We measure the topological charge and its fluctuation for the gauge configurations generated by the RBC and UKQCD Collaborations using 2+1 flavors of domain-wall fermions on the 16^3 x 32 lattice (L \simeq 2 fm) with length 16 in the fifth dimension at inverse lattice spacing a^{-1} \simeq 1.62 GeV. From the spectral flow of the Hermitian operator H_w (2 + γ_5 H_w)^{-1}, we obtain the topological charge Q_t of each gauge configuration in the three ensembles with light sea quark masses m_q a = 0.01, 0.02, and 0.03, and with the strange quark mass fixed at m_s a = 0.04. From our result of Q_t, we compute the topological susceptibilty χ_t = < Q_t^2 > /volume. In the small m_q regime, our result of χ_t agrees with the chiral effective theory. Using the formula χ_t = Σ/ (m_u^{-1} + m_d^{-1} + m_s^{-1}) by Leutwyler-Smilga, we obtain the chiral condensate Σ^MSbar(2 GeV) = [259(6)(9) MeV]^3.
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 $m_π/m_ρ\simeq0.63$ but approximately physical $s$ quark mass with $m_{η_{ss}}/m_ϕ\simeq0.74$. 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 compa…
We perform hybrid Monte-Carlo (HMC) simulation of lattice QCD with $N_f=2+1+1$ domain-wall quarks at the physical point, on the $64^3 \times (64,20,16,12,10,8,6)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this paper, we determine the topological susceptibility of the QCD vacuum for $T > T_c \sim 150 $ MeV. The topological charge of each gauge configuration is measu…
We determine the topological susceptibility of the gauge configurations generated by lattice simulations using two flavors of optimal domain-wall fermion on the $ 16^3 \times 32 $ lattice with length 16 in the fifth dimension, at the lattice spacing $ a \simeq 0.1 $ fm. Using the adaptive thick-restart Lanczos algorithm, we project the low-lying eigenmodes of the overlap Dirac operator, and obtain the topological charge of each configuration, for eight ensembles with pion masses in the range $ 220-550 $ MeV. From the topological charge, we compute the topological susceptibility and the second …
Thermodynamics of the three-flavor quark-meson model with axial anomaly is studied in the presence of external magnetic fields. The nonperturbative functional renormalization group is employed in order to incorporate quantum and thermal fluctuations beyond the mean-field approximation. We calculate the magnetic susceptibility with proper renormalization and find that the system is diamagnetic in the hadron phase and paramagnetic in the hot plasma phase. The obtained values of the magnetic susceptibility are in reasonable agreement with the data from first-principle lattice QCD. Comparison with…
We measure the topological charge of the gauge configurations generated by lattice simulations of 2 flavors QCD on a $ 16^3 \times 32 $ lattice, with Optimal Domain-Wall Fermion (ODWF) at $ N_s = 16 $ and plaquette gauge action at $ β= 5.90 $. Using the Adaptive Thick-Restart Lanczos algorithm, we project the low-lying modes of the 4D effective Dirac operator of ODWF, and obtain the topological charge and topological susceptibility. Our result of topological susceptibility agrees with the sea-quark mass dependence predicted by the chiral perturbation theory, and provides a determination of the…
We demonstrate that the QCD topological susceptibility nonperturbatively gets a significant contribution signaled by flavor-nonuniversal quark condensates at around the pseudo-critical temperature of the chiral crossover. It implies a remarkable flavor breaking in the axial anomaly as well as the QCD theta vacuum in high temperature QCD, which are almost flavor universal in the vacuum. A nontrivial flavor breaking is triggered by nonperturbative thermal loop corrections at around the chiral crossover, which is different from the trivial flavor violation just scaled by the quark mass ratio, obs…
Topological susceptibility and QCD phase transition with 2+1 flavor Möbius domain wall fermion at finite temperature
RIKEN Center for Computational Science (R-CCS)（理化学研究所计算科学中心）；Department of Physics, Osaka University（大阪大学物理系）；KEK Theory Center, High Energy Accelerator Research Organization (KEK)（高能加速器研究机构理论中心）；School of High Energy Accelerator Science, Graduate University for Advanced Studied (SOKENDAI)（高级综合大学院大学高能加速器科学学校）
I present a calculation of the topological susceptibility $χ_T$ in $SU(N_c)$ gauge theory with $N_c=3-5$ colors and $N_f=2$ degenerate flavors of fermions. The results lie on a common curve when expressed in terms of the combination $N_c m_{PS}^2 t_0$ where $m_{PS}$ is the pseudoscalar meson mass and $t_0$ is the flow parameter. $χ_T$ approaches its quenched value as the pseudoscalar mass becomes large. The lattice simulations use clover fermions. They are done at a single lattice spacing, roughly matched across $N_c$, and over a restricted range of fermion masses.
