Iwasaki Gauge Action Research Articles

Restoring canonical partition functions from imaginary chemical potential

Using GPGPU techniques and multi-precision calculation we developed the code to study QCD phase transition line in the canonical approach. The canonical approach is a powerful tool to investigate sign problem in Lattice QCD. The central part of the canonical approach is the fugacity expansion of the grand canonical partition functions. Canonical partition functions Zn(T) are coefficients of this expansion. Using various methods we study properties of Zn(T). At the last step we perform cubic spline for temperature dependence of Zn(T) at fixed n and compute baryon number susceptibility χB/T2 as function of temperature. After that we compute numerically ∂χ/∂T and restore crossover line in QCD phase diagram. We use improved Wilson fermions and Iwasaki gauge action on the 163 × 4 lattice with mπ/mρ = 0.8 as a sandbox to check the canonical approach. In this framework we obtain coefficient in parametrization of crossover line Tc(µ2B) = Tc(C−ĸµ2B/T2c) with ĸ = −0.0453 ± 0.0099.

A Numerical Study of Renormalization Group Transformations on Multiscale Lattices

The RBC and UKQCD Collaborations have shown that light hadron masses and meson decay constants measured on 2+1 flavor Mobius DWF ensembles generated with the Iwasaki gauge action and a dislocation suppressing determinant ratio (DSDR) term show few percent O(a2) scaling violations for ensembles with a-1 = 1 GeV. We call this combination the ID+MDWF action and this scaling implies that, to a good approximation, these ensembles lie on a renormalization group trajectory, where the form of the action is unchanged and only the bare parameters need to be tuned to stay on the trajectory. Here we investigate whether a single-step APE-like blocking kernel can reproduce this trajectory and test its accuracy via measurements of the light hadron spectrum and non-perturbative renormalization. As we report, we find close matching to the renormalization group trajectory from this simple blocking kernel.

Energy-momentum tensor correlation function in Nf = 2 + 1 full QCD at finite temperature

We measure correlation functions of the nonperturbatively renormalized energy-momentum tensor in Nf = 2 + 1 full QCD at finite temperature by applying the gradient flow method both to the gauge and quark fields. Our main interest is to study the conservation law of the energy-momentum tensor and to test whether the linear response relation is properly realized for the entropy density. By using the linear response relation we calculate the specific heat from the correlation function. We adopt the nonperturba-tively improved Wilson fermion and Iwasaki gauge action at a fine lattice spacing = 0:07 fm. In this paper the temperature is limited to a single value T ≃ 232 MeV. The u, d quark mass is rather heavy with mπ=mρ ≃ 0:63 while the s quark mass is set to approximately its physical value.

Critical endline of the finite temperature phase transition for 2+1 flavor QCD away from the SU(3)-flavor symmetric point

We investigate the critical end line of the finite temperature phase transition of QCD away from the SU(3)-flavor symmetric point at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively O(a)- improved Wilson-clover fermion action. The critical end line is determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method at the temporal size NT = 6 and lattice spacing as low as a ≈0.19 fm.

Equation of state in (2+1)-flavor QCD at physical point with improved Wilson fermion action using gradient flow

We study the energy-momentum tensor and the equation of state as well as the chiral condensate in (2+1)-flavor QCD at the physical point applying the method of Makino and Suzuki based on the gradient flow. We adopt a nonperturbatively O(a)- improved Wilson quark action and the renormalization group-improved Iwasaki gauge action. At Lattice 2016, we have presented our preliminary results of our study in (2+1)- flavor QCD at a heavy u; d quark mass point. We now extend the study to the physical point and perform finite-temperature simulations in the range T ≃ 155.544 MeV (Nt = 4-14 including odd Nt’s) at a ≃ 0:09 fm. We show our final results of the heavy QCD study and present some preliminary results obtained at the physical point so far.

