We report on recent results of the QCDSF/UKQCD Collaboration on investigations of baryon structure using configurations generated with N_f=2+1 dynamical flavours of O(a) improved Wilson fermions. With the strange quark mass as an additional dynamical degree of freedom in our simulations we avoid the need for a partially quenched approximation when investigating the properties of particles containing a strange quark, e.g. the hyperons. In particular, we will focus on the nucleon and hyperon axial charges and quark momentum fractions.
The axial-vector form factors and axial-vector constants of the baryon decuplet are investigated within a pion mean-field approach, which is also known as the chiral quark-soliton model. Given an axial-vector current with a specified flavor, there are four different form factors of a decuplet baryon. When we consider the singlet, triplet, and octet axial-vector currents, we have twelve different form factors for each member of the baryon decuplet. We compute all these axial-vector form factors of the baryon decuplet, taking into account the rotational $1/N_c$ corrections and effects of flavor …
We consider the axial-vector form factors of the baryon octet in flavor-SU(3) chiral perturbation theory. The baryon octet and decuplet and the pseudoscalar-meson octet are included as explicit degrees of freedom. We explore the use of on-shell meson and baryon masses in the one-loop contributions to the axial-vector form factors and focus on a consistent treatment in terms of chiral power counting. The convergence properties of such an approach are scrutinized. We discuss the potential for comparison to upcoming QCD lattice data.
We evaluate the strangeness-conserving $N N$, $ΣΣ$, $ΞΞ$, $ΛΣ$ and the strangeness-changing $ΛN$, $ΣN$, $ΛΞ$, $ΣΞ$ axial charges in lattice QCD with two flavors of dynamical quarks and extend our previous work on pseudoscalar-meson-octet-baryon coupling constants so as to include $πΞΞ$, $KΛΞ$ and $KΣΞ$ coupling constants. We find that the axial charges have rather weak quark-mass dependence and the breaking in SU(3)-flavor symmetry is small at each quark-mass point we consider.
We investigate the axial-vector transition form factors of the baryon octet to the baryon decuplet within the framework of the chiral quark-soliton model, with the effects of flavor SU(3) symmetry breaking included. We consider the rotational $1/N_c$ corrections and regard the strange current quark mass as a perturbation. We compare the present results for the $Δ\to N$ axial-vector transition with those from other models and lattice QCD. We also compute all possible axial-vector transitions from the baryon decuplet to the octet with the strangeness changed, i.e., $|ΔS|=1$. We obtain the value …
We investigate the axial-vector transition form factors of the lowest-lying singly heavy baryons within the framework of the chiral quark-soliton model. We consider the linear $m_{\mathrm{s}}$ corrections, dealing with the strange current quark mass $m_{\mathrm{s}}$ as a small perturbation. Since we have various relations between different transitions because of isospin symmetry and flavor SU(3) symmetry breaking, only two axial-vector transition form factors are independent. We present the numerical results for these form factors. The effects of the flavor SU(3) symmetry breaking turn out tin…
We consider the chiral Lagrangian with nucleon, isobar, and pion degrees of freedom. The baryon masses and the axial-vector form factor of the nucleon are derived at the one-loop level. We explore the impact of using on-shell baryon masses in the loop expressions. As compared to results from conventional chiral perturbation theory we find significant differences. An application to QCD lattice data is presented. We perform a global fit to the available lattice data sets for the baryon masses and the nucleon axial-vector form factor, and determine the low-energy constants relevant at N$^3$LO for…
We investigate the antitriplet and sextet heavy baryon systems with $J^P= \frac{1}{2}^+, \frac{3}{2}^+$ in the framework of the heavy baryon chiral perturbation theory. We first calculate the chiral corrections to the heavy baryon mass from the SU(3) flavor breaking effect up to $O(p^3)$. Then we extend the same formalism to calculate the chiral corrections to the axial charges of the heavy baryons in the isospin symmetry limit.
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 include 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.
