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 Mobius 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 and 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 x SU(2)_R symmetry breaking.
In the axial Ward identity of lattice QED we show that in the limit of infinite fermion mass m the pseudoscalar density term exactly cancels the Adler-Bell-Jackiw anomaly. Using this result we calculate the U(1) axial anomaly in a non-abelian gauge theory.
By an explicit calculation of the continuum limit of the triangle graph amplitude in lattice QED we show that in the axial Ward identity the ABJ anomaly exactly cancels the pseudoscalar density term in the limit of infinite fermion mass $m$. The result, a reflection of decoupling of the heavy fermion, provides a convenient framework for computing the flavor-singlet or U(1) axial anomaly in non-Abelian gauge theories on lattice. Our calculations on the lattice are performed using Wilson fermions but the results are general.
In our recent study of two-flavor lattice QCD using chiral fermions, we find strong suppression of axial U(1) anomaly above the critical temperature of chiral phase transition. Our simulation data also indicate suppression of topological susceptibility. In this talk, we present both of our theoretical and numerical evidence for disappearance of axial U(1) anomaly, emphasizing the importance of controlling lattice chiral symmetry violation, which is enhanced at high temperature.
A remarkable feature of a lattice Dirac operator is discussed. Unlike the Dirac operator for massless fermions in the continuum, this Ginsparg-Wilson lattice Dirac operator does not possess topological zero modes for any topologically-nontrivial background gauge fields, even though it is exponentially-local, doublers-free, and reproduces correct axial anomaly for topologically-trivial gauge configurations.
By carrying out a systematic expansion of Feynman integrals in the lattice spacing, we show that the axial anomaly in the U(1) lattice gauge theory with Wilson fermions, as determined in one-loop order from an irrelevant lattice operator in the Ward identity, must necessarily be identical to that computed from the dimensionally regulated continuum Feynman integrals for the triangle diagrams.
The axial anomaly in abelian lattice gauge theories is shown to be equal to a simple quadratic expression in the gauge field tensor plus a removable divergence term if the lattice Dirac operator satisfies the Ginsparg-Wilson relation. The theorem is a consequence of the locality, the gauge invariance and the topological nature of the anomaly and does not refer to any other properties of the lattice theory.
Evaluation of the continuum limit of the axial anomaly and index is sketched for the staggered overlap Dirac operator. There are new complications compared to the usual overlap case due to the distribution of the spin and flavor components around lattice hypercubes in the staggered formalism. The index is found to correctly reproduce the continuum index, but for the axial anomaly this is only true after averaging over the sites of a lattice hypercube.
We prove that lattice QCD generates the axial anomaly in the continuum limit under very general conditions on the lattice action, which includes the case of Ginsparg-Wilson fermions. The ingredients going into the proof are gauge invariance, locality of the Dirac operator, absence of fermion doubling, the general form of the lattice Ward identity, and the power counting theorem of Reisz. The results generalize in an obvious way to SU(N) lattice gauge theories.
The axial anomaly equation in 1+1 dimensional QED is obtained on the lattice for fermions obeying the Ginsparg-Wilson relation. We make use of the properties of the Lattice Dirac sea to investigate the connection between the anomaly and the Ginsparg-Wilson operator in the Hamiltonian picture. The correct anomaly is reproduced for gauge fields whose characteristic time is much larger than the lattice spacing, which is the regime where the adiabatic approximation applies. A non-zero Wilson $r$ parameter is necessary to get the correct anomaly. The anomaly is shown to be independent of $r$ for $r…
University of the Virgin Islands（维尔京群岛大学）；School of Physics and Astronomy, University of Minnesota（明尼苏达大学物理与天文学院）；Department of Physics, University of California San Diego（加州大学圣地亚哥分校物理系）
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem.
The topological charge in the $\U(N)$ vector-like reduced model can be defined by using the overlap Dirac operator. We obtain its large $N$ limit for a fermion in a general gauge-group representation under a certain restriction of gauge field configurations which is termed $\U(1)$ embedding.
