We present results for the reference scale r 0 in SU(3) Lattice Gauge Theory for β = 6/g 2 0 in the range 5.7 ≤ β ≤ 6.57. The high relative accuracy of 0.3-0.6% in r 0 /a was achieved through good statistics, the application of a multi-hit procedure and a variational approach in the computation of Wilson loops. A precise definition of the force used to extract r 0 has been used throughout the calculation which guarantees that r 0 /a is a smooth function of the bare coupling and that subsequent continuum extrapolations are possible. The results are applied to the continuum extrapolations of the energy gap ∆ in the static quark potential and the scale L max /r 0 used in the calculation of the running coupling constant.
We present an updated extraction of the transversity parton distribution based on the analysis of pion-pair production in deep-inelastic scattering off transversely polarized targets in collinear factorization. Data for proton and deuteron targets make it possible to perform a flavor separation of the valence components of the transversity distribution, using di-hadron fragmentation functions taken from the semi-inclusive production of two pion pairs in back-to-back jets in e + e − annihilation. The e + e − data from Belle have been reanalyzed using the replica method and a more realistic estimate of the uncertainties on the chiral-odd interference fragmentation function has been obtained. Then, the transversity distribution has been extracted by using the most recent and more precise COMPASS data for deep-inelastic scattering off proton targets. Our results represent the most accurate estimate of the uncertainties on the valence components of the transversity distribution currently available.
We determine the improvement coefficients b m and b A − b P in quenched lattice QCD for a range of β-values, which is relevant for current large scale simulations. At fixed β, the results are rather sensitive to the precise choices of parameters. We therefore impose improvement conditions at constant renormalized parameters, and the coefficients are then obtained as smooth functions of g 2 0 . Other improvement conditions yield a different functional dependence, but the difference between the coefficients vanishes with a rate proportional to the lattice spacing. We verify this theoretical expectation in a few examples and are therefore confident that O(a) improvement is achieved for physical quantities. As a byproduct of our analysis we also obtain the finite renormalization constant which relates the subtracted bare quark mass to the bare PCAC mass.
We discuss non-perturbative improvement of the vector current, using the Schrödinger Functional formalism. By considering a suitable Ward identity, we compute the improvement coefficient which gives the O(a) mixing of the tensor current with the vector current.
We explain how masses and matrix elements can be computed in lattice QCD using Schrödinger functional boundary conditions. Numerical results in the quenched approximation demonstrate that good precision can be achieved. For a statistical sample of the same size, our hadron masses have a precision similar to what is achieved with standard methods, but for the computation of matrix elements such as the pseudoscalar decay constant the Schrödinger functional technique turns out to be much more efficient than the known alternatives.
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