The extrapolation of nucleon axial charge $g_A$ is investigated within the framework of heavy baryon chiral effective field theory. The intermediate octet and decuplet baryons are included in the one loop calculation. Finite range regularization is applied to improve the convergence in the quark-mass expansion. The lattice data from three different groups are used for the extrapolation. At physical pion mass, the extrapolated $g_A$ are all smaller than the experimental value.
We calculate the nucleon axial form factor up to the leading one-loop order in a covariant chiral effective field theory with the $Δ(1232)$ resonance as an explicit degree of freedom. We fit the axial form factor to the latest lattice QCD data and pin down the relevant low-energy constants. The lattice QCD data, for various pion masses below $400$ MeV, can be well described up to a momentum transfer of $\sim 0.6$ GeV. The $Δ(1232)$ loops contribute significantly to this agreement. Furthermore, we extract the axial charge and radius based on the fitted values of the low energy constants. The re…
We present results for the $σ$-terms and axial charges for various hyperons and charmed baryons using $N_f=2+1+1$ twisted mass fermions. For the computation of the three-point function we use the fixed current method. For one of the $N_f=2+1+1$ ensembles with pion mass of 373 MeV we compare the results of the fixed current method with those obtained with a stochastic method for computing the all-to-all propagator involved in the evaluation of the three point functions.
The chiral dynamics of the doubly heavy baryons is solely governed by the light quark. In this work, We have derived the chiral corrections to the mass of the doubly heavy baryons up to N$^3$LO. The mass splitting of $Ξ_{cc}$ and $Ω_{cc}$ at the N$^2$LO depends on one unknown low energy constant $c_7$. With the experimental mass of $Ξ_{cc}(3520)$ as the input, we estimate the mass of $Ω_{cc}$ to be around 3.678 GeV. Moreover, we have also performed a systematical analysis of the chiral corrections to the axial currents and axial charges of the doubly heavy baryons. The chiral structure and ana…
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.
As a first step towards constructing chiral models on the lattice with staggered fermions, we study a U(1) model with axial-vector coupling to an external gauge field in two dimensions. In our approach gauge invariance is broken, but it is restored in the classical continuum limit. We find that the continuum divergence relations for the vector and axial-vector currents are reproduced, up to contact terms, which we determine analytically. The current divergence relations are also studied numerically for smooth external gauge fields with topological charge zero. We furthermore investigate the ef…
We study the $U(1)_A$ anomaly in the high-temperature phase of $N_f=2+1$ lattice QCD with chiral fermions. Gauge ensembles are generated with Möbius domain-wall (MDW) fermions, and in the measurements the determinant is reweighted to that of overlap fermions. We report the results for the overlap Dirac spectrum, $U(1)_A$ susceptibility, and topological susceptibility at $T=204$ and $175$ MeV.
The axial couplings of the low lying baryons are evaluated using a total of five ensembles of dynamical twisted mass fermion gauge configurations. The simulations are performed using the Iwasaki gauge action and two degenerate flavors of light quarks, and a strange and a charm quark fixed to approximately their physical values at two values of the coupling constant. The lattice spacings, determined using the nucleon mass, are $a=0.082$ fm and $a=0.065$ fm and the simulations cover a pion mass in the range of about 210 MeV to 430 MeV. We study the dependence of the axial couplings on the pion m…
We investigate the axial $U(1)$ symmetry restoration at finite temperature in two flavor QCD. We employ the Möbius domain-wall formalism that is designed to achieve good chiral symmetry. We show the measurements of a difference of meson susceptibilities, sensitive to the $U(1)_A$ symmetry breaking. The signal is dominated by zero and near-zero modes. By reweighting the measure to that of overlap fermions we find a suppression of the $U(1)_A$ breaking effects above the chiral transition temperature.
We present first results from dynamical Chirally Improved (CI) fermion simulations for the axial charge $G_A$ of various hadrons. We work with 16^3x32 lattices of spatial extent 2.4 fm and use the variational method with a suitable basis of Jacobi-smeared interpolators to suppress contaminations from excited states.