Continuum limit of hyperon vector coupling f1(0) from 2+1 flavor domain wall QCD

We determine the hyperon vector couplings $f_1(0)$ for $\Sigma^{-}\rightarrow nl^-\bar{\nu_l}$ and $\Xi^0\rightarrow\Sigma^{+}l^-\bar{\nu_l}$ semileptonic decays in the continuum limit with (2+1)-flavors of dynamical domain-wall fermions, using the Iwasaki gauge action at two different lattice spacings of $a$=0.114(2) and 0.086(2) fm. A theoretical estimation of flavor SU(3)-breaking effect on the vector coupling is required to extract $V_{us}$ from the experimental rate of hyperon beta decays. We obtain the vector couplings $f_1(0)$ for $\Sigma\rightarrow N$ and $\Xi\rightarrow \Sigma$ beta-decays with an accuracy of less than one percent. We then find that lattice results of $f_1(0)$ combined with the best estimate of $|V_{us}|$ with imposing Cabibbo-Kobayashi-Maskawa (CKM) unitarity are slightly deviated from the experimental result of $|V_{us}f_1(0)|$ for the $\Sigma\rightarrow N$ beta-decay. This discrepancy can be attributed to an assumption made in the experimental analysis on $|V_{us}f_1(0)|$, where the induced second-class form factor $g_2$ is set to be zero regardless of broken SU(3) symmetry. We report on this matter and then estimate the possible value of $g_2(0)$, which is evaluated from the experimental decay rate with our lattice result of $f_1(0)$ under the first-row CKM-unitarity condition.

Critical point phase transition for finite temperature 3-flavor QCD with nonperturbatively O(a) improved Wilson fermions at Nt=10

We study the finite temperature phase structure for three-flavor QCD with a focus on locating the critical point which separates crossover and first order phase transition region in the chiral regime of the Columbia plot. In this study, we employ the Iwasaki gauge action and the non-perturvatively O($a$) improved Wilson-Clover fermion action. We discuss the finite size scaling analysis including the mixing of magnetization-like and energy-like observables. We carry out the continuum extrapolation of the critical point using newly generated data at $N_{\rm t}=8$, $10$ and estimate the upper bound of the critical pseudo-scalar meson mass $m_{\rm PS,E} \lesssim 170 {\rm MeV}$ and the critical temperature $T_{\rm E}=134(3){\rm MeV}$. Our estimate of the upper bound is derived from the existence of the critical point as an edge of the 1st order phase transition while that of the staggered-type fermions is based on its absence.

Numerical study of tree-level improved lattice gradient flows in pure Yang-Mills theory

We study several types of tree-level improvement in the Yang-Mills gradient flow method in order to reduce the lattice discretization errors in line with Fodor et al. [arXiv:1406.0827]. The tree-level $\mathcal{O}(a^2)$ improvement can be achieved in a simple manner, where an appropriate weighted average is computed between two definitions of the action density $\langle E(t)\rangle$ measured at every flow time $t$. We further develop the idea of achieving the tree-level $\mathcal{O}(a^4)$ improvement. For testing our proposal, we present numerical results for $\langle E(t) \rangle$ obtained on gauge configurations generated with the Wilson and Iwasaki gauge actions at three lattice spacings ($a\approx 0.1, 0.07,$ and 0.05 fm). Our results show that tree-level improved flows significantly eliminate the discretization corrections on $t^2\langle E(t)\rangle$ in the relatively small-$t$ regime. To demonstrate the feasibility of our tree-level improvement proposal, we also study the scaling behavior of the dimensionless combinations of the $\Lambda_{\overline{\textrm{MS}}}$ parameter and the new reference scale $t_X$, which is defined through $t_X^2\langle E(t_X)\rangle=X$ for the smaller $X$, e.g., $X= 0.15$. It is found that $\sqrt{t_{0.15}}\Lambda_{\overline{\textrm{MS}}}$ shows a nearly perfect scaling behavior as a function of $a^2$ regardless of the types of gauge action and flow, after tree-level improvement is achieved up to $\mathcal{O}(a^4)$. Further detailed study of the scaling behavior exposes the presence of the remnant $\mathcal{O}(g^{2n} a^2)$ corrections, which are beyond the tree level. Although our proposal is not enough to eliminate all $\mathcal{O}(a^2)$ effects, we show that the $\mathcal{O}(g^{2n} a^2)$ corrections can be well under control even by the simplest tree-level $\mathcal{O}(a^2)$ improved flow.

Topological susceptibility in finite temperature ( 2+1 )-flavor QCD using gradient flow

