1,354,168 research outputs found
Improved Renormalization of Lattice Operators: A Critical Reappraisal
No full textWe systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our study: the renormalization constants of the vector and axial currents and the ratio of the renormalization constants of the scalar and pseudoscalar densities. We calculate these quantities in boosted perturbation theory, with several running boosted couplings, at the "optimal" scale q*. We find that the results of boosted perturbation theory are usually (but not always) in better agreement with non-perturbative determinations of the renormalization constants than those obtained with standard perturbation theory. The finite renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wilson and the tree-level Clover improved actions, at fixed cutoff (=6.4 and 6.0 respectively). In order to amplify finite cutoff effects, the quark masses (in lattice units) are varied in a large interval 0<am<1. We find that discretization effects are always large with the Wilson action, despite our relatively small value of the lattice spacing ( GeV). With the Clover action discretization errors are significantly reduced at small quark mass, even though our lattice spacing is larger ( GeV). However, these errors remain substantial in the heavy quark region. We have implemented a proposal for reducing O(am) effects, which consists in matching the lattice quantities to their continuum counterparts in the free theory. We find that this approach still leaves appreciable, mass dependent, discretization effects.We systematically examine various proposals which aim at increasing the accuracy in the determination of the renormalization of two-fermion lattice operators. We concentrate on three finite quantities which are particularly suitable for our study: the renormalization constants of the vector and axial currents and the ratio of the renormalization constants of the scalar and pseudoscalar densities. We calculate these quantities in boosted perturbation theory, with several running boosted couplings, at the "optimal" scale q*. We find that the results of boosted perturbation theory are usually (but not always) in better agreement with non-perturbative determinations of the renormalization constants than those obtained with standard perturbation theory. The finite renormalization constants of two-fermion lattice operators are also obtained non-perturbatively, using Ward Identities, both with the Wilson and the tree-level Clover improved actions, at fixed cutoff (=6.4 and 6.0 respectively). In order to amplify finite cutoff effects, the quark masses (in lattice units) are varied in a large interval 0<am<1. We find that discretization effects are always large with the Wilson action, despite our relatively small value of the lattice spacing ( GeV). With the Clover action discretization errors are significantly reduced at small quark mass, even though our lattice spacing is larger ( GeV). However, these errors remain substantial in the heavy quark region. We have implemented a proposal for reducing O(am) effects, which consists in matching the lattice quantities to their continuum counterparts in the free theory. We find that this approach still leaves appreciable, mass dependent, discretization effects
Non-perturbative renormalization of lattice four-fermion operators without power subtractions
No full textA general nonperturbative analysis of the renormalization properties of Delta I = 3/2 four-fermion operators in the framework of lattice regularization with Wilson fermions is presented. We discuss the nonperturbative determination of the operator renormalization constants in the lattice regularization independent (RI or MOM) scheme. We also discuss the determination of the finite lattice subtraction coefficients from Ward identities. We prove that, at large external virtualities, the determination of the lattice mixing coefficients, obtained using the RI renormalization scheme, is equivalent to that based on Ward identities, in the continuum and chiral limits. As a feasibility study of our method, we compute the mixing matrix at several renormalization scales, for three Values of the lattice coupling beta, using the Wilson and tree-level improved SW-Clover actions
Renormalization of HQET Delta B=2 operators: O(a) improvement and 1/m matching with QCD
No full textWe determine a basis of dimension-7 operators which arise at O(a) in the Symanzik expansion of the ∆B = 2 operators with static heavy quarks. We consider both Wilson-like and Ginsparg-Wilson light quarks. Exact chiral symmetry reduces the number of these O(a) counterterms by a factor of two. Only a subset of these operators has previously appeared in the literature. We then
extend the analysis to the O(1/m) operators contributing beyond the static approximation
Results from a non-perturbative renormalization of lattice operators
No full textWe 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.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 lattice, at
Lattice B-parameters for Delta S=2 and Delta I=3/2 operators
No full textWe compute several matrix elements of dimension-six four-fermion operators and extract their B-parameters. The calculations have been performed with the tree-level Clover action at beta = 6.0. The renormalization constants and mixing coefficients of the lattice operators have been obtained non-perturbatively. In the renormalization scheme, at a renormalization scale mu similar or equal to 2 GeV, we find B-K(B-9(3/2))=0.66(11), B-7(3/2)=0.72(5) and B-8(3/2)=1.03(3). The result for B-8(3/2) has important implications for the calculation of epsilon'/epsilon
Dependence of the current renormalization-constants on the quark mass
No full textWe study the behaviour of the vector and axial curr:ent 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)am(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
Non-perturbative renormalisation of the lattice S = 2 four-fermion operator
No full textWe compute the renormalised four-fermion operator O^{\Delta S=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^{\Delta S=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 \beta=6.0. We show that the use of the constants determined non-perturbatively improves the chiral behaviour of the lattice kaon matrix element \_{\latt}.We compute the renormalised four-fermion operator 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, 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 lattice, at . 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~{\Delta S=2} | K~0\>_{\latt}.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 × 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 〈 K 0 |O ΔS=2 |K 0 〉 latt
A general method for non-perturbative renormalization of lattice operators
No full textWe propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of QCD, on a 16^3 \times 32 lattice, at \beta=6.0. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of , on a lattice, at . The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed.We propose a non-perturbative method for computing the renormalization constants of generic composite operators. This method is intended to reduce some systematic errors, which are present when one tries to obtain physical predictions from the matrix elements of lattice operators. We also present the results of a calculation of the renormalization constants of several two-fermion operators, obtained, with our method, by numerical simulation of QCD, on a 16 3 x 32 lattice, at β = 6.0. The results of this simulation are encouraging, and further applications to four-fermion operators and to the heavy quark effective theory are proposed
K-meson vector and tensor decay constants and B(K)-parameter from N(f) = 2 tmQCD
No full textWe present work in progress on the computation of the K-meson vector and tensor decay constants, as well as the B-parameter in Kaon oscillations. Our simulations are performed in a partially quenched setup, with two dynamical (sea) Wilson quark flavours, having a maximally twisted mass term. Valence quarks are either of the standard or the Osterwalder-Seiler maximally twisted variety. These two regularizations can be suitably combined in order to obtain a BK parameter which is both multiplicatively renormalizable and O(a) improved
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