arXiv subjects
Publications and source records attributed to Maarten Golterman.
We discuss the phenomenological implications of assuming a Veneziano-type spectrum for the vector and axial-vector two-point functions in QCD at large Nc. We also compare the phenomenological results with those of Lowest-Meson Dominance, and find that they agree.
We compare the gauge-fixing approach proposed by Jona-Lasinio and Parrinello, and by Zwanziger (JPLZ) with the standard Fadeev-Popov procedure, and demonstrate perturbative equality of gauge-invariant quantities, up to irrelevant terms induced by the cutoff. We also show how a set of local, renormalizable Feynman rules can be constructed for the JPLZ procedure.
In this talk, I first motivate the use of Chiral Perturbation Theory in the context of Lattice QCD. In particular, I explain how partially quenched QCD, which has, in general, unequal valence- and sea-quark masses, can be used to obtain real-world (i.e. unquenched) results for low-energy constants. In the second part, I review how Chiral Perturbation Theory may be used to overcome theoretical difficulties which afflict the computation of non-leptonic kaon decay rates from Lattice QCD. I argue that it should be possible to determine at least the O(p^2) weak low-energy constants reliably from numerical computations of the K to pi and K to vacuum matrix elements of the corresponding weak operators.
I review the substantial progress which has been made recently with the non-perturbative construction of chiral gauge theories on the lattice. In particular, I discuss three different approaches: a gauge invariant method using fermions which satisfy the Ginsparg-Wilson relation, and two gauge non-invariant methods, one using different cutoffs for the fermions and the gauge fields, and one using gauge fixing. Open problems within all three approaches are addressed.
We consider overlap-Dirac fermions at non-zero bare coupling and for a small hopping parameter, or, equivalently, large $|M|$ with $M$ the domain-wall height. We prove the existence of a phase at large positive $M$ where the abelian axial group $U_A(1)$ is a symmetry, and the corresponding pseudo-scalar is an exact Goldstone boson. We also provide a conjecture for the phase diagram of asymptotically free gauge theories with overlap-Dirac fermions. In particular, we suggest that, for large gauge coupling, the massive-fermion phase at negative $M$ possibly extends to all $M<4$.
The coupling constants of the order $p^2$ low-energy weak effective lagrangian can be determined from the $K\toπ$ and $K\to 0$ weak matrix elements, choosing degenerate quark masses for the first of these. However, for typical values of quark masses in Lattice QCD computations, next-to-leading $O(p^4)$ corrections are too large to be ignored, and will need to be included in future analyses. Here we provide the complete $O(p^4)$ expressions for these matrix elements obtained from Chiral Perturbation Theory, valid for partially quenched QCD with $N$ degenerate sea quarks. Quenched QCD corresponds to the special case N=0. We also discuss the role of the $η'$ meson in some detail, and we give numerical examples of the size of chiral logarithms.
After an introduction in which we review the fundamental difficulty in constructing lattice chiral gauge theories, we summarize the analytic and numerical evidence that abelian lattice chiral gauge theories can be nonperturbatively constructed through the gauge-fixing approach. In addition, we indicate how we believe that the method may be extended to nonabelian chiral gauge theories.
We calculate the logarithmic corrections to the matrix elements for $K^+\toπ^+$ and $K\to$vacuum (which are used on the lattice to determine $K\toππ$ amplitudes), in one-loop quenched and unquenched Chiral Perturbation Theory. We find that these corrections can be large. We also discuss, and present some results for, the direct determination of $K\toππ$ amplitudes. In particular, we address effects from choosing $m_s=m_d$ and vanishing external spatial momenta, finite volume and quenching. In the quenched octet case, we find enhanced finite-volume contributions which may make numerical estimates of this matrix element unreliable for large volumes.
An explanation is proposed for the fact that Lepage--Mackenzie tadpole improvement does not work well for staggered fermions. The idea appears to work for all renormalization constants which appear in the staggered fermion self-energy. Wilson fermions are also discussed.
Partially quenched theories are theories in which the valence- and sea-quark masses are different. Here, we will discuss the nonanalytic one-loop corrections to some physical quantities, using partially quenched chiral perturbation theory. In particular, we will focus on the results for Goldstone boson masses to illustrate the general features of our calculation.
We calculate the perturbative scales (q*) for the axial and vector currents for the Wilson action, with and without tadpole improvement, using Lepage and Mackenzie's formalism. The scale for the pseudoscalar density (times the mass) is computed as well. Contrary to naive expectation, tadpole improvement reduces q* by only a small amount for the operators we consider. We also discuss the use of a nonperturbative coupling to calculate the perturbative scale.
We study a concrete lattice regularization of a U(1) chiral gauge theory. We use Wilson fermions, and include a Lorentz gauge-fixing term and a gauge-boson mass counterterm. For a reduced version of the model, in which the gauge fields are constrained to the trivial orbit, we show that there are no species doublers, and that the fermion spectrum contains only the desired states in the continuum limit, namely charged left-handed (LH) fermions and neutral right-handed (RH) fermions.
Partially quenched theories are theories in which the valence- and sea-quark masses are different. In this paper we calculate the nonanalytic one-loop corrections of some physical quantities: the chiral condensate, weak decay constants, Goldstone boson masses, B_K and the K+ to pi+ pi0 decay amplitude, using partially quenched chiral perturbation theory. Our results for weak decay constants and masses agree with, and generalize, results of previous work by Sharpe. We compare B_K and the K+ decay amplitude with their real-world values in some examples. For the latter quantity, two other systematic effects that plague lattice computations, namely, finite-volume effects and unphysical values of the quark masses and pion external momenta are also considered. We find that typical one-loop corrections can be substantial.
We study the gauge-fixing approach to the construction of lattice chiral gauge theories in one-loop weak-coupling perturbation theory. We show how infrared properties of the gauge degrees of freedom determine the nature of the continuous phase transition at which we take the continuum limit. The fermion self-energy and the vacuum polarization are calculated, and confirm that, in the abelian case, this approach can be used to put chiral gauge theories on the lattice in four dimensions. We comment on the generalization to the nonabelian case.
In this talk, I address the comparison between results from lattice QCD computations and Chiral Perturbation Theory (ChPT). I briefly discuss how ChPT can be adapted to the much-used quenched approximation and what it tells us about the special role of the $η'$ in the quenched theory. I then review lattice results for some quantities (the pion mass, pion scattering lengths and the $K^+\toπ^+π^0$ matrix element) and what quenched ChPT has to say about them.
We use one-loop chiral perturbation theory (ChPT) to compare lattice results for the K+ to pi+ pi0 decay amplitude with the experimental value. Three systematic effects: quenching, finite-volume effects, and the use of unphysical values of quark masses and pion external momenta can be investigated. We find that the corrections help in explaining the discrepancy between lattice and experimental results. We also discuss the relation to B_K.
As a first step towards a nonperturbative investigation of the gauge-fixing (Rome) approach to lattice chiral gauge theories we study a U(1) model with an action that includes a local gauge-fixing term and a mass counterterm for the gauge fields. The model is studied on the trivial orbit so that only the dynamics of the longitudinal gauge degrees of freedom is taken into account. The phase diagram of this higher-derivative scalar field theory is determined, both in the mean-field approximation and numerically. The continuum limit of the model corresponds to a continuous phase transition between a ferromagnetic (FM) phase where the global U(1) symmetry is broken, and a so-called helicoidal ferromagnetic (FMD) phase with broken U(1) symmetry and a nonvanishing condensate of the vector field. The global U(1) symmetry is restored in this continuum limit. We show that our data for the magnetization in the FM and FMD phases are in good agreement with perturbation theory.