We compute the topological charge and its susceptibility in finite temperature (2+1)-flavor QCD on the lattice applying a gradient flow method. With the Iwasaki gauge action and nonperturbatively $O(a)$-improved Wilson quarks, we perform simulations on a fine lattice with~$a\simeq0.07\,\mathrm{fm}$ at a heavy $u$, $d$ quark mass with $m_\pi/m_\rho\simeq0.63$ but approximately physical $s$ quark mass with $m_{\eta_{ss}}/m_\phi\simeq0.74$. In a temperature range from~$T\simeq174\,\mathrm{MeV}$ ($N_t=16$) to $697\,\mathrm{MeV}$ ($N_t=4$), we study two topics on the topological susceptibility. One is a comparison of gluonic and fermionic definitions of the topological susceptibility. Because the two definitions are related by chiral Ward-Takahashi identities, their equivalence is not trivial for lattice quarks which violate the chiral symmetry explicitly at finite lattice spacings. The gradient flow method enables us to compute them without being bothered by the chiral violation. We find a good agreement between the two definitions with Wilson quarks. The other is a comparison with a prediction of the dilute instanton gas approximation, which is relevant in a study of axions as a candidate of the dark matter in the evolution of the Universe. We find that the topological susceptibility shows a decrease in $T$ which is consistent with the predicted $\chi_\mathrm{t}(T) \propto (T/T_{\rm pc})^{-8}$ for three-flavor QCD even at low temperature $T_{\rm pc} < T\le1.5 T_{\rm pc}$.

Critical endline of the finite temperature phase transition for 2+1 flavor QCD around the SU(3)-flavor symmetric point

We investigate the critical endline of the finite temperature phase transition of QCD around the SU(3)-flavor symmetric point at zero chemical potential. We employ the renormalization-group improved Iwasaki gauge action and non-perturbatively $O(a)$-improved Wilson-clover fermion action. The critical endline is determined by using the intersection point of kurtosis, employing the multi-parameter, multi-ensemble reweighting method to calculate observables off the SU(3)-symmetric point, at the temporal size $N_{\rm T}$=6 and lattice spacing as low as $a \approx 0.19$ fm. We confirm that the slope of the critical endline takes the value of $-2$, and find that the second derivative is positive, at the SU(3)-flavor symmetric point on the Columbia plot parametrized with the strange quark mass $m_s$ and degenerated up-down quark mass $m_{\rm l}$.

Lattice QCD for Baryon Rich Matter – Beyond Taylor Expansions

We discuss our study for exploring the QCD phase diagram based on the lattice QCD. To go beyond the Taylor expansion and to reach higher density regions, we employ the canonical approach. In order to produce lattice data which meet experimental situation as much as possible, we propose a canonical approach with the charge and baryon number. We present our lattice QCD GPU code for this project which employs the clover improved Wilson fermions and Iwasaki gauge action to investigate pure imaginary chemical potential.

Axial charges of hyperons and charmed baryons usingNf=2+1+1twisted mass fermions

The axial couplings of the low lying baryons are evaluated using a total of five ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using the Iwasaki gauge action and two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values at two values of the coupling constant. The lattice spacings, determined using the nucleon mass, are $a=0.082$ fm and $a=0.065$ fm and the simulations cover a pion mass in the range of about 210 MeV to 430 MeV. We study the dependence of the axial couplings on the pion mass in the range of about 210 MeV to 430 MeV as well as the $SU(3)$ breaking effects as we decrease the light quark mass towards its physical value.

Neutron and proton electric dipole moments fromNf=2+1domain-wall fermion lattice QCD

We present a lattice calculation of the neutron and proton electric dipole moments (EDM's) with $N_f=2+1$ flavors of domain-wall fermions. The neutron and proton EDM form factors are extracted from three-point functions at the next-to-leading order in the $\theta$ vacuum of QCD. In this computation, we use pion masses 0.33 and 0.42 GeV and 2.7 fm$^3$ lattices with Iwasaki gauge action and a 0.17 GeV pion and 4.6 fm$^3$ lattice with I-DSDR gauge action, all generated by the RBC and UKQCD collaborations. The all-mode-averaging technique enables an efficient and high statistics calculation. Chiral behavior of lattice EDM's is discussed in the context of baryon chiral perturbation theory. In addition, we also show numerical evidence on relationship of three- and two-point correlation function with local topological distribution.

Λb→Λℓ+ℓ−form factors, differential branching fraction, and angular observables from lattice QCD with relativisticbquarks

Using $(2+1)$-flavor lattice QCD, we compute the 10 form factors describing the $\Lambda_b \to \Lambda$ matrix elements of the $b \to s$ vector, axial vector, and tensor currents. The calculation is based on gauge field ensembles generated by the RBC and UKQCD Collaborations with a domain-wall action for the $u$, $d$, and $s$ quarks and the Iwasaki gauge action. The $b$ quark is implemented using an anisotropic clover action, tuned nonperturbatively to the physical point, and the currents are renormalized with a mostly nonperturbative method. We perform simultaneous chiral, continuum, and kinematic extrapolations of the form factors through modified $z$ expansions. Using our form factor results, we obtain precise predictions for the $\Lambda_b \to \Lambda(\to p^+ \pi^-) \mu^+ \mu^-$ differential branching fraction and angular observables in the Standard Model.

