We present our result for the $Ktopipi$ decay amplitudes for both the $Delta I=1/2$ and $3/2$ processes with the improved Wilson fermion action. Expanding on the earlier works by Bernard {it et al.} and by Donini {it et al.}, we show that mixings wit
h four-fermion operators with wrong chirality are absent even for the Wilson fermion action for the parity odd process in both channels due to CPS symmetry. Therefore, after subtraction of an effect from the lower dimensional operator, a calculation of the decay amplitudes is possible without complications from operators with wrong chirality, as for the case with chirally symmetric lattice actions. As a first step to verify the possibility of calculations with the Wilson fermion action, we consider the decay amplitudes at an unphysical quark mass $m_K sim 2 m_pi$. Our calculations are carried out with $N_f=2+1$ gauge configurations generated with the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson fermion action at $a=0.091,{rm fm}$, $m_pi=280,{rm MeV}$, and $m_K=580,{rm MeV}$ on a $32^3times 64$ ($La=2.9,{rm fm}$) lattice. For the quark loops in the penguin and disconnected contributions in the $I=0$ channel, the combined hopping parameter expansion and truncated solver method work very well for variance reduction. We obtain, for the first time with a Wilson-type fermion action, that ${rm Re}A_0 = 60(36) times10^{ -8},{rm GeV}$ and ${rm Im}A_0 =-67(56) times10^{-12},{rm GeV}$ for a matching scale $q^* =1/a$. The dependence on the matching scale $q^*$ for these values is weak.
We investigate SU(3) gauge theories in four dimensions with Nf fundamental fermions, on a lattice using the Wilson fermion. Clarifying the vacuum structure in terms of Polyakov loops in spatial directions and properties of temporal propagators using
a new method local analysis, we conjecture that the conformal region exists together with the confining region and the deconfining region in the phase structure parametrized by beta and K, both in the cases of the large Nf QCD within the conformal window (referred as Conformal QCD) with an IR cutoff and small Nf QCD at T/Tc>1 with Tc being the chiral transition temperature (referred as High Temperature QCD). Our numerical simulation on a lattice of the size 16^3 x 64 shows the following evidence of the conjecture. In the conformal region we find the vacuum is the nontrivial Z(3) twisted vacuum modified by non-perturbative effects and temporal propagators of meson behave at large t as a power-law corrected Yukawa-type decaying form. The transition from the conformal region to the deconfining region or the confining region is a sharp transition between different vacua and therefore it suggests a first order transition both in Conformal QCD and in High Temperature QCD. Within our fixed lattice simulation, we find that there is a precise correspondence between Conformal QCD and High Temperature QCD in the temporal propagators under the change of the parameters Nf and T/Tc respectively. In particular, we find the correspondence between Conformal QCD with Nf = 7 and High Temperature QCD with Nf=2 at T ~ 2 Tc being in close relation to a meson unparticle model. From this we estimate the anomalous mass dimension gamma* = 1.2 (1) for Nf=7. We also show that the asymptotic state in the limit T/Tc --> infty is a free quark state in the Z(3) twisted vacuum.
In the exploration of viable models of dynamical electroweak symmetry breaking, it is essential to locate the lower end of the conformal window and know the mass anomalous dimensions there for a variety of gauge theories. We calculate, with the Schro
dinger functional scheme, the running coupling constant and the mass anomalous dimension of SU(2) gauge theory with six massless Dirac fermions in the fundamental representation. The calculations are performed on $6^4$ - $24^4$ lattices over a wide range of lattice bare couplings to take the continuum limit. The discretization errors for both quantities are removed perturbatively. We find that the running slows down and comes to a stop at $0.06 lesssim 1/g^2 lesssim 0.15$ where the mass anomalous dimension is estimated to be $0.26 lesssim gamma^*_m lesssim 0.74$.
We investigate the chiral properties of SU(2) gauge theory with six flavors, i.e. six light Dirac fermions in the fundamental representations by lattice simulation, and point out that the spontaneous breakdown of chiral symmetry does not occur in thi
s system. The quark mass dependence of the mesonic spectrum provides an evidence for such a possibility. The decay constant tends to be increased by the finite size effect, which is opposite to the behavior predicted by chiral perturbation theory and indicates that the long distance dynamics in the six-flavor theory could be different from the theory with chiral symmetry breaking. The subtracted chiral condensate, whose utility is demonstrated by the simulation of two-flavor theory, is shown to vanish in the chiral limit within the precision of available data.
