We present a calculation of $< x >_s$ for the strange quark in the nucleon. We also report the ratio of the strange $< x >$ to that of $u/d$ in the disconnected insertion which will be useful in constraining the global fit of parton distribution functions at small $x$. We adopt overlap fermion action on $2 + 1$ flavor domain-wall fermion configurations on the $24^3 \times 64$ lattice with a light sea quark mass which corresponds to $m_π=330$ MeV. Smeared grid $Z_3$ sources are deployed to calculate the nucleon propagator with low-mode substitution. Even-odd grid sources and time-dilution technique with stochastic noises are used to calculate the high mode contribution to the quark loop. Low mode averaging (LMA) for the quark loop is applied to reduce the statistical error of the disconnected insertion calculation. We find the ratio $< x >_s/< x >_{u/d}^{\mathrm{DI}}= 0.78(3)$ in this study.
The charmed-strange meson spectrum is calculated with the overlap valence fermions on 2+1 flavor domain wall dynamical configurations for $32^3\times 64$ lattices with a spatial size of 2.7 fm. Both charm and strange quark propagators are calculated with the overlap fermion action. The calculated scalar meson at 2304(22) MeV and axial-vector meson at 2546(27) MeV are in good agreement with the experimental masses of $D{s0}^*$(2317) and $D_{s1}$(2536).
The calculation of the strangeness and charmness of the nucleon is presented with overlap fermion action on 2+1 flavor domain wall fermion configurations. We adopt stochastic grid sources and the low mode substitution technique to improve the signals of nucleon correlation functions and the loops. The calculation is done on a $24^3\times 64$ lattice with $m_l=0.005$, $m_h=0.04$, and $a^{-1}=1.73\,{\rm GeV}$. We find $ f_{T_{s}} = 0.048(15)$ and $f_{T_{c}} = 0.029(43)$.
The strange quark mass has been computed using a lattice action which possesses continuum--like chiral symmetry to good precision, namely the domain wall fermion action. This talk surveys this action and the recent calculation of m_s by the RIKEN/BNL/CU collaboration. This result is put into context by briefly summarizing other recent lattice studies.
We report here results on charm and strange hadron spectra. Adopting a mixed action approach, we use overlap fermions for valence quarks, on a background of 2+1+1 flavours HISQ gauge configurations of MILC collaboration. Two lattice spacings (0.09 fm and 0.06 fm) are used. We find the hyperfine splitting of 1S charmonia to be 114(3)(-2) MeV and 109(4)(-3) MeV, and the splitting (m(Omega_ccc)-3/2 m(JΨ)) is found to be 110(20)(-10) MeV and 120(10) MeV, corresponding to lattices with spacings a = 0.09 and 0.06 fm respectively. We also look at the ratio of the leptonic decay constant f_Ds*/f_Ds.
We present a first calculation of the strange quark mass using domain wall fermions. This paper contains an overview of the domain wall discretization and a pedagogical presentation of the perturbative calculation necessary for computing the mass renormalization. We combine the latter with numerical simulations to estimate the strange quark mass. Our final result in the quenched approximation is 95(26) MeV in the ${\bar{MS}}$ scheme at a scale of 2 GeV. We find that domain wall fermions have a small perturbative mass renormalization, similar to Wilson quarks, and exhibit good scaling behavior.
We study the sigma term and the strange quark content of nucleon in 2+1-flavor QCD with dynamical overlap fermions. We analyze the lattice data of nucleon mass taken at two different strange quark masses with five values of up and down quark masses each. Using the reweighting technique, we study the strange quark mass dependence of the nucleon and extract the strange quark content.
We study the nucleon matrix elements of the quark scalar-density operator using maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. We demonstrate that in this setup the nucleon matrix elements of the light and strange quark densities can be obtained with good statistical accuracy, while for the charm quark counterpart only a bound can be provided. The present calculation which is performed at only one value of the lattice spacing and pion mass serves as a benchmark for a future more systematic computation of the scalar quark content of the nuc…
Lattice QCD calculations with chiral fermions of the $π$N sigma term $σ_{πN}$ and strangeness sigma term $σ_{sN}$ including chiral interpolation with continuum and volume corrections are provided in this work, with the excited-state contaminations subtracted properly. We calculate the scalar matrix element for the light/strange quark directly and find $σ_{πN}=45.9(7.4)(2.8)$ MeV, with the disconnected insertion part contributing 20(12)(4)\%, and $σ_{sN}=40.2(11.7)(3.5)$ MeV, which is somewhat smaller than $σ_{πN}$. The ratio of the strange/light scalar matrix elements is $y$ = 0.09(3)(1).