B*Bπcoupling using relativistic heavy quarks

We report on a calculation of the B*Bpi coupling in lattice QCD. The strong matrix element for a B* to Bpi transition is directly related to the leading order low-energy constant in heavy meson chiral perturbation theory (HMChPT) for B mesons. We carry out our calculation directly at the b-quark mass using a non-perturbatively tuned clover action that controls discretization effects of order pa and (ma)^n for all n. Our analysis is performed on RBC/UKQCD gauge configurations using domain-wall fermions and the Iwasaki gauge action at two lattice spacings of ainverse = 1.729(25) GeV, ainverse = 2.281(28) GeV, and unitary pion masses down to 290 MeV. We achieve good statistical precision and control all systematic uncertainties, giving a final result for the HMChPT coupling g_b = 0.56(3)stat(7)sys in the continuum and at the physical light-quark masses. This is the first calculation performed directly at the physical b-quark mass and lies in the region one would expect from carrying out an interpolation between previous results at the charm mass and at the static point.

Phase structure of two-color QCD at real and imaginary chemical potentials: Lattice simulations and model analyses

We investigate the phase structure of two-color QCD at both real and imaginary chemical potentials mu, performing lattice simulations and analyzing the data with the Polyakov-loop extended Nambu--Jona-Lasinio (PNJL) model. Lattice QCD simulations are done on an 8^3 times 4 lattice with the clover-improved two-flavor Wilson fermion action and the renormalization-group improved Iwasaki gauge action. We test the analytic continuation of physical quantities from imaginary mu to real mu by comparing lattice QCD results calculated at real mu with the result of analytic function the coefficients of which are determined from lattice QCD results at imaginary mu. We also test the validity of the PNJL model by comparing model results with lattice QCD ones. The PNJL model is good in the deconfinement region, but less accurate in the transition and confinement regions. This problem is improved by introducing the baryon degree of freedom to the model. It is also found that the vector-type four-quark interaction is necessary to explain lattice data on the quark number density.

Towards the quark-gluon plasma Equation of State with dynamical strange and charm quarks

We present an ongoing project aimed at determining the thermodynamic Equation of State (EoS) of quark-gluon matter from lattice QCD with two generations of dynamical quarks. We employ the Wilson twisted mass implementation for the fermionic fields and the improved Iwasaki gauge action. Relying on T = 0 data obtained by the ETM Collaboration the strange and charm quark masses are fixed at their physical values, while the pion mass takes four values in the range from 470 MeV down to 210 MeV. The temperature is varied within a fixed-lattice scale approach. The values for the pseudocritical temperature are obtained from various observables. For the EoS we show preliminary results for the pure gluonic contribution obtained at the pion mass value 370 MeV, where we can compare with previously obtained results with Nf = 2 degenerate light flavours.

Topological charge using cooling and the gradient flow

The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\tau$ and show that the results for the topological charge become equivalent when rescaling $\tau \simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\tau \simeq n_c/({3-15 c_1})$ leads to equivalent results.

Calculation ofK→ππdecay amplitudes with improved Wilson fermion action in lattice QCD

We present our result for the $K\to\pi\pi$ 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 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 $m_K \sim 2 m_\pi$. 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 $32^3\times 64$ ($La=2.9\,{\rm fm}$) 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.

Study of quark mass dependence of binding energy for light nuclei in2+1flavor lattice QCD

We investigate the formation of light nuclei with the nuclear mass number less than or equal to four in $2+1$ flavor QCD using a nonperturbative improved Wilson quark and Iwasaki gauge actions. The quark mass is decreased from our previous work to the one corresponding to the pion mass of 0.30 GeV. In each multinucleon channel, the energy shift of the ground state relative to the assembly of free nucleons is calculated on two volumes, whose spatial extents are 4.3 and 5.8 fm. From the volume dependence of the energy shift, we distinguish a bound state of multinucleons from an attractive scattering state. We find that all the ground states measured in this calculation are bound states. As in the previous studies at larger ${m}_{\ensuremath{\pi}}$, our result indicates that at ${m}_{\ensuremath{\pi}}=0.30\text{ }\text{ }\mathrm{GeV}$ the effective interaction between nucleons in the light nuclei is relatively stronger than the one in nature, since the results for the binding energies are larger than the experimental values and a bound state appears in the dineutron channel, which is not observed in experiment. Possible sources of systematic error in this calculation are discussed.