Octet baryon axial, induced pseudoscalar, and pseudoscalar form factors are computed using a symmetry-preserving treatment of a vector$\,\times\,$vector contact interaction (SCI), thereby unifying them with an array of other baryon properties and analogous treatments of semileptonic decays of pseudoscalar mesons. The baryons are treated as quark--plus--interacting-diquark bound states, whose structure is obtained by solving a Poincaré-covariant Faddeev equation. The approach is marked by algebraic simplicity, involves no free parameters, and since it is symmetry preserving, all consequences of…
The divergence of the axial current is used to relate the spatial derivative of the fermion density to the bare fermion mass and scalar/pseudoscalar condensates in 1+1 dimensional Gross-Neveu models. This serves as a novel test of known results, to explain simple features of the continuous chiral model and to resolve a conflict concerning the assignment of baryon number to certain multi-fermion bound states.
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…
We present a quenched lattice calculation of the nucleon isovector vector and axial-vector charges gV and gA. The chiral symmetry of domain wall fermions makes the calculation of the nucleon axial charge particularly easy since the Ward-Takahashi identity requires the vector and axial-vector currents to have the same renormalization, up to lattice spacing errors of order O(a^2). The DBW2 gauge action provides enhancement of the good chiral symmetry properties of domain wall fermions at larger lattice spacing than the conventional Wilson gauge action. Taking advantage of these methods and perfo…
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…
We examine the axial U(1) symmetry near and above the finite temperature phase transition in two-flavor QCD using lattice QCD simulations. Although the axial U(1) symmetry is always violated by quantization, (i.e.) the chiral anomaly, the correlation functions may manifest effective restoration of the symmetry in the high temperature phase. We explicitly study this possibility by calculating the meson correlators as well as the Dirac operator spectral density near the critical point. Our numerical simulations are performed on a $16^3\times 8$ lattice with two flavors of dynamical quarks repres…
We study the weak interaction axial form factors of the octet baryons, within the covariant spectator quark model, focusing on the dependence of four-momentum transfer squared, Q^2. In our model the axial form factors G_A(Q^2) (axial-vector form factor) and G_P(Q^2) (induced pseudoscalar form factor), are calculated based on the constituent quark axial form factors and the octet baryon wave functions. The quark axial current is parametrized by the two constituent quark form factors, the axial-vector form factor g_A^q(Q^2), and the induced pseudoscalar form factor g_P^q(Q^2). The baryon wave fu…
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.
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.
We report the current status of RBCK calculations on nucleon structure with both quenched and unquenched lattice QCD. The combination of domain wall fermions and DBW2 gauge action works well for isovector vector and axial charges, and moments of structure functions <x>_q, d_1, and <1>_{δq}.
This paper develops in detail a lattice definition of QCD based on the chiral defect fermions recently introduced by Kaplan. The revised version provides missing technical details in the proof that non-singlet axial symmetries become exact in the limit of an infinite fifth dimension. Also several minor errors are corrected.
We study the restoration of the spontaneously broken chiral symmetry and the anomalously broken axial U(1) symmetry in finite temperature QCD at zero chemical potential. We use 2 flavors lattice QCD with optimal domain-wall fermion on the $ 16^3 \times 6 $ lattice, with the extent $ N_s = 16 $ in the fifth dimension, in the temperature range $ T = 130-230 $ MeV. To examine the restoration of the chiral symmetry and the axial $ U(1) $ symmetry, we use diluted $ Z_2 $ noises to calculate the chiral condensate, and the chiral susceptibilities in the scalar and pseudoscalar meson channels, for fla…
We report lattice QCD results on the axial charges of ground and excited nucleon states of both parities. This is the first study of these quantities with approximately chiral (CI) fermions. Two energy levels in the range of the negative parity resonances N*(1535) and N*(1650) are observed and we determine the axial charge for both. We obtain a small axial charge for one of them, which is consistent with the chiral symmetry restoration in this state as well as with the small axial charge of the N*(1535) predicted within the quark model. This result agrees with the findings of Takahashi et al. …
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 $.
