arXiv subjects

K. -I. Ishikawa

Publications and source records attributed to K. -I. Ishikawa.

At least 19 recordsLinked to original sources

arXiv2019

Finite size effect on vector meson and baryon sectors in 2+1 flavor QCD at the physical point

We investigate the finite size effect on the vector meson and the baryon sectors using a subset of the "PACS10" configurations which are generated, keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. Comparing the results on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices the ground states of octet baryons , which are stable on the lattice, show no finite size effect within less than 0.5% level of statistical errors. For those of vector mesons, which are unstable on the lattice, we observe that the effective masses are well below the experimental resonance levels both on (5.5 fm$)^4$ and (10.9 fm$)^4$ lattices. For the decuplet baryon sector we have found that the time dependence of the effective mass looks quite similar to that for the vector meson sector including the $Ω$ baryon channel. We discuss its origin due to a possible mixing with the nearby multihadron states. Since the $Ξ$ baryon mass can be determined with the smallest ambiguity among the vector meson and the baryon masses, we use it together with the pion and kaon masses as the physical inputs to determine the physical point.

hep-lat↗

arXiv2019

Finite size effect on pseudoscalar meson sector in 2+1 flavor QCD at the physical point

We investigate the finite size effect on pseudoscalar meson masses and decay constants using a subset of the "PACS10" configurations which are generated keeping the space-time volumes over (10 fm$)^4$ in 2+1 flavor QCD at the physical point. We have tried two kinds of analyses, fixing $κ$ values or measured axial Ward identity quark masses. Comparing the results on (5.4 fm$)^4$ and (10.8 fm$)^4$ lattices, we have found a sizable finite size effect on the pseudoscalar meson sector in the former analysis: a 2.1(8)%, 4.8(1.6)%, and 0.36(31)% finite size effect on $m_π$, $m_{\rm ud}$, and $f_π$, respectively, on the (5.4 fm$)^4$ lattice. For the latter analysis, the finite size effect on the pseudoscalar meson decay constants is 0.66(33)% for $f_π$, 0.26(13)% for $f_K$, and 0.40(32)% for $f_K/f_π$. These values with two-sigma error bars are consistent with the predictions from the full one-loop SU(3) chiral perturbation theory, which are 0.20% for $f_π$, 0.08% for $f_K$, and 0.13% for $f_K/f_π$. The finite size effect on the pseudoscalar meson masses is hardly detected under the current statistical precision.

hep-lat↗

arXiv2018

Calculation of $K \to ππ$ decay amplitudes with an improved Wilson fermion action in a nonzero momentum frame in lattice QCD

We present our result for the $K\toππ$ decay amplitudes for both the $ΔI=1/2$ and $3/2$ processes with the improved Wilson fermion action. In order to realize the physical kinematics, where the pions in the final state have finite momenta, we consider the decay process $K({\bf p}) \to π({\bf p}) + π({\bf 0})$ in the nonzero momentum frame with momentum ${\bf p}=(0,0,2π/L)$ on the lattice. 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 $a=0.091\,{\rm fm}$ ($1/a=2.176\,{\rm GeV}$), $m_π=260\,{\rm MeV}$, and $m_K=570\,{\rm MeV}$ on a $48^3\times 64$ ($La=4.4\,{\rm fm}$) lattice. For these parameters the energy of the $K$ meson is set at that of two-pion in the final state. We obtain ${\rm Re}A_2 = 2.431(19) \times10^{ -8}\,{\rm GeV}$, ${\rm Re}A_0 = 51(28) \times10^{ -8}\,{\rm GeV}$, and $ε'/ε= 1.9(5.7) \times10^{-3}$ for a matching scale $q^* =1/a$ where the errors are statistical. The dependence on the matching scale $q^*$ of these values is weak. The systematic error arising from the renormalization factors is expected to be around $1.3\%$ for ${\rm Re}A_2$ and $11 \%$ for ${\rm Re}A_0$. Prospects toward calculations with the physical quark mass are discussed.

hep-lat↗

arXiv2017

Nature of chiral phase transition in two-flavor QCD

We investigate the nature of the chiral phase transition in the massless two-flavor QCD using the renormalization group improved gauge action and the Wilson quark action on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$ lattices. We calculate the spacial and temporal propagators of the iso-triplet mesons in the pseudo-scalar ($PS$), scalar ($S$), vector ($V$) and axial-vector ($AV$) channels on the lattice of three sizes. We first verify that the RG scaling is excellently satisfied for all cases. This is consistent with the claim that the chiral phase transition is second order. Then we compare the spacial and temporal effective masses between the axial partners, i.e. $PS$ vs $S$ and $V$ vs $AV$, on each of the three size lattices. We find the effective masses of all of six cases for the axial partners agree remarkably. This is consistent with the claim that at least $Z_4$ subgroup of the $U_A(1)$ symmetry in addition to the $SU_A(2)$ symmetry is recovered at the chiral phase transition point.

hep-lat↗

arXiv2017

RG scaling relations at chiral phase transition in two-flavor QCD

We investigate the nature of the chiral phase transition in the massless two-flavor QCD using the renormalization group improved gauge action and the Wilson quark action on $32^3\times 16$, $24^3\times 12$, and $16^3\times 8$ lattices. Based on the renormalization group equation, we derive the scaling relation for the effective masses of mesons at the chiral phase transition point. If the chiral phase transition is second order, the effective masses as a function of the rescaled time/space do not depend on the lattice size and show the universal behavior. We find that our numerical simulations on the three sizes of lattices are excellently on the scaling curves, which is consistent with the second order phase transition.

