arXiv subjects
Publications and source records attributed to M. Talevi.
We discuss the status and the problems related to the application of the off-shell non-perturbative renormalization method in a fixed gauge to operators relevant to weak decays. In particular, we critically reappraise the method recently proposed for the $ΔI=1/2$ rule. We also present a general analysis of the renormalization for the $ΔI=3/2$ operators, and apply it to the $ΔS=2$ operator.
Some recent developments in the calculation of weak matrix elements on the lattice are reviewed. In particular, we concentrate on the application of MPSTV non-perturbative renormalization method to the operators relevant to kaon physics. The chiral behaviour of the $B_K$ parameter and the long-standing question of the $ΔI=1/2$ rule are discussed.
We study a random resistors network model on a euclidean geometry $\bt{Z}^d$. We formulate the model in terms of a variational principle and show that, under appropriate boundary conditions, the thermodynamic limit of the dissipation per unit volume is finite almost surely and in the mean. Moreover, we show that for a particular thermodynamic limit the result is also independent of the boundary conditions.
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 $ΔI=1/2$ 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.
We apply a recently introduced non-perturbative renormalization method to two types of lattice operators: the $ΔS=2$ four fermion operator and the heavy-light static axial current, which are relevant for the physics of $K$ and $B$ mesons respectively. The results of the non-perturbative calculations of the renormalization constants are compared with the corresponding perturbative ones.
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 $β=6.0$. We compare results obtained by renormalizing the relevant operator with different ``boosted" values of the strong coupling constant $α_s$. 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 $α_s$, 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, $\hat B_K=0.86 \pm 0.15$.
We compute the renormalised four-fermion operator $O^{ΔS=2}$ using a non-perturbative method recently introduced for determining the renormalisation constants of generic lattice composite operators. Because of the presence of the Wilson term, $O^{ΔS=2}$ mixes with operators of different chiralities. A projection method to determine the mixing coefficients is implemented. The numerical results for the renormalisation constants have been obtained from a simulation performed using the SW-Clover quark action, on a $16^3 \times 32$ lattice, at $β=6.0$. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element $\<\bar K^0| O^{ΔS=2} | K^0\>_{\latt}$.