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 use lattice simulations to compute the baryon spectrum of SU(4) lattice gauge theory coupled to dynamical fermions in the fundamental and two-index antisymmetric (sextet) representations simultaneously. This model is closely related to a composite Higgs model in which the chimera baryon made up of fermions from both representations plays the role of a composite top-quark partner. The dependence of the baryon masses on each underlying fermion mass is found to be generally consistent with a quark-model description and large-Nc scaling. We combine our numerical results with experimental bounds…
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.
We investigate the high-temperature phase of QCD using lattice QCD simulations with $N_f = 2$ dynamical Möbius domain-wall fermions. On generated configurations, we study the axial $U(1)$ symmetry, overlap-Dirac spectra, screening masses from mesonic correlators, and topological susceptibility. We find that some of the observables are quite sensitive to lattice artifacts due to a small violation of the chiral symmetry. For those observables, we reweight the Möbius domain-wall fermion determinant by that of the overlap fermion. We also check the volume dependence of observables. Our data near t…
We present preliminary results for the axial and tensor charge of the nucleon obtained from simulations with N_f=2 clover fermions. A comparison with chiral perturbation theory is attempted.
We calculate the axial couplings of mesons and baryons containing a heavy quark in the static limit using lattice QCD. These couplings determine the leading interactions in heavy hadron chiral perturbation theory and are central quantities in heavy quark physics, as they control strong decay widths and the light-quark mass dependence of heavy hadron observables. Our analysis makes use of lattice data at six different pion masses, 227 MeV < m_π< 352 MeV, two lattice spacings, a=0.085, 0.112 fm, and a volume of (2.7 fm)^3. Our results for the axial couplings are g_1=0.449(51), g_2=0.84(20), and …
A non-perturbative determination of the axial current improvement coefficient cA is performed with two flavors of dynamical improved Wilson fermions and plaquette gauge action. The improvement condition is formulated with Schroedinger functional boundary conditions and enforced at constant physical volume. Large sensitivity is obtained by using two different pseudo-scalar states in the PCAC relation. We estimate the resulting correction to F_PS at beta=5.2 to be around 10%.
We employ dimension-4 operators to improve the local vector and axial-vector currents and calculate the nucleon isovector axial coupling $g^3_A$ with overlap valence on $2+1$-flavor Domain Wall Fermion sea. Using the equality of $g^3_A$ from the spatial and temporal components of the axial-vector current as a normalization condition, we find that $g_A^3$ is increased by a few percent towards the experimental value. The excited-state contamination has been taken into account with three time separations between the source and sink. The improved axial charges $g_A^{3}(24I)=1.22(4)$ and $g_A^{3}(3…
We describe our recent lattice study of SU(4) gauge theory with fermions in the fundamental and sextet representations. In this theory, a new type of baryon consists of quarks in both representations. The spectrum of these "chimera baryons" has a straightforward interpretation in terms of a non-relativistic quark model based on SU(4). Our results are particularly relevant to composite Higgs models in which the top quark is partially composite.
The domain wall fermion (DWF) method, with its almost perfectly preserved chiral symmetry on the lattice, makes the calculation of the nucleon axial charge particularly easy. By maintaining chiral symmetry and using the Ward-Takahashi (WT) identity, one has Z_A = Z_V and the bare lattice calculation yields the physical value without explicit renormalization. The DBW2 improved gauge action provides further enhancement of the symmetry and hence a more accurate WT identity at coarse lattice spacing. Taking advantage of these methods, we confirmed a significant volume dependence of the nucleon axi…
We present simulation results employing overlap fermions for the axial correlation functions in the epsilon-regime of chiral perturbation theory. In this regime, finite size effects and topology play a dominant role. Their description by quenched chiral perturbation theory is compared to our numerical results in quenched QCD. We show that lattices with a linear extent L > 1.1 fm are necessary to interpret the numerical data obtained in distinct topological sectors in terms of the epsilon-expansion. Such lattices are, however, still substantially smaller than the ones needed in standard chiral …
We present results for the nucleon electromagnetic and axial form factors using an N$_f$=2 twisted mass fermion ensemble with pion mass of about 131 MeV. We use multiple sink-source separations to identify excited state contamination. Dipole masses for the momentum dependence of the form factors are extracted and compared to experiment, as is the nucleon magnetic moment and charge and magnetic radii.
