 34 figure

The SU(2) and SU(3) chiral phase transitions within Chiral Perturbation Theory

The SU(2) and SU(3) chiral phase transitions in a hot gas made of pions, kaons and etas are studied within the framework of Chiral Perturbation Theory. By using the meson meson scattering phase shifts in a second order virial expansion, we are able to describe the temperature dependence of the quark condensates. We have estimated the critical temperatures where the different condensates melt. In particular, the SU(3) formalism yields a lower critical temperature for the non-strange condensates than within SU(2), and also suggests that the strange condensate may melt at a somewhat higher temperature, due to the different strange and non-strange quark masses.Comment: 4 pages, two figures. Final version to appear in Phys Rev D. Complete model independent calculation. Unitarized ChPt only used to check extrapolation at high T. References added and numerical bug correcte

Computational Physics on Graphics Processing Units

The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory.Comment: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 201

Pi-eta scattering and the resummation of vacuum fluctuation in three-flavour ChPT

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the ss-pairs and the scenario with smaller value of the chiral condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with pi-eta scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p^4) LEC's, namely to the values of the fluctuation parameters L4 and L6. We discuss several issues in detail, namely the choice of `good' observables and properties of their bare expansions, the `safe' reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and their estimates. We make a detailed comparison with standard chiral perturbation theory and use generalized ChPT as well as resonance chiral theory to estimate the higher order remainders.Comment: Version submitted to EPJ