Domain Wall Fermions Research Articles

Mass spectroscopy of excited light mesons using truncated overlap fermions

We study excited light mesons by quenched lattice quantum chromodynamics (QCD) simulations with a truncated overlap fermion formalism based on domain wall fermions. Truncated overlap fermions satisfy lattice chiral symmetry instead of chiral symmetry in continuum field theory, as for domain wall fermions, but offer lower simulation costs. Our results show good agreement with the experimental values for the excited state of a 1, ρ, and π mesons, and demonstrate that a 1(1260) and a 1(1640) are simple two-quark states, whereas a 1(1420) may have a more complicated structure. The results are similar to those of previous dynamical studies using clover-Wilson fermions or chirally improved fermions, even though our lattice QCD calculations are performed with the quenched approximation. The study shows that lattice QCD simulations using truncated overlap fermions are essential in lattice studies of excited states.

Form factors of B→πℓν and a determination of |Vub| with Möbius domain-wall fermions

Using a fully relativistic lattice fermion action, we compute the form factors of the semileptonic decay $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}\ensuremath{\nu}$, which is required for the determination of the Cabibbo-Kobayashi-Maskawa matrix element $|{V}_{ub}|$. We employ the M\"obius domain-wall fermion formalism for the generation of lattice ensembles with $2+1$ sea quark flavors as well as for the valence heavy and light quarks. We compute the form factors at various values of the lattice spacing and multiple light and heavy quark masses, and extrapolate the results to the physical point. We combine our lattice results with the available experimental data to obtain $|{V}_{ub}|=(3.93\ifmmode\pm\else\textpm\fi{}0.41)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$.

Search for b¯b¯us and b¯c¯ud tetraquark bound states using lattice QCD

We use lattice QCD to investigate the existence of strong-interaction-stable antiheavy-antiheavy-light-light tetraquarks. We study the $\overline{b}\overline{b}us$ system with quantum numbers ${J}^{P}={1}^{+}$ as well as the $\overline{b}\overline{c}ud$ systems with quantum numbers $I({J}^{P})=0({0}^{+})$ and $I({J}^{P})=0({1}^{+})$. We carry out computations on five gauge-link ensembles with $2+1$ flavors of domain-wall fermions, including one at the physical pion mass. The bottom quarks are implemented using lattice nonrelativistic QCD, and the charm quarks using an anisotropic clover action. In addition to local diquark-antidiquark and local meson-meson interpolating operators, we include nonlocal meson-meson operators at the sink, which facilitates the reliable determination of the low-lying energy levels. We find clear evidence for the existence of a strong-interaction-stable $\overline{b}\overline{b}us$ tetraquark with binding energy $(\ensuremath{-}86\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$ and mass $(10609\ifmmode\pm\else\textpm\fi{}22\ifmmode\pm\else\textpm\fi{}10)\text{ }\text{ }\mathrm{MeV}$. For the $\overline{b}\overline{c}ud$ systems we do not find any indication for the existence of bound states, but cannot rule out their existence either.

Induced topological gravity and anomaly inflow from Kähler-Dirac fermions in odd dimensions

We show that the effective action that results from integrating out massive K\"ahler-Dirac fermions propagating on a curved three-dimensional space is a topological gravity theory of Chern-Simons type. In the presence of a domain wall, massless, two-dimensional K\"ahler-Dirac fermions appear that are localized to the wall. Potential gravitational anomalies arising for these domain wall fermions are canceled via anomaly inflow from the bulk gravitational theory. We also study the invariance of the theory under large gauge transformations. The analysis and conclusions generalize straightforwardly to higher dimensions.

Curved domain-wall fermions

Abstract We consider fermion systems on a square lattice with a mass term having a curved domain-wall. Like conventional flat domain-wall fermions, massless and chiral edge states appear on the wall. In the cases of S1 and S2 domain-walls embedded into flat hypercubic lattices, we find that these edge modes feel gravity through the induced spin or spinc connections. The gravitational effect is encoded in the Dirac eigenvalue spectrum as a gap from zero. In the standard continuum extrapolation of the square lattice, we find good agreement with the analytic prediction in the continuum theory. We also find that the rotational symmetry of the edge modes is automatically recovered in the continuum limit. Subject Index B38