The charmed-strange meson masses are calculated on a quenched lattice QCD. The charm and strange quark propagators are calculated on the same lattice with the overlap fermion. $16^3\times 72$ lattice with Wilson gauge action at $β=0.6345$ are used. The charm and strange quark masses are determined by fitting the $J/ψ$ and $ϕ$ masses respectively. The charmed strange meson spectrum for the scalar, axial, pseudoscalar and vector channels are calculated. They agree with experiments. In particular, we find the scalar meson mass to be 2248(78)MeV which is in agreement with that of D_{s0}^*(2317).
We calculate the nucleon strange quark content directly from disconnected three-point functions. Numerical simulations are carried out in two-flavor QCD using the overlap quark action with up and down quark masses down to a fifth of the physical strange quark mass. To improve the statistical accuracy, we calculate the nucleon two-point functions with the low-mode averaging technique, whereas the all-to-all quark propagator is used for the disconnected quark loop. We obtain the y parameter, which is the ratio of the strange and light quark contents, y = 0.024(45) at the physical point. This is …
The explicit breaking of chiral symmetry of the Wilson fermion action results in additive quark mass renormalization. Moreover, flavour singlet and non-singlet scalar currents acquire different renormalization constants with respect to continuum regularization schemes. This complicates keeping the renormalized strange quark mass fixed when varying the light quark mass in simulations with $N_f=2+1$ sea quark flavours. Here we present and validate our strategy within the CLS (Coordinated Lattice Simulations) effort to achieve this in simulations with non-perturbatively order-$a$ improved Wilson …
In the simulation of QCD with 2+1 flavors of Wilson fermions, the positivity of the fermion determinant is generally assumed. We present evidence that this assumption is in general not justified and discuss the consequences of this finding.
We present a calculation of the nucleon sigma term on two-flavor QCD configurations with dynamical overlap fermions. We analyse the lattice data for the nucleon mass using the baryon chiral perturbation theory. Using partially quenched data sets, we extract the connected and disconnected contributions to the nucleon sigma term separately. Chiral symmetry on the lattice simplifies the determination of the disconnected contribution. We find that the strange quark content, which determines the neutralino dark matter reaction rate with nucleon through the Higgs boson exchange, is much smaller than…
We present a calculation of the strange and charm quark contributions to the nucleon spin from the anomalous Ward identity (AWI). It is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations on a $24^3 \times 64$ lattice with the light sea mass at $m_π = 330$ MeV. To satisfy the AWI, the overlap fermion for the pseudoscalar density and the overlap Dirac operator for the topological density, which do not have multiplicative renormalization, are used to normalize the form factor of the local axial-vector current at finite $q^2$. For the charm quark, we find …
We present preliminary results for the strange leading-order hadronic contribution to the anomalous magnetic moment of the muon using RBC/UKQCD physical point domain wall fermions ensembles. We discuss various analysis strategies in order to constrain the systematic uncertainty in the final result.
We present results for the light, strange and charm quark masses using $N_f=2+1+1$ twisted mass fermion ensembles at three values of the lattice spacing, including two ensembles simulated with the physical value of the pion mass. The analysis is done both in the meson and baryon sectors. The difference in the mean values found in the two sectors is included as part of the systematic error. The presentation is based on the work of Ref. [1], where more details can be found.
We determine the masses of the light and the strange quarks in the $\bar{MS}$-scheme using our high-statistics lattice simulation of QCD with dynamical Wilson fermions. For the light quark mass we find $m^{light}_{\bar{MS}}(2 GeV) = 2.7(2) MeV$, which is lower than in quenched simulations. For the strange quark, in a sea of two dynamical light quarks, we obtain $m^{strange}_{\bar{MS}}(2 GeV) = 140(20) MeV$.