We present results on the isovector and isoscalar nucleon axial form factors including disconnected contributions,using an ensemble of $N_f =2$ twisted mass clover- improved Wilson fermions simulated with approximately the physical value of the pion mass. The light disconnected quark loops are computed using exact deflation, while the strange and the charm quark loops are evaluated using the truncated solver method. Techniques such as the summation and the two-state fits have been employed to access ground-state dominance.
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 present a new normalization condition for the axial current, derived from the PCAC relation with non-vanishing quark mass. This condition is expected to reduce mass effects in the chiral extrapolation of the results for the normalization factor Z_A. The application to the two-flavor theory with improved Wilson fermions shows that this expectation is indeed fulfilled. Using the Schroedinger functional setup we calculate Z_A(g_0^2) as well as the vector current normalization factor Z_V(g_0^2) for beta = 6/g_0^2 >= 5.2.
Lattice gauge theories with Wilson fermions break chiral symmetry. In the U(1) axial vector current this manifests itself in the anomaly. On the other hand it is generally expected that the axial vector flavour mixing current is non-anomalous. We give a short, but strict proof of this to all orders of perturbation theory, and show that chiral symmetry restauration implies a unique multiplicative renormalization constant for the current. This constant is determined entirely from an irrelevant operator in the Ward identity. The basic ingredients going into the proof are the lattice Ward identity…
We present the results of a full QCD lattice calculation of the flavor singlet axial vector coupling $G_A^1$ of the proton. The simulation has been carried out on a $16^3\times 32$ lattice at $β=5.6$ with $n_f=2$ dynamical Wilson fermions. It turns out that the statistical quality of the connected contribution to $G_A^1$ is excellent, whereas the disconnected part is accessible but suffers from large statistical fluctuations. Using a 1st order tadpole improved renormalization constant $Z_A$, we estimate $G_A^1 = 0.20(12)$.
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) susceptibili…
We report on the determination of the improvement coefficient $c_{\rm A}$ for the non-singlet axial-vector current $A^{a}_μ(x)$ in the framework of stabilised Wilson-Clover fermions within three flavour lattice QCD. This is done by requiring the PCAC relation to hold for two different pseudo-scalar states. To generate these states, wavefunctions altering spatial structures on the boundaries of a Schrödinger functional lattice are employed and some variations of the (previously applied) wavefunction method are explored. The improvement coefficient is determined on a few ensembles for a range of…
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…
With twisted boundary conditions on the quark fields, we study nucleon matrix elements of the axial current utilizing twisted heavy baryon chiral perturbation theory. One can explore the momentum transfer dependence of the axial form factors more easily than by using ordinary lattice quantized momenta alone. As examples, we derive expressions for the nucleon axial radius and pseudoscalar form factor.
We non-perturbatively determine the renormalization factor of the axial vector current in lattice QCD with $N_f=3$ flavors of Wilson-clover fermions and the tree-level Symanzik-improved gauge action. The (by now standard) renormalization condition is derived from the massive axial Ward identity and it is imposed among Schrödinger functional states with large overlap on the lowest lying hadronic state in the pseudoscalar channel, in order to reduce kinematically enhanced cutoff effects. We explore a range of couplings relevant for simulations at lattice spacings of $\approx 0.09$ fm and below. …
