Going chiral: overlap versus twisted mass fermions

We present a comparison of a number of iterative solvers of linear systems of equations for obtaining the fermion propagator in lattice QCD. In particular, we consider chirally invariant overlap and chirally improved Wilson (maximally) twisted mass fermions. The comparison of both formulations of lattice QCD is performed at four fixed values of the pion mass between 230MeV and 720MeV. For overlap fermions we address adaptive precision and low mode preconditioning while for twisted mass fermions we discuss even/odd preconditioning. Taking the best available algorithms in each case we find that calculations with the overlap operator are by a factor of 30-120 more expensive than with the twisted mass operator.

The quenched chiral logs are examined on a $16^3 \times 28$ lattice with Iwasaki gauge action and overlap fermions. The pion decay constant $f_{\pi}$ is used to set the lattice spacing, $a = 0.200(3) {\rm fm}$. With pion mass as low as $\sim 180 {\rm MeV}$, we see the quenched chiral logs clearly in $m_{\pi}^2/m$ and $f_P$, the pseudoscalar decay constant. We analyze the data to determine how low the pion mass needs to be in order for the quenched one-loop chiral perturbation theory ($\chi$PT) to apply. With the constrained curve-fitting method, we are able to extract the quenched chiral log parameter $\delta$ together with other low-energy parameters. Only for $m_{\pi} \leq 300 {\rm MeV}$ do we obtain a consistent and stable fit with a constant $\delta$ which we determine to be 0.24(3)(4) (at the chiral scale $\Lambda_{\chi}=0.8 {\rm GeV}$). By comparing to the $12^3 \times 28$ lattice, we estimate the finite volume effect to be about 2.7% for the smallest pion mass. We also fitted the pion mass to the form for the re-summed cactus diagrams and found that its applicable region is extended farther than the range for the one-loop formula, perhaps up to $m_{\pi} \sim 500-600$ MeV. The scale independent $\delta$ is determined to be 0.20(3) in this case. We study the quenched non-analytic terms in the nucleon mass and find that the coefficient $C_{1/2}$ in the nucleon mass is consistent with the prediction of one-loop $\chi$PT\@. We also obtain the low energy constant $L_5$ from $f_{\pi}$. We conclude from this study that it is imperative to cover only the range of data with the pion mass less than $\sim 300 {\rm MeV}$ in order to examine the chiral behavior of the hadron masses and decay constants in quenched QCD and match them with quenched one-loop $\chi$PT\@.

Using Chiral Perturbation Theory at one-loop we analyze the consequences of twisted boundary conditions. We point out that due to the broken Lorentz and reflection symmetry a number of unexpected terms show up in the expressions. We explicitly discuss the pseudo-scalar octet masses, axial-vector and pseudo-scalar decay constants and electromagnetic form-factors. We show how the Ward identities are satisfied using the momentum dependent masses and the non-zero vacuum-expectation-values values for the electromagnetic (vector) currents. Explicit expressions at one-loop are provided and an appendix discusses the needed one-loop twisted finite volume integrals.

A comparison is made of the (quenched) light hadron spectrum and of simple matrix elements for a hypercubic fermion action (based on a fixed point action) and the clover action, both using fat links, at a lattice spacing a= 0.18 fm. Renormalization constants for the naive and improved vector current and the naive axial current are computed using Ward identities. The renormalization factors are very close to unity, and the spectroscopy of light hadrons and the pseudoscalar and vector decay constants agree well with simulations at smaller lattice spacings (and with experiment).

We present renormalization constants of overlap quark bilinear operators on 2+1-flavor domain wall fermion configurations.Both overlap and domain wall fermions have chiral symmetry on the lattice.The scale independent renormalization constant for the local axial vector current is computed using a Ward Identity.The renormalization constants for the scalar, pseudoscalar and vector current are calculated in the RI-MOM scheme.Results in the MS scheme are obtained by using perturbative conversion ratios.The analysis uses in total six ensembles with lattice sizes 24 3 × 64 and 32 3 × 64.

The normal and anomalous chiral Ward identities are reexamined from the point of view of chiral and 1/ perturbation theory. Constraints of psi ..-->.. eta ..gamma.. and psi ..-->.. eta' ..gamma.. and pseudoscalar two photon decays are imposed, yielding a system of six simultaneous equations. A solution for the pseudoscalar decay constants is found which is relatively insensitive to the unknown gluonic bound states. The decay eta ..-->.. 3..pi.. is then calculated using these results, with good agreement with recent measurements.

The large number of quarkonium excited states with their masses and decay widths have been recorded experimentally. Here, we study their decay properties. We have computed the mass spectra of quarkonia using Martin-like potential in Dirac relativistic formalism. The predicted results of quarkonia are found to be in agreement with experimental results and also with other available theoretical results. The computed vector and pseudo scalar decay constants, laptonic decay width, digamma decay width and digluonic width are compared with the available experimental values.

We calculate the nucleon electric dipole moment (EDM) from the $\ensuremath{\theta}$ term with overlap fermions on three domain wall lattices with different sea pion masses at lattice spacing 0.11 fm. Due to the chiral symmetry conserved by the overlap fermions, we have well-defined topological charge and chiral limit for the EDM. Thus, the chiral extrapolation can be carried out reliably at nonzero lattice spacings. We use three to four different partially quenched valence pion masses for each sea pion mass and find that the EDM dependence on the valence and sea pion masses behaves oppositely, which can be described by partially quenched chiral perturbation theory. With the help of the cluster decomposition error reduction technique, we determine the neutron and proton EDM at the physical pion mass to be ${d}_{n}=\ensuremath{-}0.00148(14)(31)\overline{\ensuremath{\theta}}\text{ }\text{ }\mathrm{e}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{fm}$ and ${d}_{p}=0.0038(11)(8)\overline{\ensuremath{\theta}}\text{ }\text{ }\mathrm{e}\ifmmode\cdot\else\textperiodcentered\fi{}\mathrm{fm}$. This work is a clear demonstration of the advantages of using chiral fermions in the nucleon EDM calculation and paves the road to future precise studies of the strong $CP$ violation effects.

