arXiv subjects

A. Duncan

Publications and source records attributed to A. Duncan.

47 records · Page 3Linked to original sources

arXiv1997

Light Quarks, Zero Modes, and Exceptional Configurations

In continuum QCD, nontrivial gauge topologies give rise to zero eigenvalues of the massless Dirac operator. In lattice QCD with Wilson fermions, these zero modes appear as exactly real eigenvalues of the Wilson-Dirac operator and hence as poles in the quark propagator in the vicinity of critical hopping parameter. It is shown that "exceptional configurations" which arise in the quenched approximation at small quark mass are the result of the fluctuation of the position of zero mode poles to sub-critical values of the hopping parameter on particular gauge configurations. We describe a procedure for correcting these lattice artifacts by first isolating the contribution of zero mode poles to the quark propagator and then shifting the sub-critical poles to the critical point. This procedure defines a modified quenched approximation in which accurate calculations can be carried out for arbitrarily small quark masses.

hep-lat↗

arXiv1996

Electromagnetic Splittings and Light Quark Masses

A method for computing electromagnetic properties of hadrons in lattice QCD is described. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At $β=5.7$ with Wilson action, the $π^+-π^0$ splitting is found to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting, we also find $m_u/m_d = .512(6)$. Systematic errors are discussed. Preliminary results for vector meson splittings are also presented.}

hep-lat↗

arXiv1996

Electromagnetic Structure of Light Baryons in Lattice QCD

A method in which electromagnetic properties of hadrons are studied by direct simulation of dynamical photon effects is applied to the extraction of the isomultiplet structure of the octet baryons. Using 187 configurations at $β=5.7$ with Wilson action, and up and down quark masses determined from the meson spectrum, the nucleon splitting is found to be $1.55(\pm 0.56\; \rm stat)$ MeV; the hyperon splittings are found to be $Σ^{0}-Σ^{+}=2.47\pm 0.39$, $Σ^{-}-Σ^{0}=4.63\pm 0.36$, $Ξ^{-}-Ξ^{0}=5.68\pm 0.24$ MeV. Estimated systematic corrections arising from finite volume and the quenched approximation are included in these results.

hep-lat↗

arXiv1996

Quenched Chiral Logs, the $η'$ Mass, and the Hairpin Diagram

Limits on the size of quenched chiral logs in the pion mass for Wilson fermions are investigated. The smallness of chiral logs is shown to be a result of the suppression of the hairpin diagram for small $p^2$, such that the value of the hairpin on the pion mass shell is much smaller than the physical $m_{η'}^2$. A direct calculation of the topological susceptibility from the same data gives $m_{η'}\approx 1$ GeV.

hep-lat↗

arXiv1996

Electromagnetic Structure of Light Baryons in Lattice QCD

A method for computing electromagnetic properties of hadrons in lattice QCD is applied to the extraction of electromagnetic properties of the octet baryons. This allows a determination of the full dependence of the baryon masses on the charges and masses of the valence quarks. Results of a first numerical study (at $β=5.7$ with Wilson action and light quark masses fixed from the pseudoscalar meson spectrum) are reported. The octet baryon isomultiplet splittings (with statistical errors) are found to be: ${\rm N} - {\rm P} = 1.55(\pm 0.56)$, $Σ^0 - Σ^+ = 2.47(\pm 0.39)$, $Σ^- - Σ^0 = 4.63(\pm 0.36)$ and $Ξ^- - Ξ^0 = 5.68(\pm 0.24)$ MeV. Estimates of the systematic corrections arising from finite volume and the quenched approximation are included in these results.

hep-lat↗

arXiv1996

Nonperturbative Renormalon Structure of Infrared Unstable Theories

The properties of a generalized version of the Borel Transform in infrared unstable theories with dynamical mass generation are studied. The reconstruction of the nonperturbative structure is unambiguous in this version. Various methods for extracting the singularity structure of the Borel Transform for lattice formulations of such theories are explored, and illustrated explicitly with the O(N) sigma model. The status of the first infrared renormalon in QCD is discussed. The feasibility of a proposed technique for analytically continuing from the left hand Borel plane (where nonperturbative information is available via simulation of lattice field theory) to the positive real axis is examined using the sigma model.

