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Register a new userPartially conserved axial vector current and applications
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We investigate implications of the use of the point-split axial vector current derived from a Wilson like fermionic action. We compute the corresponding renormalization factor nonperturbatively for one beta value. The axial charge gA calculated from this nonlocal current is found to be nearer to the physical value than computed with the local axial vector current -- computed both on the same lattice with the same action.
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For Wilson and clover fermions traditional formulations of the axial vector current do not respect the continuum Ward identity which relates the divergence of that current to the pseudoscalar density. Here we propose to use a point-split or one-link axial vector current whose divergence exactly satisfies a lattice Ward identity, involving the pseudoscalar density and a number of irrelevant operators. We check in one-loop lattice perturbation theory with SLiNC fermion and gauge plaquette action that this is indeed the case including order $O(a)$ effects. Including these operators the axial Ward identity remains renormalisation invariant. First preliminary results of a nonperturbative check of the Ward identity are also presented.
We present analytical results for the Euclidean 2-point correlator of the flavor-singlet vector current evolved by the gradient flow at next-to-leading order ($O(g^2)$) in perturbatively massless QCD-like theories. We show that the evolved 2-point correlator requires multiplicative renormalization, in contrast to the nonevolved case, and confirm, in agreement with other results in the literature, that such renormalization ought to be identified with a universal renormalization of the evolved elementary fermion field in all evolved fermion-bilinear currents, whereas the gauge coupling renormalizes as usual. We explicitly derive the asymptotic solution of the Callan-Symanzik equation for the connected 2-point correlators of these evolved currents in the limit of small gradient-flow time $sqrt{t}$, at fixed separation $|x-y|$. Incidentally, this computation determines the leading coefficient of the operator-product expansion (OPE) in the small $t$ limit for the evolved currents in terms of their local nonevolved counterpart. Our computation also implies that, in the evolved case, conservation of the vector current, hence transversality of the corresponding 2-point correlator, is no longer related to the nonrenormalization, in contrast to the nonevolved case. Indeed, for small flow time the evolved vector current is conserved up to $O(t)$ softly violating effects, despite its $t$-dependent nonvanishing anomalous dimension.
Recently, Grabowska and Kaplan suggested a non-perturbative formulation of a chiral gauge theory, which consists of the conventional domain-wall fermion and a gauge field that evolves by the gradient flow from one domain wall to the other. In this paper, we discuss the U(1) axial-vector current in 4 dimensions using this formulation. We introduce two sets of domain-wall fermions belonging to complex conjugate representations so that the effective theory is a 4-dimensional vector-like gauge theory. Then, as a natural definition of the axial-vector current, we consider a current that generates the simultaneous phase transformations for the massless modes in 4 dimensions. However, this current is exactly conserved and does not reproduce the correct anomaly. In order to investigate this point precisely, we consider the mechanism of the conservation. We find that this current includes not only the axial current on the domain wall but also a contribution from the bulk, which is non-local in the sense of 4-dimensional fields. Therefore, the local current is obtained by subtracting the bulk contribution from it.
Using the axial-vector coupling and the electromagnetic form factors of the D and D* mesons in 2+1 flavor Lattice QCD, we compute the D*Dpi, DDrho and D*D*rho coupling constants, which play an important role in describing the charm hadron interactions in terms of meson-exchange models. We also extract the charge radii of D and D* mesons and determine the contributions of the light and charm quarks separately.
We present an updated analysis of the quark mass dependence of the nucleon mass and nucleon axial-vector coupling g_A, comparing different formulations of SU(2) Baryon Chiral Effective Field Theory, with and without explicit delta (1232) degrees of freedom. We discuss the outcome of the corresponding interpolations between lattice QCD data and the physical values for these two nucleon observables. It turns out that in order to obtain successful interpolating functions at one-loop order, the inclusion of explicit delta (1232) degrees of freedom is not decisive for the nucleon mass but crucial for g_A. A chiral extrapolation of recent lattice results by the LHP collaborations is also shown.
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