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We present our implementation of the RHMC algorithm for staggered fermions on Graphics Processing Units using the NVIDIA CUDA programming language. While previous studies exclusively deal with the Dirac matrix inversion problem, our code performs the complete MD trajectory on the GPU. After pointing out the main bottlenecks and how to circumvent them, we discuss the performance of our code.
The use of the absolute measure of local chirality is championed since it has a uniform distribution for randomly reshuffled chiral components so that any deviations from uniformity in the associated "X-distribution" are directly attributable to QCD-induced dynamics. We observe a transition in the qualitative behavior of this absolute X-distribution of low-lying eigenmodes which, we propose, defines a chiral polarization scale of the QCD vacuum.
We present results for matching factors for staggered four-fermion operators constructed using HYP-smeared fat links both in the action and the operators. We use perturbation theory to calculate the matching factors and work to one-loop order. The new feaure of this work is the use of the Symanzik-improved gauge action, as opposed to the Wilson gauge action. Our results are needed for our ongoing calculation of weak matrix elements using HYP-smeared staggered valence quarks and operators on MILC lattices. We give explicit results for matching factors of the operator needed to calculate $B_K$. We compare the impact of the improvement of the gauge action on one-loop coefficients with that of mean-field improvement of the operators.
Gauge fixing is a useful tool to simplify calculations. It is also valuable to combine different methods, in particular lattice and continuum methods. However, beyond perturbation theory the Gribov-Singer ambiguity requires further gauge conditions for a well-defined gauge-fixing prescription. Different additional conditions can, in principle, lead to different results for gauge-dependent correlation functions, as will be discussed for the example of Landau gauge. Also the relation of lattice and continuum gauge fixing beyond perturbation theory will be briefly outlined.
Using generalized Landau gauge, we study the continuous change of gluon properties from the Landau gauge toward the Coulomb gauge in SU(3) lattice QCD. We investigate "instantaneous interquark potential", which is defined by the spatial correlation of the temporal link-variable $U_4$ and is an interesting gauge-dependent concept. In the Coulomb gauge, the instantaneous potential is expressed by the Coulomb plus linear potential, where the slope is, however, 2-3 times as large as the physical string tension. In the Landau gauge, the instantaneous potential has no linear part. We find that the linear part is continuously growing by varying gauge from the Landau gauge toward the Coulomb gauge. We also find that the instantaneous potential approximately reproduces the physical interquark potential in a specific intermediate gauge, $λ_C$-gauge. This $λ_C$-gauge is expected to be a useful gauge for modeling effective theories such as the quark potential model.
Lattice QCD has the sign problem at real quark chemical potential. There are some regions with no sign problem; one is the imaginary quark chemical potential region and the others are the real and imaginary isospin chemical potential regions. We show that the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model can reproduce LQCD data in the regions. We also determine the model parameters from the data and predict the QCD phase diagram in the real quark chemical potential region.
We model the electrons on a monolayer graphene in terms of the compact and non-compact U(1) lattice gauge theories. The system is analyzed by the strong coupling expansion and is shown to be an insulator due to dynamical gap formation in/around the strong coupling limit. This is similar to the spontaneous chiral symmetry breaking in strong coupling gauge theories. The results from the compact and non-compact formulations are compared up to the next-to-leading order of the strong coupling expansion. Excitonic modes and their dispersion relations in the insulating phase are also investigated: it is found that there arises a pseudo-Nambu--Goldstone mode obeying the Gell-Mann--Oakes--Renner type formula.
We present a Monte Carlo renormalisation group study of the SU(2) gauge theory with two Dirac fermions in the adjoint representation. Using the two lattice matching technique recently advocated and exploited in [arXiv:0907.0919], we measure the running of the coupling and the anomalous mass dimension.
We study the effect of a potential fourth fermion generation on the upper and lower Higgs boson mass bounds. This investigation is based on the numerical evaluation of a chirally invariant lattice Higgs-Yukawa model emulating the same Higgs-fermion coupling structure as in the Higgs sector of the electroweak Standard Model. In particular, the considered model obeys a Ginsparg-Wilson version of the underlying ${SU}(2)_L\times {U}(1)_Y$ symmetry, being a global symmetry here due to the neglection of gauge fields in this model. We present our results on the modification of the upper and lower Higgs boson mass bounds induced by the presence of a hypothetical very heavy fourth quark doublet. Finally, we compare these findings to the standard scenario of three fermion generations.
A numerical study of Orientifold Planar Equivalence is performed in SU(N) Yang-Mills theories for N=2,3,4,6. Quenched meson masses are extracted in the antisymmetric, symmetric and adjoint representations for the pseudoscalar and vector channels. An extrapolation of the vector mass as a function of the pseudoscalar mass to the large-N limit shows that the numerical results agree within errors for the three theories, as predicted by Orientifold Planar Equivalence. As a byproduct of the extrapolation, the size of the corrections up to O(1/N^3) are evaluated. A crucial prerequisite for the extrapolation is the determination of an analytical relationship between the corrections in the symmetric and in the antisymmetric representations, order by order in a 1/N expansion.
The lowest-lying glueball masses are computed in SU($N$) gauge theory on a spacetime lattice for constant value of the lattice spacing $a$ and for $N$ ranging from 3 to 8. The lattice spacing is fixed using the deconfinement temperature at temporal extension of the lattice $N_T = 6$. The calculation is conducted employing in each channel a variational ansatz performed on a large basis of operators that includes also torelon and (for the lightest states) scattering trial functions. This basis is constructed using an automatic algorithm that allows us to build operators of any size and shape in any irreducible representation of the cubic group. A good signal is extracted for the ground state and the first excitation in several symmetry channels. It is shown that all the observed states are well described by their large $N$ values, with modest ${\cal O}(1/N^2)$ corrections. In addition spurious states are identified that couple to torelon and scattering operators.