The asymptotic approach to the continuum of lattice QCD spectral observables

We consider spectral quantities in lattice QCD and determine the asymptotic behaviour of their discretization errors. Wilson fermion with O(a)-improvement, (Möbius) Domain wall fermion (DWF), and overlap Dirac operators are considered in combination with the commonly used gauge actions. Wilson fermions and DWF with domain wall height M5=1+O(g02) have the same, approximate, form of the asymptotic cutoff effects: Ka2[g¯2(a−1)]0.760. A domain wall height M5=1.8, as often used, introduces large mass-dependent K′(m)a2[g¯2(a−1)]0.518 effects. Massless twisted mass fermions have the same form as Wilson fermions when the Sheikholeslami-Wohlert term [1] is included. For their mass-dependent cutoff effects we have information on the exponents Γˆi of g¯2(a−1) but not for the pre-factors. For staggered fermions there is only partial information on the exponents.We propose that tree-level O(a2) improvement, which is easy to do [2], should be used in the future – both for the fermion and the gauge action. It improves the asymptotic behaviour in all cases.

Mod-two APS index and domain-wall fermion

We show a mathematical relation between the mod-two Atiyah–Patodi–Singer (APS) index of a massless Dirac operator and massive domain-wall fermion determinant. The domain-wall fermion is given on a closed manifold, which is extended from the original manifold with boundary, where we instead give a fermion mass term changing its sign at the location of the original boundary. This new setup does not need the APS boundary condition, which is non-local. A mathematical proof of equivalence between the two different formulations is given by two different evaluations of the same index of a Dirac operator on a higher-dimensional manifold. The domain-wall fermion allows us to separate the edge and bulk mode contributions in a natural but not in a gauge invariant way, which offers a straightforward description of the global anomaly inflow.

Reconstructing QCD spectral functions with Gaussian processes

We reconstruct ghost and gluon spectral functions in 2+1 flavor QCD with Gaussian process regression. This framework allows us to largely suppress spurious oscillations and other common reconstruction artifacts by specifying generic magnitude and length scale parameters in the kernel function. The Euclidean propagator data are taken from lattice simulations with domain wall fermions at the physical point. For the infrared and ultraviolet extensions of the lattice propagators as well as the low-frequency asymptotics of the ghost spectral function, we utilize results from functional computations in Yang-Mills theory and QCD. This further reduces the systematic error significantly. Our numerical results are compared against a direct real-time functional computation of the ghost and an earlier reconstruction of the gluon in Yang-Mills theory. The systematic approach presented in this work offers a promising route towards unveiling real-time properties of QCD.

Lattice QCD Calculation of the Pion Mass Splitting.

We use the infinite volume reconstruction method to calculate the charged and neutral pion mass difference. The hadronic tensor is calculated using lattice QCD and then combined with an analytic photon propagator, and the mass splitting is calculated with exponentially suppressed finite-volume errors. The calculation is performed using six gauge ensembles generated with 2+1-flavor domain wall fermions, and five ensembles are at the physical pion mass. Both Feynman and Coulomb gauges are adopted in the calculation and agree well when the lattice spacing approaches zero. After performing the continuum extrapolation and examining the residual finite-volume effects, we obtain the pion mass splitting Δm_{π}=4.534(42)_{stat}(43)_{sys} MeV, which agrees well with experimental measurements.

Lattice fermions as spectral graphs

We study lattice fermions from the viewpoint of spectral graph theory (SGT). We find that a fermion defined on a certain lattice is identified as a spectral graph. SGT helps us investigate the number of zero eigenvalues of lattice Dirac operators even on the non-torus and non-regular lattice, leading to understanding of the number of fermion species (doublers) on lattices with arbitrary topologies. The procedure of application of SGT to lattice fermions is summarized as follows: (1) One investigates a spectral graph corresponding to a lattice fermion. (2) One obtains a matrix corresponding to the graph. (3) One finds zero eigenvalues of the matrix by use of the discrete Fourier transformation (DFT). (4) By taking an infinite-volume and continuum limits, one finds the number of species. We apply this procedure to the known lattice fermion formulations including Naive fermions, Wilson fermions and Domain-wall fermions, and reproduce the known fact on the number of species. We also apply it to the lattice fermion on the discretized four­dimensional hyperball and discuss the number of fermion species on the bulk. In the end of the paper, we discuss the application of the analysis to lattice fermions on generic lattices with arbitrary topologies, which could lead to constructing a new theorem regarding the number of species.

