15179667
Rigorous treatment of the lattice renormalization problem of fB.
The B-meson decay constant can be measured on the lattice using a 1/m b expansion. To relate the physical quantity to Monte Carlo data one has to know the renormalizaton coefficient Z between the lattice operators and their continuum counterparts. We come back to this computation to resolve discrepancies found in previous calculations. We define and discuss in detail the renormalization procedure that allows the (perturbative) computation of Z. Comparing the one-loop calculations in the effective Lagrangian approach with the direct two-loop calculation of the two-point B-meson correlator in the limit of large b-quark mass, we prove that the two schemes give consistent results to order α s
3222091
New results in the deformed N=4 SYM theory
We investigate various perturbative properties of the deformed N=4 SYM theory. We carry out a three-loops calculation of the chiral matter superfield propagator and derive the condition on the couplings for maintaining finiteness at this order. We compute the 2-, 3- and 4-point functions of composite operators of dimension 2 at two loops. We identify all the scalar operators (chiral and non-chiral) of bare dimension 4 with vanishing one-loop anomalous dimension. We compute some 2- and 3-point functions of these operators at two loops and argue that the observed finite corrections cannot be absorbed by a finite renormalization of the operators.
119677053
Chiral lattice theories without redundant variables
Abstract We discuss a lattice regularization of chiral gauge theories which does not make use of unphysical auxiliary degrees of freedom. Chiral fermions are described by Weyl spinors and the fermion doubling problem is solved by a Wilson term which explicitely breaks fermion number. The resulting anomalous baryon number non-conservation, in the continuum limit, is discussed.
18796229
Deep inelastic scattering in improved lattice QCD (I). The first moment of structure functions
Abstract In this paper we present the 1-loop perturbative computation of the renormalization constants and mixing coefficients of the lattice quark operators of rank three whose hadronic elements enter in the determination of the second moment of Deep Inelastic Scattering (DIS) structure functions. We have employed in our calculations the nearest-neighbor improved “clover-leaf” lattice QCD action. The interest of using this action in Monte Carlo simulations lies in the fact that all terms which in the continuum limit are effectively of order a ( a being the lattice spacing) have been demonstrated to be absent from on-shell hadronic lattice matrix elements. We have limited our computations to the quenched case, in which quark operators do not mix with gluon operators. We have studied the transformation properties under the hypercubic group of the operators up to the rank five (which are related to moments up to the fourth of DIS structure functions), and we discuss the choice of the operators considered in this paper together with the feasibility of lattice computations for operators of higher ranks. To perform the huge amount of calculations required for the evaluation of all the relevant Feynman diagrams, we have extensively used the symbolic manipulation languages Schoonschip and Form.
15827509
On the all-order perturbative finiteness of the deformed N=4 SYM theory
Abstract We prove that the chiral propagator of the deformed N = 4 SYM theory can be made finite to all orders in perturbation theory for any complex value of the deformation parameter. For any such value the set of finite deformed theories can be parametrized by a whole complex function of the coupling constant g . We reveal a new protection mechanism for chiral operators of dimension three. These are obtained by differentiating the Lagrangian with respect to the independent coupling constants. A particular combination of them is a CPO involving only chiral matter. Its all-order form is derived directly from the finiteness condition. The procedure is confirmed perturbatively through order g 6 .
123087867
Yukawa lattice theory and non-perturbative upper bounds to the fermion mass
Abstract We consider the construction of a chiral, lattice Yukawa theory. To compensate for the chiral symmetry breaking introduced by the Wilson terms, we find that one has to add three further counterterms to the naive lattice action. We discuss how counterterm coefficients are to be fixed in a numerical simulation. We also point out a possible pathology which could prevent the regularized theory to reach the desired continuum theory. Once counterterms are fixed, one can obtain a non-perturbative upper bound to the fermion mass along similar lines to those discussed a time ago by Dashen and Neuberger for the Higgs boson mass.
14329676
Simplicial chiral models.
Principal chiral models on a d-1 dimensional simplex are introduced and studied analytically in the large $N$ limit. The $d = 0, 2, 4$ and $\infty$ models are explicitly solved. Relationship with standard lattice models and with few-matrix systems in the double scaling limit are discussed.
42450422
Strong-coupling analysis of two-dimensional O(N) sigma models with N >= 3 on square, triangular, and honeycomb lattices.
Recently generated long strong-coupling series for the two-point Green{close_quote}s functions of asymptotically free O({ital N}) lattice {sigma} models are analyzed, focusing on the evaluation of dimensionless renormalization-group-invariant ratios of physical quantities and applying resummation techniques to series in the inverse temperature {beta} and in the energy {ital E}. Square, triangular, and honeycomb lattices are considered, as a test of universality and in order to estimate systematic errors. Large-{ital N} solutions are carefully studied in order to establish benchmarks for series coefficients and resummations. Scaling and universality are verified. All invariant ratios related to the large-distance properties of the two-point functions vary monotonically with {ital N}, departing from their large-{ital N} values only by a few per mille even down to {ital N}=3. {copyright} {ital 1996 The American Physical Society.}