We give a new perspective on the properties of quarks and gluons at finite temperature T in N_f = 2 ~ 6 QCD. We point out the existence of an IR fixed point for the gauge coupling constant at T>T_c (T_c is the chiral phase transition temperature). Ba
sed on this observation we predict theoretically and verify numerically that the correlation functions of a meson G(t) at T/T_c > 1 decay with a power-law corrected Yukawa-type decaying form, G(t)=c exp(-m t)/t^alpha in the conformal region defined by m < c Lambda_IR, where Lambda_IR is the IR cutoff, m is the characteristic scale of the spectrum in the meson cannel and c is a constant of order 1. The decaying form is the characteristics of conformal theories with an IR cutoff. We discuss in detail how the resulting hyper scaling relation of physical observables may modify the existing argument about the order of the chiral phase transition in the N_f=2 case.
We give a new perspective on the dynamics of conformal theories realized in the SU(N) gauge theory, when the number of flavors N_f is within the conformal window. Motivated by the RG argument on conformal theories with a finite IR cutoff Lambda_{IR},
we conjecture that the propagator of a meson G_H(t) on a lattice behaves at large t as a power-law corrected Yukawa-type decaying form G_H(t) = c_H exp{(-m_H t)}/t^{alpha_H} instead of the exponentially decaying form c_Hexp{(-m_H t)}, in the small quark mass region where m_H le c Lambda_{IR}: m_H is the mass of the ground state hadron in the channel H and c is a constant of order 1. The transition between the conformal region and the confining region is a first order transition. Our numerical results verify the predictions for the N_f=7 case and the N_f=16 case in the SU(3) gauge theory with the fundamental representation.
We investigate the charmed baryon mass spectrum using the relativistic heavy quark action on 2+1 flavor PACS-CS configurations previously generated on $32^3 times 64$ lattice. The dynamical up-down and strange quark masses are tuned to their physical
values, reweighted from those employed in the configuration generation. At the physical point, the inverse lattice spacing determined from the $Omega$ baryon mass gives $a^{-1}=2.194(10)$ GeV, and thus the spatial extent becomes $L = 32 a = 2.88(1)$ fm. Our results for the charmed baryon masses are consistent with experimental values, except for the mass of $Xi_{cc}$, which has been measured by only one experimental group so far and has not been confirmed yet by others. In addition, we report values of other doubly and triply charmed baryon masses, which have never been measured experimentally.
We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. We implement the Luschers SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to severa
l sub-blocks to extract enough parallelism for the 8-core CPU SPARC64$^{mathrm{TM}}$ VIIIfx of the K computer. To achieve a better convergence property we use the symmetric successive over-relaxation (SSOR) iteration with {it locally-lexicographical} ordering for the sub-blocks in obtaining the block inverse. The SAP preconditioner is included in the single precision BiCGStab solver of the nested BiCGStab solver. The single precision part of the computational kernel are solely written with the SIMD oriented intrinsics to achieve the best performance of the SPARC on the K computer. We benchmark the single precision BiCGStab solver on the three lattice sizes: $12^3times 24$, $24^3times 48$ and $48^3times 96$, with fixing the local lattice size in a node at $6^3times 12$. We observe an ideal weak-scaling performance from 16 nodes to 4096 nodes. The performance of a computational kernel exceeds 50% efficiency, and the single precision BiCGstab has $sim26% susutained efficiency.
We present the results of 1+1+1 flavor QCD+QED simulation at the physical point, in which the dynamical quark effects in QED and the up-down quark mass difference are incorporated by the reweighting technique. The physical quark masses together with
the lattice spacing are determined with $m_{pi^+}$, $m_{K^+}$, $m_{K^0}$ and $m_{Omega^-}$ as physical inputs. Calculations are carried out using a set of 2+1 flavor QCD configurations near the physical point generated by the non-perturbatively $O(a)$-improved Wilson quark action and the Iwasaki gauge action at $beta=1.9$ on a $32^3times 64$ lattice. We evaluate the values of the up, down and strange quark masses individually with non-perturbative QCD renormalization.
We present results for application of block BiCGSTAB algorithm modified by the QR decomposition and the SAP preconditioner to the Wilson-Dirac equation with multiple right-hand sides in lattice QCD on a $32^3 times 64$ lattice at almost physical quar
k masses. The QR decomposition improves convergence behaviors in the block BiCGSTAB algorithm suppressing deviation between true residual and recursive one. The SAP preconditioner applied to the domain-decomposed lattice helps us minimize communication overhead. We find remarkable cost reduction thanks to cache tuning and reduction of number of iterations.