In order to understand the role of QCD in the early universe, we perform hybrid Monte-Carlo simulation of lattice QCD with $N_f=2+1+1$ optimal domain-wall quarks at the physical point, on the $64^3 \times (6,8,10,12,16,20,64)$ lattices, each with three lattice spacings. The lattice spacings and the bare quark masses are determined on the $64^4$ lattices. The resulting gauge ensembles provide a basis for studying finite temperature QCD with $N_f=2+1+1 $ domain-wall quarks at the physical point. In this Proceeding, we present our first result on the topological susceptibility of the QCD vacuum. …
We study the topological susceptibility and the fourth cumulant of the QCD vacuum in the presence of a uniform, background magnetic field in two-and-three flavor QCD finding novel, model-independent sum rules relating the shift in the topological susceptibility due to the background field to the shift in the quark condensates, and the shift in the fourth cumulant to the shifts in the quark condensates and susceptibilities
We study the 'spectral projector' method for the computation of the chiral condensate and the topological susceptibility, using $N_f=2+1+1$ dynamical flavors of maximally twisted mass Wilson fermions. In particular, we perform a study of the quark mass dependence of the chiral condensate $Σ$ and topological susceptibility $χ_{top}$ in the range $270 MeV < m_π < 500 MeV$ and compare our data with analytical predictions. In addition, we compute $χ_{top}$ in the quenched approximation where we match the lattice spacing to the $N_f=2+1+1$ dynamical simulations. Using the Kaon, $η$ and $η^{\prime}$…
We present a calculation of the B -> pi l nu form factors with domain-wall light quarks and relativistic b-quarks on the lattice. We work with the 2+1 flavor domain-wall fermion and Iwasaki gauge-field ensembles generated by the RBC and UKQCD Collaborations. The chiral-continuum extrapolation is performed using SU(2) hard-pion chiral perturbation theory. To extrapolate the lattice form factors to the full kinematic range, we use the model independent z-parameterization and impose the kinematic constraint f_+(0) = f_0(0) at zero momentum transfer.
We compute the topological susceptibility $χ_t$ of 2+1-flavor lattice QCD with dynamical Möbius domain-wall fermions, whose residual mass is kept at 1 MeV or smaller. In our analysis, we focus on the fluctuation of the topological charge density in a "slab" sub-volume of the simulated lattice, as proposed by Bietenholz et al. The quark mass dependence of our results agrees well with the prediction of the chiral perturbation theory, from which the chiral condensate is extracted. Combining the results for the pion mass $M_π$ and decay constant $F_π$, we obtain $χ_t$ = 0.227(02)(11)$M_π^2 F_π^2$ …
We investigate the chiral phase transition in the soft-wall model of AdS/QCD at zero chemical potential for two-flavor and three-flavor cases, respectively. We show that there is no spontaneous chiral symmetry breaking in the original soft-wall model. After detailed analysis, we find that in order to realize chiral symmetry breaking and restoration, both profiles for the scalar potential and the dilaton field are essential. The scalar potential determines the possible solution structure of the chiral condensate, except the mass term, it takes another quartic term for the two-flavor case, and f…
We compare the performances of the exact one-flavor algorithm (EOFA) and the rational hybrid Monte Carlo algorithm (RHMC), for dynamical simulations of lattice QCD with domain-wall fermion.
We construct positive-definite pseudofermion actions for one fermion flavor in lattice field theory, for Wilson and domain-wall fermions respectively. The positive definiteness of these actions ensures that they can be simulated with the Hybrid Monte Carlo (HMC) method. For lattice QCD with optimal domain-wall quarks, we compare the efficiency of HMC simulations of 2-flavor and (1+1)-flavor, and find that the efficiency ratio is about 3:2.
We perform hybrid Monte Carlo (HMC) simulatons of two flavors QCD with the optimal domain-wall fermion (ODWF) on the 16^3 x 32 lattice (with lattice spacing a ~ 0.1 fm), for eight sea-quark masses corresponding to pion masses in the range 228-565 MeV. We calculate the mass and the decay constant of the pseudoscalar meson, and compare our data with the chiral perturbation theory (ChPT). We find that our data is in good agreement with the sea-quark mass dependence predicted by the next-to-leading order (NLO) ChPT, and provides a determination of the low-energy constants \bar{l}_3 and \bar{l}_4, …
The RBC and UKQCD Collaborations continue to produce 2+1 flavor domain wall fermion ensembles, currently focusing on an ensemble with a $96^3 \times 192$ volume on SUMMIT at ORNL with $1/a \approx 2.8$ GeV, and smaller ensembles at stronger couplings. The $1/a \approx 2.8$ GeV ensemble uses the Exact One Flavor Algorithm for the strange quark, along with the Multisplitting Preconditioned Conjugate Gradient for solving the Dirac equation. We report on our progress and experience to date with the evolution of this ensemble.