We present a lattice calculation of the Hadronic Vacuum Polarization (HVP) contribution of the strange and charm quarks to the anomalous magnetic moment of the muon including leading-order electromagnetic corrections. We employ the gauge configurations generated by the European Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ dynamical quarks at three values of the lattice spacing ($a \simeq 0.062, 0.082, 0.089$ fm) with pion masses in the range $M_π\simeq 210 - 450$ MeV. The strange and charm quark masses are tuned at their physical values. Neglecting disconnected diagrams and after the e…
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.
We present a calculation of the strangeness and charmness contents <N|\bar{s}s|N> and <N|\bar{c}c|N> of the nucleon from dynamical lattice QCD with 2+1 flavors. The calculation is performed with overlap valence quarks on 2+1-flavor domain-wall fermion gauge configurations. The configurations are generated by the RBC collaboration on a 24^3*64 lattice with sea quark mass am_l=0.005, am_s=0.04, and inverse lattice spacing a^{-1}=1.73GeV. Both actions have chiral symmetry which is essential in avoiding contamination due to the operator mixing with other flavors. Nucleon propagator and the quark l…
We use overlap fermions as valence quarks to calculate meson masses in a wide quark mass range on the $2+1$-flavor domain-wall fermion gauge configurations generated by the RBC and UKQCD Collaborations. The well-defined quark masses in the overlap fermion formalism and the clear valence quark mass dependence of meson masses observed from the calculation facilitate a direct derivation of physical current quark masses through a global fit to the lattice data, which incorporates $O(a^2)$ and $O(m_c^4a^4)$ corrections, chiral extrapolation, and quark mass interpolation. Using the physical masses o…
We present first, exploratory results of a hybrid Monte-Carlo algorithm for dynamical, n_f=2, four-dimensional QCD with overlap fermions. As expected, the computational requirements are typically two orders of magnitude larger for the dynamical overlap formalism than for the more conventional (Wilson or staggered) formulations.
We present results for the strange contribution to the electromagnetic form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of $\mathcal{O}(a)$-improved Wilson fermions and an $\mathcal{O}(a)$-improved vector current. Several source-sink separations are investigated in order to estimate the excited-state contamination. We calculate the form factors on six ensembles with lattice spacings in the range of $a=0.049-0.086\,\text{fm}$ and pion masses in the range of $m_π=200-360\,\text{MeV}$, which allows for a controlled chiral and continuum extrapolation. In the computa…
We present a study of charm physics using RBC/UKQCD 2+1 flavour physical point domain wall fermion ensembles for the light quarks as well as for the valence charm quark. After a brief motivation of domain wall fermions as a suitable heavy quark discretisation we will show first results for masses and matrix elements.
We discuss recent progress in studying Quantum Chromodynamics at finite temperature using $N_f=2+1+1$ Wilson twisted mass fermions. Particular interest is in QCD symmetries and their breaking and restoration. First, we discuss the behaviour of the $η'$ meson at finite temperature, which is tightly connected to the axial and chiral symmetries. The results suggest a small decrease of the $η'$ mass in the pseudo-critical region coming close to the non-anomalous contribution and subsequent growth at large temperatures. Second, we present the first results of lattice simulations of Quantum Chromody…
The recently discovered charmed-strangemeson Ds0*(2317) has been speculated to be a tetraquark mesonium. We study this suggestion with overlap fermions on 2+1 flavor domain wall fermion configurations. We use 4-quark interpolating operatorswith Z4 grid sources on two lattices (16\times16\times16\times32 and 24\times24\times24 times64) to study the volume dependence of the states in an attempt to discern the nature of the states in the four-quark correlator to see if they are all two-meson scattering states or if one is a tetraquark mesonium. We also use the hybrid boundary condition method for…
Using the O(a) Symanzik improved action an estimate is given for the strange quark mass for unquenched (nf=2) QCD. The determination is via the axial Ward identity (AWI) and includes a non-perturbative evaluation of the renormalisation constant. Numerical results have been obtained at several lattice spacings, enabling the continuum limit to be taken. Results indicate a value for the strange quark mass (in the MSbar-scheme at a scale of 2GeV) in the range 100 - 130MeV.