There is a long standing challenge in lattice QCD concerning the relationship between $\mathcal{CP}$-symmetry and lattice chiral symmetry: naïvely the chiral symmetry transformations are not invariant under $\mathcal{CP}$. With results similar to a recent work by Igarashi and Pawlowski, I show that this is because charge conjugation symmetry has been incorrectly realised on the lattice. The naive approach, to directly use the continuum charge conjugation relations on the lattice, fails because the renormalisation group blockings required to construct a doubler free lattice theory from the continuum are not invariant under charge conjugation. Correctly taking into account the transformation of these blockings leads to a modified lattice $\mathcal{CP}$ symmetry for the fermion fields, which, for gauge field configurations with trivial topology, has a smooth limit to continuum $\mathcal{CP}$ as the lattice spacing tends to zero. After constructing $\mathcal{CP}$ transformations for one particular group of lattice chiral symmetries, I construct a lattice chiral gauge theory which is $\mathcal{CP}$ invariant and whose measure is invariant under gauge transformations and $\mathcal{CP}$.
For the non-perturbative analysis of the topological content of Yang-Mills theories, it is essential to disentangle long-range structures from short-range fluctuations. Some time ago, one of us proposed to use the adjoint modes of the Dirac operator for this purpose. In this talk we analyse an implementation of this idea that associates two Weyl fermionic modes in the adjoint representation to every gauge field configuration. The densities of these modes provide a filtered image of the self-dual and anti self-dual parts of the gauge action density. We present successful tests on the performance of this proposal on a set of initial gauge field configurations.
We present the first two-loop calculation of the heavy quark energy shift in lattice nonrelativistic QCD (NRQCD). This calculation allow us to extract a preliminary prediction of $m_b(m_b, n_f = 5) = 4.25(12)$ GeV for the mass of the b quark from lattice NRQCD simulations performed with a lattice of spacing $a=0.12$fm. Our result is an improvement on a previous determination of the b quark mass from unquenched lattice NRQCD simulations, which was limited by the use of one-loop expressions for the energy shift. Our value is in good agreement with recent results of $m_b(m_b) = 4.163(16)$ GeV from QCD sum rules and $m_b(m_b, n_f = 5) = 4.170(25)$ GeV from realistic lattice simulations using highly-improved staggered quarks. We employ a mixed strategy to simplify our calculation. Ghost, gluon and counterterm contributions to the energy shift and mass renormalisation are extracted from quenched high-beta simulations whilst fermionic contributions are calculated using automated lattice perturbation theory. Our results demonstrate the effectiveness of such a strategy.
We study the gluon propagator in the Landau gauge in SU(3) lattice QCD at $β$=5.7, 5.8 and 6.0 at the quenched level. The Euclidean Landau-gauge gluon propagator $D(r)\equiv D_{μμ}^{aa}(x)/24$ is found to be well described by four-dimensional Yukawa-type function $e^{-mr}/r$ in the infrared and intermediate region of $r \equiv (x_μx_μ)^{1/2}$ = 0.1 $\sim$ 1.0fm. The infrared effective gluon mass is obtained as $m \simeq$ 600MeV. Associated with the 4D Yukawa-type gluon propagator, we derive analytical expressions for the zero-spatial-momentum propagator $D_0(t)$, the effective mass $M_{\rm eff}(t)$, and the spectral function $ρ(ω)$ of the gluon field. Remarkably, the obtained gluon spectral function $ρ(ω)$ is almost negative definite, except for a positive $δ$-functional peak at $ω=m$. Since the Yukawa-type propagation indicates a three-dimensional space-time character, we consider a hypothesis of an effective dimensional reduction by generalized Parisi-Sourlas mechanism in a stochastic color-magnetic vacuum of infrared QCD.
Lattice Yang-Mills theories at finite temperature can be mapped onto effective 3d spin systems, thus facilitating their numerical investigation. Using strong-coupling expansions we derive effective actions for Polyakov loops in the $SU(2)$ and $SU(3)$ cases and investigate the effect of higher order corrections. Once a formulation is obtained which allows for Monte Carlo analysis, the nature of the phase transition in both classes of models is investigated numerically, and the results are then used to predict -- with an accuracy within a few percent -- the deconfinement point in the original 4d Yang-Mills pure gauge theories, for a series of values of $N_τ$ at once.
We present an evaluation of the quark mass renormalization factor for Nf=2+1 QCD. The Schroedinger functional scheme is employed as the intermediate scheme to carry out non-perturbative running from the low energy to deep in the high energy perturbative region. The regularization independent step scaling function of the quark mass is obtained in the continuum limit. Renormalization factors for the pseudo scalar density and the axial vector current are also evaluated for the same action and the bare couplings as two recent large scale Nf=2+1 simulations; previous work of the CP-PACS/JLQCD collaboration, which covered the up-down quark mass range heavier than m_pi=500 MeV and that of PACS-CS collaboration on the physical point using the reweighting technique.
We construct the transfer matrix for the ghost sector of partially quenched QCD. This transfer matrix is not hermitian, but we show that it is still bounded. We thus expect that all euclidean correlation functions will decay exponentially with distance (up to possible powers), and demonstrate that this is indeed the case for free ghost quarks.