The Calculation of Force in Lattice Quantum Chromodynamics

Quantum chromodynamics (QCD) is the fundamental quantum field theory of quarks and gluons. To discuss it in a mathematically well-defined way, the theory has to be regularized by replacing space-time with a Euclidean lattice. This regularized theory, called lattice QCD (LQCD), has proven to be an efficient approach which allows for both theoretical understanding and computational analysis. LQCD has become a standard tool in elementary particle physics, which can be solved by the hybrid Monte Carlo method. The calculation of force is most difficult part in the hybrid Monte Carlo method. This lecture gives the details of the force calculation in one-loop Symanzik improved action, Wilson fermion with clover term, asqtad fermion, HISQ fermion, rooted staggered fermion, smeared fermion, staggered Wilson fermion, overlap fermion and domain wall fermion. The even-odd precondition are also considered in these calculations.

From quantum link models to D-theory: a resource efficient framework for the quantum simulation and computation of gauge theories.

Quantum link models provide an extension of Wilson's lattice gauge theory in which the link Hilbert space is finite-dimensional and corresponds to a representation of an embedding algebra. In contrast to Wilson's parallel transporters, quantum links are intrinsically quantum degrees of freedom. In D-theory, these discrete variables undergo dimensional reduction, thus giving rise to asymptotically free theories. In this way [Formula: see text] [Formula: see text] models emerge by dimensional reduction from [Formula: see text] [Formula: see text] quantum spin ladders, the [Formula: see text] confining [Formula: see text] gauge theory emerges from the Abelian Coulomb phase of a [Formula: see text] quantum link model, and [Formula: see text] QCD arises from a non-Abelian Coulomb phase of a [Formula: see text] [Formula: see text] quantum link model, with chiral quarks arising naturally as domain wall fermions. Thanks to their finite-dimensional Hilbert space and their economical mechanism of reaching the continuum limit by dimensional reduction, quantum link models provide a resource efficient framework for the quantum simulation and computation of gauge theories. This article is part of the theme issue 'Quantum technologies in particle physics'.

Linking continuum and lattice quark mass functions via an effective charge

The quark mass function is computed both by solving the quark propagator Dyson-Schwinger equation and from lattice simulations implementing overlap and Domain-Wall fermion actions for valence and sea quarks, respectively. The results are confronted and seen to produce a very congruent picture, showing a remarkable agreement for the explored range of current-quark masses. The effective running-interaction is based on a process-independent charge rooted on a particular truncation of the Dyson-Schwinger equations in the gauge sector, establishing thus a link from there to the quark sector and inspiring a correlation between the emergence of gluon and hadron masses.

Domain wall AdS/QCD

We construct a new holographic description of QCD using domain wall fermions. The construction consists of probe D7 branes in a D5 brane geometry describing quarks on a 4+1d defect in a 5+1d gauge theory. We then compactify one dimension of the D5 to introduce confinement in the gauge degrees of freedom. In addition we allow a spatial dependent mass term for the D7 brane quarks to isolate chiral fermions on 3+1d domain walls. The D7 world volume fields, when restricted to the domain wall position, provide an AdS/QCD description. We compute the spectrum and compare to data. We include higher dimension operators to systematically improve the description.

More about the Grassmann tensor renormalization group

We derive a general formula of the tensor network representation for d-dimensional lattice fermions with ultra-local interactions, including Wilson fermions, staggered fermions, and domain-wall fermions. The Grassmann tensor is concretely defined with auxiliary Grassmann variables that play a role in bond degrees of freedom. Compared to previous works, our formula does not refer to the details of lattice fermions and is derived by using the singular value decomposition for the given Dirac matrix without any ad-hoc treatment for each fermion. We numerically test our formula for free Wilson and staggered fermions and find that it properly works for them. We also find that Wilson fermions show better performance than staggered fermions in the tensor renormalization group approach, unlike the Monte Carlo method.

Domain wall fermions on the brane

We study domain wall fermions and their condensation in the D3/probe D7 system. A spatially dependent mass term for the N=2 hypermultiplet can be arranged to isolate distinct two component fermions on two 2+1 dimensional domain walls. We argue that the system shows condensation/mass generation analogous to the D3/probe D5 anti-D5 system. The chiral condensate and pion mass can be directly computed on the domain wall. We provide evidence that these systems with the domains separated by a width w have a bare (current) quark mass that scales as 1/w when the spatial dependent mass is large. Adding a magnetic field does not induce chiral symmetry breaking between the separated domain wall fermions, but a similar phenomenological dilaton factor can be made strong enough to introduce spontaneous symmetry breaking. We show a Gell-Man-Oakes-Renner relation for the pions in that case and also for the case where the D7 probe is in a back-reacted dilaton flow geometry. The vacuum configurations can also be interpreted as having a spontaneously generated mass by a Nambu-Jona-Lasinio four fermion operator, depending on the choice of boundary conditions on fluctuations, according to Witten's multi-trace prescription.