We present high statistics results for the structure of the nucleon from a mixed-action calculation using 2+1 flavors of asqtad sea and domain wall valence fermions. We perform extrapolations of our data based on different chiral effective field theory schemes and compare our results with available information from phenomenology. We discuss vector and axial form factors of the nucleon, moments of generalized parton distributions, including moments of forward parton distributions, and implications for the decomposition of the nucleon spin.
We investigate the axial $U(1)_A$ symmetry breaking above the critical temperature in two-flavor lattice QCD. The ensembles are generated with dynamical Möbius domain-wall or reweighted overlap fermions. The $U(1)_A$ susceptibility is extracted from the low-modes spectrum of the overlap Dirac eigenvalues. We show the quark mass and temperature dependences of $U(1)_A$ susceptibility. Our results at $T=220 \, \mathrm{MeV}$ imply that the $U(1)_A$ symmetry is restored in the chiral limit. Its coincidence with vanishing topological susceptibility is observed.
We study an SU(3) gauge theory with Nf=8 degenerate flavors of light fermions in the fundamental representation. Using the domain wall fermion formulation, we investigate the light hadron spectrum, chiral condensate and electroweak S parameter. We consider a range of light fermion masses on two lattice volumes at a single gauge coupling chosen so that IR scales approximately match those from our previous studies of the two- and six-flavor systems. Our results for the Nf=8 spectrum suggest spontaneous chiral symmetry breaking, though fits to the fermion mass dependence of spectral quantities do…
The current status is reported of joint lattice numerical calculations by LHP and RBC collaborations of isovector nucleon form factors using 2+1-flavor physical-mass domain-wall fermions ensemble at a lattice cutoff $a^{-1}$ of 1.730(4) GeV and spatial volume of $(La=\mbox{\rm 5.471(13)fm})^3$ generated jointly by RBC and UKQCD collaborations.
We report on our ongoing study of nucleon properties, the nucleon mass and the strange quark content (<N|ss|N>) in particular. These calculations are done on (2+1)-flavor Domain Wall Fermion (DWF) ensembles with Iwasaki gauge action with 2 different lattice spacings (a ~ 0.08, 0.11fm) and DWF with Dislocation Suppressing Determinant Ratio(DSDR) (a ~ 0.14fm), generated by RBC/UKQCD collaborations.
Nucleon-structure calculations of isovector vector- and axialvector-current form factors, transversity and scalar charge, and quark momentum and helicity fractions are reported from two recent 2+1-flavor dynamical domain-wall fermions lattice-QCD ensembles generated jointly by the RIKEN-BNL-Columbia and UKQCD Collaborations with Iwasaki $\times$ dislocation-suppressing-determinatn-ratio gauge action at inverse lattice spacing of 1.378(7) GeV and pion mass values of 249.4(3) and 172.3(3) MeV.
We present an exact pseudofermion action for hybrid Monte Carlo simulation (HMC) of one-flavor domain-wall fermion (DWF), with the effective 4-dimensional Dirac operator equal to the optimal rational approximation of the overlap-Dirac operator with kernel $ H = c H_w (1 + d γ_5 H_w)^{-1} $, where $ c $ and $ d $ are constants. Using this exact pseudofermion action, we perform HMC of one-flavor QCD, and compare its characteristics with the widely used rational hybrid Monte Carlo algorithm (RHMC). Moreover, to demonstrate the practicality of the exact one-flavor algorithm (EOFA), we perform the …
We compute the topological susceptibility $χ_t$ of lattice QCD with $2+1$ dynamical quark flavors described by the Möbius domain wall fermion. Violation of chiral symmetry as measured by the residual mass is kept at $\sim$1 MeV or smaller. We measure the fluctuation of the topological charge density in a `slab' sub-volume of the simulated lattice using the method proposed by Bietenholz {\it et al.} The quark mass dependence of $χ_t$ is consistent with the prediction of chiral perturbation theory, from which the chiral condensate is extracted as $Σ^{\overline{\rm MS}} (\mbox{2GeV}) = [274(13)(2…
We investigate the finite temperature QCD phase transition with three degenerate quark flavors using Möbius domain wall fermions. To explore the order of phase transition on the lower left corner of Columbia plot and if possible, to locate the critical endpoint we performed simulations at temperatures around 181 and 121 MeV with lattice spacing $a=0.1361(20)$ fm corresponding to temporal lattice extent $N_τ=8,12$ with varying quark mass for two different volumes with aspect ratios $N_σ/N_τ$ ranging from 2 to 3. By analyzing the volume and mass dependence of the chiral condensate, disconnected …
In this work we compute the axion mass and, from this (exploiting a well-known relation), we also derive an expression for the QCD topological susceptibility in the finite-temperature case, both below and above the chiral phase transition at $T_c$, making use of a chiral effective Lagrangian model which includes the axion, the scalar and pseudoscalar mesons and implements the $U(1)$ axial anomaly of the fundamental theory. We also provide a numerical estimate of the topological susceptibility at $T=0$ (in the physical case of three light quark flavors) and discuss the question of the temperatu…
We report the status of our nucleon structure calculations with 2+1 flavors of domain wall fermions on the RBC-UKQCD $32^3\times64$ gauge ensembles with the Iwasaki+DSDR action. These ensembles have a fixed lattice scale of 1/a = 1.37 GeV, and two pion masses of about 170 and 250 MeV. Preliminary results for the isovector electromagnectic form factors and their corresponding root-mean-squared (r.m.s.) radii will be presented.