Using the method of finite differences a scheme is proposed to solve exactly the Klein-Gordon and Dirac free field equations, in a (1+1)-dimensional lattice. The hamiltonian of the Dirac field is translational invariant, hermitian, avoids fermion doubling, and, for the massless case, preserves global chiral symmetry. Coupling the fermion field to the electromagnetic vector potential we construct a gauge invariant vector current leading to the correct axial anomaly.
We give a perturbative proof that U(1) lattice gauge theories generate the axial anomaly in the continuum limit under very general conditions on the lattice Dirac operator. These conditions are locality, gauge covariance and the absense of species doubling. They hold for Wilson fermions as well as for realizations of the Dirac operator that satisfy the Ginsparg-Wilson relation. The proof is based on the lattice power counting theorem. The results generalize to non-abelian gauge theories.
We discuss the weak coupling expansion of massless QCD with the Dirac operator which is derived by Neuberger based on the overlap formalism and satisfies the Ginsparg-Wilson relation. The axial U(1) anomaly associated to the chiral transformation proposed by Luscher is calculated as an application and is shown to have the correct form of the topological charge density for perturbative backgrounds. The coefficient of the anomaly is evaluated as a winding number related to a certain five-dimensional fermion propagator.
We compute the flavor singlet meson correlators and screening masses in quenched and $N_f=2$ QCD at $N_t=8$. The consequences of our results for the realization of the $U_A(1)$ symmetry at finite T are discussed and an interpretation of our measurements in terms of the behaviour of the low lying fermionic modes is proposed.
We calculate one-loop correction to the axial charges of the octet baryons using quenched chiral perturbation theory, in order to understand chiral behavior of the axial charges in quenched approximation to quantum chromodynamics (QCD). In contrast to regular behavior of the full QCD chiral perturbation theory result, $c_0+c_{l2}m_π^2\,\ln{m_π^2}+\cdots$, we find that the quenched chiral perturbation theory result, $c_0^Q+(c_{l0}^Q+c_{l2}^Qm_π^2)\ln{m_π^2}+c_2^Q m_π^2+\cdots$, is singular in the chiral limit.
Axial anomaly of lattice abelian gauge theory in hyper-cubic regular lattice in arbitrary even dimensions is investigated by applying the method of exterior differential calculus. The topological invariance, gauge invariance and locality of the axial anomaly determine the explicit form of the topological part. The anomaly is obtained up to a multiplicative constant for finite lattice spacing and can be interpreted as the Chern character of the abelian lattice gauge theory.
We study the axial anomaly defined on a finite-size lattice by using a Dirac operator which obeys the Ginsparg-Wilson relation. When the gauge group is U(1), we show that the basic structure of axial anomaly on the infinite lattice, which can be deduced by a cohomological analysis, persists even on (sufficiently large) finite-size lattices. For non-abelian gauge groups, we propose a conjecture on a possible form of axial anomaly on the infinite lattice, which holds to all orders in perturbation theory. With this conjecture, we show that a structure of the axial anomaly on finite-size lattices …
We evaluate for arbitrary even dimensions the classical continuum limit of the lattice axial anomaly defined by the overlap-Dirac operator. Our calculational scheme is simple and systematic. In particular, a powerful topological argument is utilized to determine the value of a lattice integral involved in the calculation. When the Dirac operator is free of species doubling, the classical continuum limit of the axial anomaly in various dimensions is combined into a form of the Chern character, as expected.