The renormalization of the most general dimension-six four-fermion operators without power subtractions is studied at one loop in lattice perturbation theory using overlap fermions. As expected, operators with different chirality do not mix among themselves and parity-conserving and parity-violating multiplets renormalize in the same way. The renormalization constants of unimproved and improved operators are also the same. These mixing factors are necessary to determine physical matrix elements relevant to many phenomenological applications of weak interactions. The most important are the K0-K…
We calculate $m_{ud}=(m_u+m_d)/2$, $m_s$, $f_π$ and $f_K$ in the quenched continuum limit with UV-filtered overlap fermions. We see rather small scaling violations on lattices as coarse as $a^{-1} \simeq 1 \mathrm{GeV}$ and conjecture that similar advantages would be manifest in unquenched studies.
Using a reweighting technique combined with a low-mode truncation of the fermionic determinant, we estimate the quark-mass dependence of the QCD topological susceptibility with overlap fermions. In contrast to previous lattice simulations which all used non-chiral fermions, our results appear to be consistent with the simple continuum model of Dürr. This indicates that at current lattice spacings the use of the index theorem might not be justified and the fermionic definition of the charge might be needed.
The masses of the low-lying strange and charm baryons are evaluated using two degenerate flavors of twisted mass sea quarks for pion masses in the range of about 260 MeV to 450 MeV. The strange and charm valence quark masses are tuned to reproduce the mass of the kaon and D-meson at the physical point. The tree-level Symanzik improved gauge action is employed. We use three values of the lattice spacing, corresponding to $β=3.9$, $β=4.05$ and $β=4.2$ with $r_0/a=5.22(2)$, $r_0/a=6.61(3)$ and $r_0/a=8.31(5)$ respectively. %spacings $a=0.0855(5)$ and $a=0.0667(3)$ determined from the pion decay c…
We present preliminary results for strangeness form factors of the nucleon computed on the CLS ensembles with $N_f=2+1$ flavors of O($a$)-improved Wilson fermions. Our calculations are performed at two values of the lattice spacing ($a \in \{0.064, 0.086\} \,\mathrm{fm}$) and three values of the pion mass ($m_π\in \{ 200, 280, 340\} \,\mathrm{MeV}$). The determination of strangeness form factors proceeds by computing quark-disconnected diagrams, for which we employ hierarchical probing in four dimensions in order to deal with this most challenging part of the calculation. Furthermore, we inves…
I present first results from an in-progress calculation of B_K in quenched approximation using overlap fermions. My particular implementation of the overlap uses a kernel with nearest and next-nearest neighbor interactions and HYP-blocked gauge connections. Matching to the continuum NDR regularization is done perturbatively. I present preliminary results at beta=5.9 and 6.1 (lattice spacings 0.125 and 0.09 fm) for quark masses, pseudoscalar decay constants, and B-parameter -- B_K(NDR(mu=2 GeV) is 0.66(3-4).
We present the QCD simulation of the first gauge ensemble of two degenerate light quarks, a strange and a charm quark with all quark masses tuned to their physical values within the twisted mass fermion formulation. Results for the pseudoscalar masses and decay constants confirm that the produced ensemble is indeed at the physical parameters of the theory. This conclusion is corroborated by a complementary analysis in the baryon sector. We examine cutoff and isospin breaking effects and demonstrate that they are suppressed through the presence of a clover term in the action.
We investigate excited state contaminations in a direct computation of the nucleon $σ$-terms. This is an important source of systematic effects that needs to be controlled besides the light quark mass dependence and lattice artefacts. We use maximally twisted mass fermions with dynamical light ($u$,$d$), strange and charm degrees of freedom. Employing an efficient stochastic evaluation of the disconnected contribution available for twisted mass fermions, we show that the effect of excited states is large in particular for the strange $σ$-terms, where it can be as big as $O(\gtrsim 40%$). This …
We report on our calculation of the strange contribution to the vector and axial vector form factors. The strange charge radii, magnetic moment, and axial charge are extracted by model independent $z$-expansion fits to the $Q^2$-dependence of the respective form factors. Furthermore, the isoscalar contribution to the axial and tensor charge is investigated by combining the calculation of connected and disconnected diagrams. The required renormalization is performed with the Rome-Southampton method. We make use of the CLS $N_f=2+1$ $\mathcal{O}(a)$-improved Wilson fermion ensembles. Results are…
We present the N_f=2+1 clover fermion lattice QCD calculation of the nucleon strangeness form factors. We evaluate disconnected insertions using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. We find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consistent with experimental values, and has an order of magnitude smaller error.