Simulations for the thermodynamics of the 2+1 flavor QCD are performed employing chiral fermions. The use of Möbius domain-wall fermions with stout-link smearing is more effective on the finer lattices where all the relevant chiral symmetries are realized more accurately. We report on the initial simulations near the (pseudo) critical point using the line of constant physics with an average $ud$ quark mass slightly heavier than physical at $a\lesssim 0.1$ fm.
The current status of the LHP and RBC joint calculations of the nucleon isovector form factors and low moments of structure functions with a 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD ensemble at the physical pion mass generated by RBC and UKQCD Collaborations with a momentum cutoff of 1.730(4) GeV and lattice spatial extent of 5.476(12) fm is reported. About ten percent of the statistics reported in Lattice 2014 were found with an incorrect boundary condition in time but correcting for it resulted in less than one-percent difference.
Analyses on possible systematics in some isovector nucleon observables in the RBC+UKQCD 2+1-flavor dynamical domain-wall fermion (DWF) lattice-QCD are presented. The vector charge, axial charge, quark momentum and helicity fractions, and transversity are discussed using mainly the Iwasaki\(\times\)DSDR ensemble at pion mass of 170 MeV. No autocorrelation issue is observed in the vector charge and quark momentum and helicity fractions. Blocked Jack-knife analyses expose significant growth of estimated error for the axial charge with increasing block sizes that are similar to or larger than the …
We find that the chiral phase transition (chiral crossover) in QCD at physical point is triggered by big imbalance among three fundamental quantities essential for the QCD vacuum structure: susceptibility functions for the chiral symmetry, axial symmetry, and the topological charge. The balance, dobbed the QCD trilemma, is unavoidably violated when one of the magnitudes among them is highly dominated, or suppressed. Based on a three-flavor Nambu-Jona-Lasinio model, we explicitly evaluate the amount of violation of the QCD trilemma at physical point, and show that the violation takes place not …
$F_K/F_π$ as a precision test of a new four flavor Domain Wall Fermion action
Carnegie Mellon University（卡内基梅隆大学）；Liverpool Hope University（利物浦霍普大学）；University of Liverpool（利物浦大学）；Lawrence Berkeley National Laboratory（劳伦斯伯克利国家实验室）；Kent State University（肯特州立大学）；Oak Ridge National Laboratory（橡树岭国家实验室）；University of North Carolina, Chapel Hill（北卡罗来纳大学教堂山分校）；University of California, Berkeley（加州大学伯克利分校）；University of Bern（伯尔尼大学）
We study the region of the QCD phase transition using 2+1 flavors of domain wall fermions (DWF) and a $16^3 \times 8$ lattice volume with a fifth dimension of $L_s = 32$. The disconnected light quark chiral susceptibility, quark number susceptibility and the Polyakov loop suggest a chiral and deconfining crossover transition lying between 155 and 185 MeV for our choice of quark mass and lattice spacing. In this region the lattice scale deduced from the Sommer parameter $r_0$ is $a^{-1} \approx 1.3$ GeV, the pion mass is $\approx 300$ MeV and the kaon mass is approximately physical. The peak in…
I analyze the lattice simulation data of the Domain Wall Fermion in quaternion basis. As pointed out by Atiyah and Ward, the minimum action solution for SU(2) Yang-Mills fields in Euclidean 4-space correspond, via Penrose twistor transform, to algebraic bundles on the complex projective 3-space. Assuming dominance of correlation between the fermions on the domain walls via exchange of instantons, I extract parameters necessary for defining gauge fields of Atiyah-Ward ansatz. The QCD effective coupling in the infrared and the relation between the number of flavors and the infrared fixed point i…