Exact chiral symmetry at finite lattice spacing would preclude the axial anomaly. In order to describe a continuum quantum field theory of Dirac fermions, lattice actions with purported exact chiral symmetry must break the flavor-singlet axial symmetry. We demonstrate that this is indeed the case by using a minimally doubled fermion action. For simplicity we consider the Abelian axial anomaly in two dimensions. At finite lattice spacing and with gauge interactions, the axial anomaly arises from non-conservation of the flavor-singlet current. Similar non-conservation also leads to the axial ano…
The axial anomaly in lattice gauge theories has a topological nature when the Dirac operator satisfies the Ginsparg-Wilson relation. We study the axial anomaly in Abelian gauge theories on an infinite hypercubic lattice by utilizing cohomological arguments. The crucial tool in our approach is the non-commutative differential calculus~(NCDC) which makes the Leibniz rule of exterior derivatives valid on the lattice. The topological nature of the ``Chern character'' on the lattice becomes manifest in the context of NCDC. Our result provides an algebraic proof of Lüscher's theorem for a four-dimen…
The axial anomaly arising from the fermion sector of $\U(N)$ or $\SU(N)$ reduced model is studied under a certain restriction of gauge field configurations (the ``$\U(1)$ embedding'' with $N=L^d$). We use the overlap-Dirac operator and consider how the anomaly changes as a function of a gauge-group representation of the fermion. A simple argument shows that the anomaly vanishes for an irreducible representation expressed by a Young tableau whose number of boxes is a multiple of $L^2$ (such as the adjoint representation) and for a tensor-product of them. We also evaluate the anomaly for general…
We study flavor mixing and the axial anomaly in QCD at zero and finite temperature. Using the instanton liquid model, we show that the strength of the anomaly is essentially unchanged near the critical temperature for chiral symmetry restoration. We demonstrate that nevertheless, chiral symmetry restoration has important consequences for the eta and eta prime. In particular, the strange and non-strange components of the eta unmix near T_c. The anomaly does not affect the strange eta, so we expect a light purely strange pseudoscalar meson near the phase transition.
The axial anomaly of Ginsparg-Wilson fermion operator $D$ is discussed in general for the operator $R$ which enters the chiral symmetry breaking part in the Ginsparg-Wilson relation. The axial anomaly and the index of $D$ as well as the exact realization of the Atiyah-Singer index theorem on the lattice are determined solely by the topological characteristics of the chirally symmetric operator $D_c$ in the chiral limit $ R \to 0 $.
We study the transition form factors of the light mesons in the kinematics, where one photon is real and other is virtual. Using the dispersive approach to axial anomaly we show that the axial anomaly in this case reveals itself as a collective effect of meson spectrum. This allows us to get the relation between possible corrections to continuum and to lower states within QCD method which does not rely on factorization hypothesis. We show, relying on the recent data of BaBar Collaboration, that the relative correction to continuum is quite small, and small correction to continuum can dramatica…
We use two-flavor heavy baryon chiral perturbation theory to investigate the isovector axial charges of the spin one-half hyperons. Expressions for these hyperon axial charges are derived at next-to-leading order in the chiral expansion. We utilize phenomenological and lattice QCD inputs to assess the convergence of the two-flavor theory, which appears to be best for cascades.
We evaluate the axial anomaly for the general Ginsparg-Wilson fermion operator $D = D_c (\Id + R D_c)^{-1}$ with $R = r \Id$. For any chirally symmetric $D_c$ which in the free fermion limit, is free of species doubling and behaves like $i γ_μp_μ$ as $p \to 0$, the axial anomaly $\tr[γ_5 (R D) (x,x)]$ for U(1) lattice gauge theory with single fermion flavor is equal to $e^2/(32 π^2) ε_{μνλσ} F_{μν}(x) F_{λσ}(x+\hatμ+\hatν)$ plus terms which are higher orders and/or non-perturbative contribtuons. The $F \tilde{F}$ term is r-invariant and has the correct continuum limit.
We study the momentum and the quark mass dependence of the axial nucleon to Delta(1232) transition form factors in the framework of non-relativistic chiral effective field theory to leading-one-loop order. The outcome of our analysis provides a theoretical guidance for chiral extrapolations of lattice QCD results with dynamical fermions.
We study the complete set of flavor changing hyperon axial current matrix elements at small momentum transfer. Using partially quenched heavy baryon chiral perturbation theory, we derive the chiral and momentum behavior of the axial and induced pseudoscalar form factors. The meson pole contributions to the latter posses a striking signal for chiral physics. We argue that the study of hyperon axial matrix elements enables a systematic lattice investigation of the efficacy of three flavor chiral expansions in the baryon sector. This can be achieved by considering chiral corrections to SU(3) symm…
A recent proposal suggests that even if a Ginsparg-Wilson lattice Dirac operator does not possess any topological zero modes in topologically-nontrivial gauge backgrounds, it can reproduce correct axial anomaly for sufficiently smooth gauge configurations, provided that it is exponentially-local, doublers-free, and has correct continuum behavior. In this paper, we calculate the axial anomaly of this lattice Dirac operator in weak coupling perturbation theory, and show that it recovers the topological charge density in the continuum limit.