We report on a lattice QCD calculation of the I=2 $ππ$ scattering length using the overlap fermion formulation for both sea and valence quarks. We investigate the consistency of the lattice data with the prediction of the next-to-next-to-leading order chiral perturbation theory after correcting finite volume effects. The calculation is performed on gauge ensembles of two-flavor QCD generated by the JLQCD collaboration on a $16^3\times 32$ lattice at a lattice spacing $\sim$ 0.12 fm.
A fully non-perturbative lattice determination of the up/down and strange quark masses is given for quenched QCD using both, $O(a)$ improved Wilson fermions and ordinary Wilson fermions. For the strange quark mass with $O(a)$ improved fermions we obtain $m^{\msbar}_s(μ=2 {GeV}) = 105(4) {MeV}$, using the interquark force scale $r_0$. Due to quenching problems fits are only possible for quark masses larger than the strange quark mass. If we extrapolate our fits to the up/down quark mass we find for the average mass $m^{\msbar}_l(μ=2 {GeV}) = 4.4(2) {MeV}$.
In this talk I will emphasize the role of the Truncated Overlap Fermions in showing the equivalence between the Domain Wall and Overlap Fermions up to an irrelevant factor in the fermionic integration measure. I will also show how Domain Wall type fermions with a finite number of flavors can be used to accelerate propagator calculations of their light partner in the infinite flavor limit.
We study the strangeness electromagnetic form factors of the nucleon from the N_f=2+1 clover fermion lattice QCD calculation. The disconnected insertions are evaluated using the Z(4) stochastic method, along with unbiased subtractions from the hopping parameter expansion. In addition to increasing the number of Z(4) noises, we find that increasing the number of nucleon sources for each configuration improves the signal significantly. We obtain G_M^s(0) = -0.017(25)(07), where the first error is statistical, and the second is the uncertainties in Q^2 and chiral extrapolations. This is consisten…
By imposing the constraints of charge symmetry we show that the strangeness magnetic moment of the nucleon can be expressed in terms of empirical magnetic moments and ratios of valence quark magnetic moments. The latter are determined using modern chiral extrapolation techniques and recent low mass lattice QCD simulations of the individual quark contributions to the magnetic moments of the nucleon octet. The result is a precise determination of G_M^s, namely -0.043 +/- 0.026 mu_N, which is consistent with the latest experimental measurements.
We present results on the mass of the baryon octet and decuplet using two flavors of light dynamical twisted mass fermions. The strange quark mass is fixed to its physical value from the kaon sector in a partially quenched set up. Calculations are performed for light quark masses corresponding to a pion mass in the range 270-500 MeV and lattice sizes of 2.1 fm and 2.7 fm. We check for cut-off effects and isospin breaking by evaluating the baryon masses at two different lattice spacings. We carry out a chiral extrapolation for the octet baryons and discuss results for the Omega.
The nature of QCD phase transition is studied with massless up and down quarks and a light strange quark, using the Wilson formalism for quarks on a lattice with the temporal direction extension $N_t=4$. We find that the phase transition is first order in the cases of both about 150 MeV and 400 MeV for the strange quark mass. These results together with those for three degenerate quarks suggest that QCD phase transition in nature is first order.
We calculate the intrinsic strangeness of the nucleon, <N|ss|N> - <0|ss|0>, using the MILC library of improved staggered gauge configurations using the Asqtad and HISQ actions. Additionally, we present a preliminary calculation of the intrinsic charm of the nucleon using the HISQ action with dynamical charm. The calculation is done with a method which incorporates features of both commonly-used methods, the direct evaluation of the three-point function and the application of the Feynman- Hellman theorem. We present an improvement on this method that further reduces the statistical error, and c…
An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted to 2 dimensions but generalizations to 2+8k dimensions should be straightforward.
