arXiv subjects
Publications and source records attributed to C. Alexandrou.
We calculate the $\bar{s}s$ condensate in the D - and B - mesons using the unquenched hopping parameter expansion at infinite coupling for the Wilson lattice action. We discuss the phenomenological relevance of our result.
We investigate Lüscher's method of including dynamical Wilson fermions in a lattice simulation of QCD with two quark flavours. We measure the accuracy of the approximation by comparing it with Hybrid Monte Carlo results for gauge plaquette and Wilson loops. We also introduce an additional global Metropolis step in the update. We show that the complexity of Lüscher's algorithm compares favourably with that of the Hybrid Monte Carlo.
Heavy-light bound states are studied in Lattice QCD with emphasis on parameters of the B-system relevant to experiment. Results are obtained on lattices with lattice spacings from about 0.15 fm to 0.06 fm corresponding to $β=5.74, 6.0$ and 6.26, and covering sizes from about 0.7 fm to 2 fm. From our results at the infinite quark mass limit and from propagating heavy quarks with mass of about 1-2.5 GeV we extrapolate to the b-quark mass to obtain the decay constant of the B-meson as well as the mass of $Λ_b$ in the continuum. The necessary extrapolations introduce rather large errors and lead to the value $f_B=180(50)$ MeV. We compare with the results from other lattice groups as well as with predictions coming from sum rules. The phenomenological consequences of this value of $f_B$, together with new experimental constraints, are briefly discussed.
We extend the polaron variational treatment previously developed for the propagator to the case where one nucleon and $n$ external mesons are present. Using the particle representation of the scalar Wick-Cutkosky model this is done in lowest order of an expansion of the exact action around a retarded quadratic trial action. In particular, we evaluate the form factor for scattering of mesons from the scalar nucleon and determine the radius of the dressed particle. After analytic continuation to Minkowski space we study elastic meson-nucleon scattering both analytically and numerically near threshold and show that it is essential to incorporate the correct behaviour of the retardation function at large proper times. Only if this is done the optical theorem is approximately fulfilled over a range of energies and coupling constants.
The variational approach, used by Feynman in the study of the polaron problem, is generalized to treat a system of N non-relativistic particles interacting with scalar and vector mesons. After integrating out the meson fields in the path integral formulation we perform a variational calculation for the effective N-body two-time action to obtain the energy and the mass of the system. The interplay of self energies and exchange terms in attaining binding and saturation is examined. We estimate the size of the particles in the medium and give the mean number of mesons as a function of N.
We present lattice estimates of the mass of the heavy-light baryons $Λ_b$ and $Ξ_b$ obtained using propagating heavy quarks. For $Λ_b$ our result is $M_{Λ_b}=5.728 \pm 0.144 \pm 0.018$ GeV, after extrapolation to the continuum limit and in the quenched approximation.
We perform a lattice study of heavy baryons, containing one ($Λ_b$) or two $b$-quarks ($Ξ_b$). Using the quenched approximation we obtain for the mass of $Λ_b$ $$ M_{Λ_b}= 5.728 \pm 0.144 \pm 0.018 {\rm GeV}.$$ The mass splitting between the $Λ_b$ and the B-meson is found to increase by about 20\% if the light quark mass is varied from the chiral limit to the strange quark mass.
We present a high statistics study of the leptonic decay constant $f_P$ of heavy pseudoscalar mesons using propagating heavy Wilson quarks within the quenched approximation, on lattices covering sizes from about 0.7~fm to 2~fm. Varying $β$ between 5.74 and 6.26 we observe a sizeable $a$ dependence of $f_P$ when one uses the quark field normalization that was suggested by Kronfeld and Mackenzie, compared with the weaker dependence observed for the standard relativistic norm. The two schemes come into agreement when one extrapolates to $a \rightarrow 0$. The extrapolations needed to reach the continuum quantity $f_B$ introduce large errors and lead to the value $f_B=0.18(5)$~GeV in the quenched approximation. This suggests that much more effort will be needed to obtain an accurate lattice prediction for $f_B$.
A high statistics calculation, performed at $β=5.74,\;6.00$ and $6.26$, enables us to study the variation of the leptonic decay constants $f_P$ of heavy pseudoscalar mesons with the lattice spacing $a$. We observe only a weak $a$ dependence when the standard $\sqrt{2κ}$ normalization is used for the quark fields, whereas application of the Kronfeld-Mackenzie normalization induces a stronger variation with $a$. Increasing the meson mass from $1.1GeV$ to $2.3GeV$ this situation becomes even more pronounced.
We present a study of {\it finite} $a$ and {\it volume} effects of the leptonic decay constant $f$ of heavy pseudoscalar mesons in the static approximation. This study is performed on a number of lattices at $β=$ 5.74,~6.0 and 6.26 covering sizes from about 0.7~$fm$ to 2~$fm$. We confirm that beyond 1.5~$fm$ the volume dependence is negligible. By carefully analysing results obtained using different trial wave functions for the heavy meson we find no dependence on the smearing. We also give results for the mass difference of the scalar - pseudoscalar and the $Λ_{b}$ - pseudoscalar. Using the mass of the pseudoscalar meson we estimate the distance of string breaking in the static quark potential.
We present a comprehensive study of finite volume and lattice spacing effects on observables calculated in the static approximation. Ground state projection using smearing techniques is studied at $β=6.26$. We give high statics results for the pseudoscalar decay constant after extrapolating to the chiral and continuum limit. In addition results for mass splittings and the distance of string breaking in the $Q\bar{Q}$ potential are presented.