Chiral corrections to the delta axial charge are determined using heavy baryon chiral perturbation theory. Knowledge of this axial coupling is necessary to assess virtual-delta contributions to nucleon and delta observables. We give isospin relations useful for a lattice determination of the axial coupling. Furthermore we detail partially quenched chiral corrections, which are relevant to address partial quenching and/or mixed action errors in lattice calculations of the delta axial charge.
A regularization-independent universal formula for the energy--momentum tensor in gauge theory in the flat spacetime can be written down by employing the so-called Yang--Mills gradient flow. We examine a possible use of the formula in the calculation of the axial $U(1)$ anomaly in a gravitational field, the anomaly first obtained by Toshiei Kimura [Prog.\ Theor.\ Phys.\ {\bf 42}, 1191 (1969)]. As a general argument indicates, the formula reproduces the correct non-local structure of the (axial $U(1)$ current)--(energy--momentum tensor)--(energy--momentum tensor) triangle diagram in a way that …
The chiral susceptibility, or the first derivative of the chiral condensate with respect to the quark mass, is often used as a probe for the QCD phase transition since the chiral condensate is an order parameter of $SU(2)_L \times SU(2)_R$ symmetry breaking. However, the chiral condensate also breaks the axial $U(1)$ symmetry, which is usually not paid attention to as it is already broken by anomaly and apparently gives little impact on the transition. We investigate the susceptibilities in the scalar and pseudoscalar channels in order to quantify how much the axial $U(1)$ breaking contributes…
Following the recent work by Braguta et al., we perform an indirect calculation of the chiral vortical conductivity with free lattice overlap fermions by measuring the response of the energy flow to the constant axial magnetic field. We find that the measurements are contaminated by very large finite-volume artifacts. However, the continuum result for finite-temperature contribution to the chiral vortical conductivity (T^2/12) is still reproduced in the limit of infinite volume at fixed temperature.
We study the hybrid mesons with the exotic quantum number $I^GJ^{PC} = 0^+1^{-+}$ and investigate their decays into the $ηη^\prime$, $a_1(1260) π$, $f_1(1285) η$, $f_1(1420) η$, $K^*(892) \bar K$, $K_1(1270) \bar K$, and $K_1(1400) \bar K$ channels. We find that the QCD axial anomaly enhances the decay width of the $ηη^\prime$ channel although this mode is strongly suppressed by the small $P$-wave phase space. Our results support the interpretation of the $η_1(1855)$ recently observed by BESIII as the $\bar s s g$ hybrid meson of $I^GJ^{PC}=0^+1^{-+}$. The QCD axial anomaly ensures the $ηη^\pr…
Prior to the establishment of $QCD$ as the correct theory describing hadronic physics, it was realized that the essential ingredients of the hadronic world at low energies are chiral symmetry and its spontaneous breaking. Spontaneous symmetry breaking is a non-perturbative phenomenon and thanks to massive $QCD$ simulations on the lattice we have at present a good understanding on the vacuum realization of the non-abelian chiral symmetry as a function of the physical temperature. As far as the $U_A(1)$ anomaly is concerned, and especially in the high temperature phase, the current situation is …
We address the issue of energy and charge dependence of global polarization of $Λ$ hyperons in peripheral $Au-Au$ collisions recently observed by the STAR collaboration at RHIC. We compare different contributions to the anomalous mechanism relating polarization to vorticity and hydrodynamic helicity in QCD matter. We stress that the suppression of the gravitational anomaly contribution in strongly correlated matter observed in lattice simulations confirms our earlier prediction of rapid decrease of polarization with increasing collision energy. Our mechanism leads to polarization of $\bar Λ$ o…