We compute nonperturbatively the renormalization constants of composite operators on a quenched ${16}^{3}\ifmmode\times\else\texttimes\fi{}28$ lattice with lattice spacing $a=0.20\text{ }\text{ }\mathrm{fm}$ for the overlap fermion by using the regularization-independent (RI) scheme. The quenched gauge configurations were generated with the Iwasaki action. We test the relations ${Z}_{A}={Z}_{V}$ and ${Z}_{S}={Z}_{P}$ and find that they agree well (less than 1%) above $\ensuremath{\mu}=1.6\text{ }\text{ }\mathrm{GeV}$. We also perform a Renormalization Group (RG) analysis at the next-to-next-to-leading order and match the renormalization constants to the $\overline{\mathrm{MS}}$ scheme. The wave function renormalization ${Z}_{\ensuremath{\psi}}$ is determined from the vertex function of the axial current and ${Z}_{A}$ from the chiral Ward identity. Finally, we examine the finite quark mass behavior for the renormalization factors of the quark bilinear operators. We find that the $(pa{)}^{2}$ errors of the vertex functions are small and the quark mass dependence of the renormalization factors to be quite weak.

Simulations at physical quark masses are affected by the critical slowing down of the solvers. Multigrid preconditioning has proved to deal effectively with this problem. Multigrid accelerated simulations at the physical value of the pion mass are being performed to generate Nf = 2 and Nf = 2 + 1 + 1 gauge ensembles using twisted mass fermions. The adaptive aggregation-based domain decomposition multigrid solver, referred to as DD-αAMG method, is employed for these simulations. Our simulation strategy consists of an hybrid approach of different solvers, involving the Conjugate Gradient (CG), multi-mass-shift CG and DD-αAMG solvers. We present an analysis of the multigrid performance during the simulations discussing the stability of the method. This significant speeds up the Hybrid Monte Carlo simulation by more than a factor 4 at physical pion mass compared to the usage of the CG solver.

We determine the nucleon axial, scalar, and tensor charges and the nucleon σ-terms using twisted mass fermions. We employ three ensembles with approximately equal physical volume of about 5.5 fm, three values of the lattice spacing, approximately 0.06, 0.07, and 0.08 fm, and with the mass of the degenerate up and down, strange and charm quarks tuned to approximately their physical values. We compute both isovector and isoscalar charges and σ-terms and their flavor decomposition including the disconnected contributions. We use the Akaike information criterion to evaluate systematic errors due to excited states and the continuum extrapolation. For the nucleon isovector axial charge we find gAu−d=1.250(24), in agreement with the experimental value. Moreover, we extract the nucleon σ-terms and find for the light quark content σπN=41.9(8.1) MeV and for the strange σs=30(17) MeV.

We present results for the flavor non-singlet u-d parton distribution functions within the nucleon using the quasi-PDF approach. The lattice calculation is performed by employing the twisted mass formulation and two gauge ensembles, having $N_f = 2$ and $N_f = 2 + 1 + 1$ dynamical fermions with masses tuned to their physical value. For the $N_f = 2$ physical point ensemble, the unpolarized, helicity and transversity distributions are computed for three values of the nucleon momentum, namely [6, 8, 10]$\pi$/L corresponding to [0.83,1.11,1.38] GeV. Upon renormalization, we find that, as the nucleon momentum increases, the lattice results approach the phenomenological distributions resulting from analyses of deep inelastic scattering data, opening a promising path for a direct evaluation of parton distributions from the QCD Lagrangian. For the $N_f = 2 + 1 + 1$ physical point ensemble, we present preliminary results for the unpolarized distribution extracted from a nucleon boosted by 8$\pi$/L or 0.97 GeV.

Using the approach proposed a few years ago by X. Ji, it has become feasible to extract parton distribution functions (PDFs) from lattice QCD, a task thought to be extremely difficult before Ji's proposal. In this talk, we discuss this approach, in particular different systematic effects that need to be controlled to ultimately have precise determinations of PDFs. Special attention is paid to the analysis of excited states. We emphasize that it is crucial to control excited states contamination and we show an analysis thereof for our lattice data, used to calculate quasi-PDFs and finally light-cone PDFs in the second part of this proceeding (C. Alexandrou et al., Quasi-PDFs from Twisted mass fermions at the physical point).

We present results on the nucleon scalar, axial and tensor charges, as well as, on the first moments of the unpolarized, polarized and transversity parton distributions using N f = 2 and N f = 2+1+1 twisted mass fermions. These including an ensemble that yields the physical value of the ratio of the nucleon to the pion mass. Results on the axial charges of hyperons and charmed baryons are also presented for a range of pion masses including the physical one.

We present first results from runs performed with N f = 2 + 1 + 1 flavours of dynamical twisted mass fermions at maximal twist: a degenerate light doublet and a mass split heavy doublet.An overview of the input parameters and tuning status of our ensembles is given, together with a comparison with results obtained with N f = 2 flavours.The problem of extracting the mass of the Kand D-mesons is discussed, and the tuning of the strange and charm quark masses examined.Finally we compare two methods of extracting the lattice spacings to check the consistency of our data and we present some first results of χPT fits in the light meson sector.