Lattice computation of structure functions

Recent lattice calculations of hadron structure functions are described.Comment: Plenary talk presented at LATTICE96, LaTeX, 7 pages, 5 figures, espcrc2.sty and epsfig.sty include

Results from a Non-Perturbative Renormalization of Lattice Operators

We propose a general renormalization method, which avoids completely the use of lattice perturbation theory. We present the results from its numerical applications to two-fermion operators on a $16^3 \times 32$ lattice, at $\beta=6.0$.Comment: 3 pages postscript file. Contribution to Lattice '9

Non-perturbative renormalization in kaon decays

We discuss the application of the MPSTV non-perturbative method \cite{NPM} to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the $\Delta I=1/2$ rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the $B_K$ parameter.Comment: Talk presented at LATTICE96(improvement), LaTeX 3 pages, uses espcrc2, 2 postscript figure

DEPENDENCE OF THE CURRENT RENORMALISATION CONSTANTS ON THE QUARK MASS

We study the behaviour of the vector and axial current renormalisation constants $Z_V$ and $Z_A$ as a function of the quark mass, $m_q$. We show that sizeable $O(am_q)$ and $O(g_0^2 a m_q)$ systematic effects are present in the Wilson and Clover cases respectively. We find that the prescription of Kronfeld, Lepage and Mackenzie for correcting these artefacts is not always successful.Comment: Contribution to Lattice'94, 3 pages PostScript, uuencoded compressed

Non-Perturbative Renormalisation of Composite Operators

It is shown that the renormalisation constants of two quark operators can be accurately determined (to a precision of a few per-cent using 18 gluon configurations) using Chiral Ward identities. A method for computing renormalisation constants of generic composite operators without the use of lattice perturbation theory is proposed.Comment: 3 pages, uuencoded compressed postscript file, to appear in the Proceedings of the International Symposium on Lattice Field Theory, Dallas, Texas, 12-17 October 1993, Southampton Preprint 93/94-0

Hermite Calculus

We develop a new method of umbral nature to treat blocks of Her mite and of Hermite like poly- nomials as independent algebraic quantities. The Calculus we propose allows the formulation of a number of ”practical rules” allowing significant simplific ations in computational problem

Chiral behaviour of the lattice BKB_K-parameter with the Wilson and Clover Actions at β=6.0\beta = 6.0

We present results for the kaon $B$-parameter $B_K$ from a sample of $200$ configurations using the Wilson action and $460$ configurations using the SW-Clover action, on a $18^3 \times 64$ lattice at $\beta=6.0$. We compare results obtained by renormalizing the relevant operator with different ``boosted" values of the strong coupling constant $\alpha_s$. In the case of the SW-Clover action, we also use the operator renormalized non-perturbatively. In the Wilson case, we observe a strong dependence of $B_K$ on the prescription adopted for $\alpha_s$, contrary to the results of the Clover case which are almost unaffected by the choice of the coupling. We also find that the matrix element of the operator renormalized non-perturbatively has a better chiral behaviour. This gives us our best estimate of the renormalization group invariant $B$-parameter, $\hat B_K=0.86 \pm 0.15$.Comment: LaTeX, 17 pages, 3 postscript figures uuencode