hep-th↗

arXiv1996

Pion Wavefunctions and Truncation Sensitivity of QCD Sum Rules

The systematic errors inherent in the QCD sum rule approach to meson wavefunctions are examined in the context of QCD in 1+1 spacetime dimensions in the large N limit where the theory is exactly solvable. It is shown that the truncation of high momentum modes induced in a lattice discretization automatically produces a Chernyak-Zhitnitsky \cite{CZ} type meson wavefunction. Such a truncation alters the balance of leading and higher twist terms in correlators. We find that the reliable extraction of (a few) higher moments is possible provided a reasonably accurate uniform approximation to the Euclidean correlator over a suitable $Q^2$ range is available, but that the extracted values are particularly sensitive to the balance of lower and higher twist contributions. Underestimates of lower twist contributions or overestimates of the highest twist term may lead to too high values for the second and fourth moments of the pion wavefunction, suggesting a doubly peaked structure of the Chernyak-Zhitnitsky type.

hep-ph↗

arXiv1996

Electromagnetic Splittings and Light Quark Masses in Lattice QCD

A method for computing electromagnetic properties of hadrons in lattice QCD is described and preliminary numerical results are presented. The electromagnetic field is introduced dynamically, using a noncompact formulation. Employing enhanced electric charges, the dependence of the pseudoscalar meson mass on the (anti)quark charges and masses can be accurately calculated. At $β=5.7$ with Wilson action, the $π^+-π^0$ splitting is found to be $4.9(3)$ MeV. Using the measured $K^0-K^+$ splitting, we also find $m_u/m_d = .512(6)$. Systematic errors are discussed.

hep-lat↗

arXiv1994

Properties of B-Mesons in Lattice QCD

The results of an extensive study of B-meson properties in quenched lattice QCD are presented. The studies are carried out in the static quark limit where the b-quark is taken to be infinitely massive. Our computations rely on a multistate smearing method introduced previously, with smearing functions generated from a relativistic lattice quark model. Systematic errors arising from excited state contamination, finite volume effects, and the chiral extrapolation for the light quarks are estimated. We obtain continuum results for the mass splitting M_{B_s}- M_{B_u} = 86 (+/-)12(stat) {+7/-9}(syst) MeV, the ratio of decay constants f_{B_s}/f_{B_u} = 1.22 (+/-)0.04(stat) (+/-)0.02 (syst). For the B-meson decay constant we separately exhibit the sizable uncertainties in the extrapolation to the continuum limit a -> 0 and higher order perturbative matching. We obtain f_{B} = 188 (+/-)23(stat) (+/-)15(syst) {+26/-0}(extrap) (+/-)14 (pert) MeV. ----- [Postscript version of paper available by anonymous ftp at fncrd6.fnal.gov. The file is fb.ps in subdirectory theory.]

hep-lat↗

arXiv1993

Convergence of the Optimized Delta Expansion for the Connected Vacuum Amplitude: Zero Dimensions

Recent proofs of the convergence of the linear delta expansion in zero and in one dimensions have been limited to the analogue of the vacuum generating functional in field theory. In zero dimensions it was shown that with an appropriate, $N$-dependent, choice of an optimizing parameter $ł$, which is an important feature of the method, the sequence of approximants $Z_N$ tends to $Z$ with an error proportional to ${\rm e}^{-cN}$. In the present paper we establish the convergence of the linear delta expansion for the connected vacuum function $W=\ln Z$. We show that with the same choice of $ł$ the corresponding sequence $W_N$ tends to $W$ with an error proportional to ${\rm e}^{-c\sqrt N}$. The rate of convergence of the latter sequence is governed by the positions of the zeros of $Z_N$.

hep-th↗

arXiv1993

Heavy-Light Wavefunctions in Lattice QCD

Using a multistate smearing method, Coulomb gauge wave functions of heavy-light mesons are studied in lattice QCD. Wave functions for the ground state, the first radially excited S-wave state, and the lowest P-wave states of a heavy-light meson are calculated in quenched approximation. The results are found to be in remarkably good agreement with the predictions of a simple relativistic quark model.

hep-lat↗