We discuss the impact of various improvements on simulations of dynamical overlap fermions using the Hybrid Monte Carlo algorithm. We focus on the usage of fat links and multiple pseudo-fermion fields.
We calculate the scalar and tensor charges of the nucleon in 2+1-flavor lattice QCD, for which the systematics of the renormalization of the disconnected diagram is well controlled. Numerical simulations are performed at a single lattice spacing a = 0.11 fm. We simulate four pion masses, which cover a range of $m_π\sim$ 290 - 540 MeV, and a single strange quark mass close to its physical value. The statistical accuracy is improved by employing the so-called low-mode averaging technique and the truncated solver method. We study up, down, and strange quark contributions to the nucleon charges by…
We briefly review the overlap formalism for chiral gauge theories, the overlap Dirac operator for massless fermions and its connection to domain wall fermions. We describe properties of the overlap Dirac operator, and methods to implement it numerically. Finally, we give some examples of quenched calculations of chiral symmetry breaking and topology with overlap fermions.
An overview of the current status of algorithmic approaches to dynamical overlap fermions is given. In particular the issue of changing the topological sector is discussed.
In order to construct improved overlap fermions, we start from a short ranged approximate Ginsparg-Wilson fermion and insert it into the overlap formula. We show that its polynomial evaluation is accelerated considerably compared to the standard Neuberger fermion. In addition the degree of locality is strongly improved.
I review the lattice formulations of vector-like gauge theories (e.g. QCD) with domain-wall/overlap fermions, and discuss how to optimize the chiral symmetry for any finite $ N_s $ (sites in the fifth dimension). In this formulation, quark propagators in gauge background can be computed efficiently through the effective 4D lattice Dirac operator.
We present a nearly final analysis of the $u/d$ and $s$ quark masses, extracted using the PCAC quark masses reported in [PRD 95 (2017) 074504]. The data is based on the CLS $N_f = 2 + 1$ simulations with Wilson/Clover quarks and Lüscher-Weisz gauge action, at four $β$ values (i.e. lattice spacings) and a range of quark masses. We use the ALPHA results of [EPJC 78 (2018) 387] for non-perturbative quark mass renormalisation and RG-running from hadronic to electroweak scales in the Schrödinger Functional scheme. Quark masses are quoted both in the $\overline{\rm MS}$ scheme and as RGI quantities.
We present first results of classical-statistical real-time simulations of anomalous transport phenomena with overlap fermions. We find that even on small lattices overlap fermions reproduce the real-time anomaly equation with much better precision than Wilson-Dirac fermions on an order of magnitude larger lattices. The difference becomes much more pronounced for quickly changing electromagnetic fields, especially if one takes into account the back-reaction of fermions on electromagnetism. As test cases, we consider chirality pumping in parallel electric and magnetic fields and mixing between …
We investigate the mass spectra of $Θ^+(udud\bar s)$ in quenched lattice QCD, with overlap and Wilson fermions respectively. Using three different interpolating operators, we measure their correlation matrix, and extract the mass spectra in even and odd parity channels, for 100 gauge configurations generated with single plaquette action at $β=6.1$ on the $20^3 \times 40$ lattice. The lowest $ 1/2^- $ state agrees with the $ KN $ s-wave scattering state, for both fermion schemes. On the other hand, for the lowest $ 1/2^+ $ state, it is different from any hadron scattering states for the overlap…
We discuss the kernel spectrum, locality properties and the axial-vector renormalization constant of UV-filtered overlap fermions. We find that UV-filtered overlap fermions have a better conditioned kernel, better locality and an axial-vector renormalization constant closer to 1 than their unfiltered counterparts, even if the shift parameter $ρ$ is simply set to 1.
We perform a systematic study of low-lying eigenmodes of $H_w$ with various gauge actions to find the optimal choice for dynamical overlap fermion simulations, with which one may achieve lower numerical cost for HMC and better locality property of the overlap kernel. For this purpose, our study is made with emphasis on the distribution of low-lying eigenvalues and the mobility edge with and without dynamical overlap fermions.