hep-lat↗

arXiv2016

Non-trivial Center Dominance in High Temperature QCD

We investigate the properties of quarks and gluons above the chiral phase transition temperature $T_c,$ using the RG improved gauge action and the Wilson quark action with two degenerate quarks mainly on a $32^3\times 16$ lattice. In the one-loop perturbation theory, the thermal ensemble is dominated by the gauge configurations with effectively $Z(3)$ center twisted boundary conditions, making the thermal expectation value of the spatial Polyakov loop take a non-trivial $Z(3)$ center. This is in agreement with our lattice simulation of high temperature QCD. We further observe that the temporal propagator of massless quarks at extremely high temperature $β=100.0 \, (T \simeq10^{58} T_c)$ remarkably agrees with the temporal propagator of free quarks with the $Z(3)$ twisted boundary condition for $t/L_t \geq 0.2$, but differs from that with the $Z(3)$ trivial boundary condition. As we increase the mass of quarks $m_q$, we find that the thermal ensemble continues to be dominated by the $Z(3)$ twisted gauge field configurations as long as $m_q \le 3.0 \, T$ and above that the $Z(3)$ trivial configurations come in. The transition is essentially identical to what we found in the departure from the conformal region in the zero-temperature many-flavor conformal QCD on a finite lattice by increasing the mass of quarks. We argue that the behavior is consistent with the renormalization group analysis at finite temperature.

hep-lat↗

arXiv2015

2+1 flavor QCD simulation on a $96^4$ lattice

We generate $2+1$ flavor QCD configurations near the physical point on a $96^4$ lattice employing the 6-APE stout smeared Wilson clover action with a nonperturbative $c_{\rm SW}$ and the Iwasaki gauge action at $β=1.82$. The physical point is estimated based on the chiral perturbation theory using several data points generated by the reweighting technique from the simulation point, wherer $m_π$,$m_K$ and $m_Ω$ are used as physical inputs. The physics results include the quark masses, the hadron spectrum, the pseudoscalar meson decay constants and nucleon sigma terms, using the nonperturbative renormalization factors evaluated with the Schrodinger functional method.

hep-lat↗

arXiv2015

Mass and Axial current renormalization in the Schrödinger functional scheme for the RG-improved gauge and the stout smeared $O(a)$-improved Wilson quark actions

We present the quark mass and axial current renormalization factors for the RG-improved Iwasaki gauge action and three flavors of the stout smeared $O(a)$-improved Wilson quark action. We employ $α=0.1$ and $n_{\mathrm{step}}=6$ for the stout link smearing parameters and all links in the quark action are replaced with the smeared links. Using the Schrödinger functional scheme we evaluate the renormalization factors at $β=1.82$ where large scale simulations are being carried out.

hep-lat↗

arXiv2015

Calculation of $K \to ππ$ decay amplitudes with improved Wilson fermion action in lattice QCD

We present our result for the $K\toππ$ decay amplitudes for both the $ΔI=1/2$ 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 with 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 $m_K \sim 2 m_π$. 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 $a=0.091\,{\rm fm}$, $m_π=280\,{\rm MeV}$, and $m_K=580\,{\rm MeV}$ on a $32^3\times 64$ ($La=2.9\,{\rm fm}$) 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.

hep-lat↗

arXiv2015

IR fixed points in $SU(3)$ gauge Theories

We propose a novel RG method to specify the location of the IR fixed point in lattice gauge theories and apply it to the $SU(3)$ gauge theories with $N_f$ fundamental fermions. It is based on the scaling behavior of the propagator through the RG analysis with a finite IR cut-off, which we cannot remove in the conformal field theories in sharp contrast with the confining theories. The method also enables us to estimate the anomalous mass dimension in the continuum limit at the IR fixed point. We perform the program for $N_f=16, 12, 8 $ and $N_f=7$ and indeed identify the location of the IR fixed points in all cases.

hep-lat↗

arXiv2014

Global Structure of Conformal Theories in the SU(3) Gauge Theory

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.

hep-lat↗

arXiv2014

Conformal Behavior in QCD

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). Based 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.

hep-lat↗

arXiv2014

Conformal Theories with an IR cutoff

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 Λ_{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^{α_H} instead of the exponentially decaying form c_H\exp{(-m_H t)}, in the small quark mass region where m_H \le c Λ_{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.

hep-lat↗

arXiv2013

Running coupling constant and mass anomalous dimension of six-flavor SU(2) gauge theory

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 Schrödinger 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 $0.26 \lesssim γ^*_m \lesssim 0.74$.

hep-lat↗

arXiv2013

Lattice Study on quantum-mechanical dynamics of two-color QCD with six light flavors

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 this 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.

hep-lat↗

arXiv2013

Charmed baryons at the physical point in 2+1 flavor lattice QCD

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 $Ω$ 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 $Ξ_{cc}$, 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.

hep-lat↗

arXiv2012

Multi-block/multi-core SSOR preconditioner for the QCD quark solver for K computer

We study the algorithmic optimization and performance tuning of the Lattice QCD clover-fermion solver for the K computer. We implement the Lüscher's SAP preconditioner with sub-blocking in which the lattice block in a node is further divided to several 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: $12^3\times 24$, $24^3\times 48$ and $48^3\times 96$, with fixing the local lattice size in a node at $6^3\times 12$. 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.

hep-lat↗

arXiv2012

Lattice study on two-color QCD with six flavors of dynamical quarks

We study the dynamics of SU(2) gauge theory with NF=6 Dirac fermions by means of lattice simulation to investigate if they are appropriate to realization of electroweak symmetry breaking. The discrete analogue of beta function for the running coupling constant defined under the Schroedinger functional boundary condition are computed on the lattices up to linear size of L/a=24 and preclude the existence of infrared fixed point below 7.6. Gluonic observables such as heavy quark potential, string tension, Polyakov loop suggest that the target system is in the confining phase even in the massless quark limit.

hep-lat↗