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Register a new userHow to identify zero modes for improved staggered fermions
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We present results of the eigenvalue spectrum for the staggered Dirac operator obtained using a modified Lanczos algorithm. We identify zero modes and non-zero modes. We derive the chiral Ward identity derived from the conserved $U(1)_A$ symmetry, and check it numerically. This is the first step toward construction of an improved method to identify zero modes reliably with staggered fermions.
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The use of improved staggered actions (HYP, Asqtad) has been proved to reduce the scaling corrections that affected previous calculations of B_K with unimproved (standard) staggered fermions in the quenched approximation. This improved behaviour allows us to perform a reliable calculation of B_K including quark vacuum polarization effects, using the MILC configurations with n_f=2+1 flavours of sea fermions. We perform such a calculation for a single lattice spacing, a=0.125 fm, and with kaons made up of degenerate quarks with m_s/2. The valence strange quark mass m_s is fixed to its physical value and we use two different values of the light sea quark masses. After a chiral extrapolation of the results to the physical value of the sea quark masses, we find hat B_K = 0.83+-0.18, where the error is dominated by the uncertainty in the lattice to continuum matching at O(alpha_s^2). The matching will need to be improved to get the precision needed to make full use of the experimental data on epsilon_K to constrain the unitarity triangle.
We apply non-perturbative renormalization to bilinears composed of improved staggered fermions. We explain how to generalize the method to staggered fermions in a way which is consistent with the lattice symmetries, and introduce a new type of lattice bilinear which transforms covariantly and avoids mixing. We derive the consequences of lattice symmetries for the propagator and vertices. We implement the method numerically for hypercubic-smeared (HYP) and asqtad valence fermion actions, using lattices with asqtad sea quarks generated by the MILC collaboration. We compare the non-perturbative results so obtained to those from perturbation theory, using both scale-independent ratios of bilinears (of which we calculate 26), and the scale-dependent bilinears themselves. Overall, we find that one-loop perturbation theory provides a successful description of the results for HYP-fermions if we allow for a truncation error of roughly the size of the square of the one-loop term (for ratios) or of size O(1) times alpha^2 (for the bilinears themselves). Perturbation theory is, however, less successful at describing the non-perturbative asqtad results.
The variational method is used widely for determining eigenstates of the QCD hamiltonian for actions with a conventional transfer matrix, e.g., actions with improved Wilson fermions. An alternative lattice fermion formalism, staggered fermions, does not have a conventional single-time-step transfer matrix. Nonetheless, with a simple modification, the variational method can also be applied to that formalism. In some cases the method also provides a mechanism for separating the commonly paired parity-partner states. We discuss the extension to staggered fermions and illustrate it by applying it to the calculation of the spectrum of charmed-antistrange mesons consisting of a clover charm quark and a staggered strange antiquark.
We investigate numerically the spectral flow introduced by Adams for the staggered Dirac operator on realistic gauge configurations. We study both the unimproved and the HISQ Dirac operators. We compare the spectral flow index with the index obtained by identifying low-lying modes of large chirality.
Moments of unpolarized, helicity, and transversity distributions, electromagnetic form factors, and generalized form factors of the nucleon are presented from a preliminary analysis of lattice results using pion masses down to 359 MeV. The twist two matrix elements are calculated using a mixed action of domain wall valence quarks and asqtad staggered sea quarks and are renormalized perturbatively. Several observables are extrapolated to the physical limit using chiral perturbation theory. Results are compared with experimental moments of quark distributions and electromagnetic form factors and phenomenologically determined generalized form factors, and the implications on the transverse structure and spin content of the nucleon are discussed.
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