Understanding the index theorems with massive fermions

The index theorems relate the gauge field and metric on a manifold to the solution of the Dirac equation on it. In the standard approach, the Dirac operator must be massless to make the chirality operator well defined. In physics, however, the index theorem appears as a consequence of chiral anomaly, which is an explicit breaking of the symmetry. It is then natural to ask if we can understand the index theorems in a massive fermion system which does not have chiral symmetry. In this review, we discuss how to reformulate the chiral anomaly and index theorems with massive Dirac operators, where we find nontrivial mathematical relations between massless and massive fermions. A special focus is placed on the Atiyah–Patodi–Singer index, whose original formulation requires a physicist-unfriendly boundary condition, while the corresponding massive domain-wall fermion reformulation does not. The massive formulation provides a natural understanding of the anomaly inflow between the bulk and edge in particle and condensed matter physics.

Lattice-fermionic Casimir effect and topological insulators

The Casimir effect arises from the zero-point energy of particles in momentum space deformed by the existence of two parallel plates. For degrees of freedom on the lattice, its energy-momentum dispersion is determined so as to keep a periodicity within the Brillouin zone, so that its Casimir effect is modified. We study the properties of Casimir effect for lattice fermions, such as the naive fermion, Wilson fermion, and overlap fermion based on the M\"obius domain-wall fermion formulation, in the $1+1$-, $2+1$-, and $3+1$-dimensional space-time with the periodic or antiperiodic boundary condition. An oscillatory behavior of Casimir energy between odd and even lattice size is induced by the contribution of ultraviolet-momentum (doubler) modes, which realizes in the naive fermion, Wilson fermion in a negative mass, and overlap fermions with a large domain-wall height. Our findings can be experimentally observed in condensed matter systems such as topological insulators and also numerically measured in lattice simulations.

Λb→Λc*(2595,2625)ℓ−ν¯ form factors from lattice QCD

We present the first lattice-QCD determination of the form factors describing the semileptonic decays ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595){\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$ and ${\mathrm{\ensuremath{\Lambda}}}_{b}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625){\ensuremath{\ell}}^{\ensuremath{-}}\overline{\ensuremath{\nu}}$, where the ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2595)$ and ${\mathrm{\ensuremath{\Lambda}}}_{c}^{*}(2625)$ are the lightest charm baryons with ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$, respectively. These decay modes provide new opportunities to test lepton flavor universality and also play an important role in global analyses of the strong interactions in $b\ensuremath{\rightarrow}c$ semileptonic decays. We determine the full set of vector, axial vector, and tensor form factors for both decays but only in a small kinematic region near the zero-recoil point. The lattice calculation uses three different ensembles of gauge-field configurations with $2+1$ flavors of domain-wall fermions, and we perform extrapolations of the form factors to the continuum limit and physical pion mass. We present Standard Model predictions for the differential decay rates and angular observables. In the kinematic region considered, the differential decay rate for the ${\frac{1}{2}}^{\ensuremath{-}}$ final state is found to be approximately 2.5 times larger than the rate for the ${\frac{3}{2}}^{\ensuremath{-}}$ final state. We also test the compatibility of our form-factor results with zero-recoil sum rules.

Study of the axial U(1) anomaly at high temperature with lattice chiral fermions

We investigate the axial $U(1)$ anomaly of two-flavor QCD at temperatures 190--330 MeV. In order to preserve precise chiral symmetry on the lattice, we employ the M\"obius domain-wall fermion action as well as overlap fermion action implemented with a stochastic reweighting technique. Compared to our previous studies, we reduce the lattice spacing to 0.07 fm, simulate larger multiple volumes to estimate finite size effect, and take more than four quark mass points, including one below physical point to investigate the chiral limit. We measure the topological susceptibility, axial $U(1)$ susceptibility, and examine the degeneracy of $U(1)$ partners in meson/baryon correlators. All the data above the critical temperature indicate that the axial $U(1)$ violation is consistent with zero within statistical errors. The quark mass dependence suggests disappearance of the $U(1)$ anomaly at a rate comparable to that of the $SU(2{)}_{L}\ifmmode\times\else\texttimes\fi{}SU(2{)}_{R}$ symmetry breaking.