Carlos Pena

Non-perturbative renormalization of static-light four-fermion operators in quenched lattice QCD

We perform a non-perturbative study of the scale-dependent renormalization factors of a multiplicatively renormalizable basis of ¢B = 2 parity-odd four-fermion op- erators in quenched lattice QCD. Heavy quarks are treated in the static approximation with various lattice discretizations of the static action. Light quarks are described by non- perturbatively O(a) improved Wilson-type fermions. The renormalization group running is computed for a family of Schrodinger functional (SF) schemes through finite volume techniques in the continuum limit. We compute non-perturbatively the relation between the renormalization group invariant operators and their counterparts renormalized in the SF at a low energy scale. Furthermore, we provide non-perturbative estimates for the matching between the lattice regularized theory and all the SF schemes considered.

Twisted mass QCD and lattice approaches to the ?I = 1/2 rule

Twisted mass lattice QCD (tmQCD), generalised to four Wilson quark flavours, can be used for the computation of some weak matrix elements related toI = 1/2 transitions. Besides eliminating unphysical zero modes, tmQCD may alleviate the four-quark oper- ator renormalisation problems encountered in the calculation of CP-conserving K → � matrix elements with traditional Wilson fermion regularisation. With an active charm quark, the renormalisation of the K → � matrix elements requires at most the sub- traction of a linearly divergent counterterm. Furthermore, in the (partially) quenched approximation the twist angles can be chosen so that only a finite counterterm needs to be subtracted.

Weyl-Dirac zero mode for calorons

In this paper, we give the exact expression for the SU(2) fermion zero mode in the field of the infinite volume caloron with a nontrivial holonomy and unit charge. Study of the gauge field configurations had, somewhat surprisingly, revealed that at nontrivial holonomy calorons have two Bogomol’nyi-Prasad-Sommerfield ~BPS! monopoles @N for SU(N)# as their constituents @1,2,3#. For the HarringtonShepard @4# solution with trivial holonomy, this is hidden because one of the constituents is massless ~it can be removed by a singular gauge transformation to show that the caloron for a large scale parameter becomes a single BPS monopole @5#!. We find that, for calorons with wellseparated constituents, the fermion zero mode is entirely supported on one of them. In itself it is not surprising that the zero mode is correlated to the monopole constituents. Independently, this observation was recently also made for gluino zero modes in the context of supersymmetric gauge theories @6#. Gluinos are in the adjoint representation of the gauge group, such that there are four zero modes that can be split in pairs associated with each of the two constituents @6#. However, for the Dirac fermion, there is only one zero mode. To understand the ‘‘affinity’’ of the zero mode to only one of the two monopoles, we will analyze in some detail what distinguishes them. Calorons are characterized by the ~fixed! holonomy @1,7#. In the gauge in which Am(x) is periodic, this holonomy is given by

Probing the chiral regime of Nf=2 QCD with mixed actions

17 paginas, 15 figuras, 9 tablas.-- El Pdf es la version pre-print del articulo: arXiv:1008.1870v2

A perturbative study of two four-quark operators in finite volume renormalization schemes

Starting from the QCD Schrodinger functional (SF), we define a family of renormalization schemes for two four-quark operators, which are, in the chiral limit, protected against mixing with other operators. With the appropriate flavour assignments these operators can be interpreted as part of either the ΔF = 1 or ΔF = 2 effective weak Hamiltonians. In view of lattice QCD with Wilson-type quarks, we focus on the parity odd components of the operators, since these are multiplicatively renormalized both on the lattice and in continuum schemes. We consider 9 different SF schemes and relate them to commonly used continuum schemes at one-loop order of perturbation theory. In this way the two-loop anomalous dimensions in the SF schemes can be inferred. As a by-product of our calculation we also obtain the one-loop cutoff effects in the step-scaling functions of the respective renormalization constants, for both O(a) improved and unimproved Wilson quarks. Our results will be needed in a separate study of the non-perturbative scale evolution of these operators.

On K ---> pi pi amplitudes with a light charm quark

We compute the leading-order low-energy constants of the DeltaS=1 effective weak Hamiltonian in the quenched approximation of QCD with up, down, strange, and charm quarks degenerate and light. They are extracted by comparing the predictions of finite-volume chiral perturbation theory with lattice QCD computations of suitable correlation functions carried out with quark masses ranging from a few MeV up to half of the physical strange mass. We observe a DeltaI=1/2 enhancement in this corner of the parameter space of the theory. Although matching with the experimental result is not observed for the DeltaI=1/2 amplitude, our computation suggests large QCD contributions to the physical DeltaI=1/2 rule in the GIM limit, and represents the first step to quantify the role of the charm-quark mass in K-->pipi amplitudes. The use of fermions with an exact chiral symmetry is an essential ingredient in our computation.

Non-perturbative renormalisation of left–left four-fermion operators with Neuberger fermions

Abstract We outline a general strategy for the non-perturbative renormalisation of composite operators in discretisations based on Neuberger fermions, via a matching to results obtained with Wilson-type fermions. As an application, we consider the renormalisation of the four-quark operators entering the Δ S = 1 and Δ S = 2 effective Hamiltonians. Our results are an essential ingredient for the determination of the low-energy constants governing non-leptonic kaon decays.

Large N corrections to the strong coupling behaviour of SU(N)/Bbb ZN lattice gauge theories

We derive a formula for the large N behaviour of the expectation values of an arbitrary product of Wilson loops in the adjoint representation. We show the consequences of our formula for the study of the large N strong coupling behaviour of SU(N)/N pure gauge theories, and theories with matter fields in the adjoint representation. This allows us to calculate large N corrections to the gluino condensate and meson propagators in the lattice version of Supersymmetric Yang-Mills. Applications to the strong coupling behaviour of the Kazakov-Migdal model are also given.

Flavour symmetry restoration and kaon weak matrix elements in quenched twisted mass QCD

We simulate two variants of quenched twisted mass QCD (tmQCD), with degenerate Wilson quarks of masses equal to or heavier than half the strange quark mass. We use Ward identities in order to measure the twist angles of the theory and thus check the quality of the tuning of mass parameters to a physics condition which stays constant as the lattice spacing is varied. Flavour symmetry breaking in tmQCD is studied in a framework of two fully twisted and two standard Wilson quark flavours, tuned to be degenerate in the continuum. Comparing pseudoscalar masses, obtained from connected quark diagrams made of tmQCD and/or standard Wilson quark propagators, we confirm that flavour symmetry breaking effects, which are at most 5%, decrease as we approach the continuum limit. We also compute the pseudoscalar decay constant in the continuum limit, with reduced systematics. As a consequence of improved tuning of the mass parameters at � = 6.1, we reanalyse our previous BK results. Our main phenomenological findings are r0fK = 0.421(7) and ˆ

Nahm dualities on the torus - a synthesis

Abstract We give a unified description of self-dual SU(2) gauge fields on tori of size lt×ls3, based on a mixture of analytical and numerical methods using the Nahm transformation, extended to the case of twisted boundary conditions. We show how torus calorons (lt/ls small) are Nahm dual to the torus instantons (lt/ls large). Holonomies are dual to the locations of constituents, this duality becoming exact in the limiting cases ls or lt→∞. Implications for the moduli spaces are discussed.