arXiv subjects

Peter Weisz

Publications and source records attributed to Peter Weisz.

At least 37 records · Page 2Linked to original sources

arXiv2009

Logarithmic corrections to O(a^2) lattice artifacts

We compute logarithmic corrections to the O(a^2) lattice artifacts for a class of lattice actions for the non-linear O(n) sigma-model in two dimensions. The generic leading artifacts are of the form $a^2[\ln(a^2)]^{(n/(n-2))}$. We also compute the next-to-leading corrections and show that for the case n=3 the resulting expressions describe well the lattice artifacts in the step scaling function, which are in a large range of the cutoff apparently of the form O(a). An analogous computation should, if technically possible, accompany any precision measurements in lattice QCD.

hep-lat↗

arXiv2008

Energy dependence of nucleon-nucleon potentials

We investigate the energy dependence of potentials defined through the Bethe-Salpeter wave functions. We analytically evaluate such a potential in the Ising field theory in 2 dimensions and show that its energy dependence is weak at low energy. We then numerically calculate the nucleon-nucleon potential at non-zero energy using quenched QCD with anti-periodic boundary condition. In this case we also observe that the potentials are almost identical at $E\simeq 0$ and $E\simeq 50$ MeV, where $E$ is the center of mass kinetic energy.

hep-lat↗

arXiv2008

Bethe--Salpeter wave functions in integrable models

We investigate some properties of Bethe--Salpeter wave functions in integrable models. In particular we illustrate the application of the operator product expansion in determining the short distance behavior. The energy dependence of the potentials obtained from such wave functions is studied, and further we discuss the (limited) phenomenological significance of zero--energy potentials.

hep-th↗

arXiv2007

Perturbative and nonperturbative correspondences between compact and non-compact sigma-models

Compact (ferro- and antiferromagnetic) sigma-models and noncompact (hyperbolic) sigma-models are compared in a lattice formulation in dimensions $d \geq 2$. While the ferro- and antiferromagnetic models are essentially equivalent, the qualitative difference to the noncompact models is highlighted. The perturbative and the large $N$ expansions are studied in both types of models and are argued to be asymptotic expansions on a finite lattice. An exact correspondence between the expansion coefficients of the compact and the noncompact models is established, for both expansions, valid to all orders on a finite lattice. The perturbative one involves flipping the sign of the coupling and remains valid in the termwise infinite volume limit. The large $N$ correspondence concerns the functional dependence on the free propagator and holds directly only in finite volume.

hep-th↗

arXiv2004

The 4d one component lattice $ϕ^4$ model in the broken phase revisited

Measurements of various physical quantities in the symmetry broken phase of the one component lattice $ϕ^4_4$ with standard action, are shown to be consistent with the critical behavior obtained by renormalization group analyses. This is in contrast to recent conclusions by another group, who further claim that the unconventional scaling behavior they observe, when extended to the complete Higgs sector of the Standard Model, would alter the conventional triviality bound on the mass of the Higgs.

hep-lat↗

arXiv2004

Structure functions of the 2d O(n) non-linear sigma models

We investigate structure functions in the 2-dimensional (asymptotically free) non-linear O(n) sigma-models using the non-perturbative S-matrix bootstrap program. In particular the exact small (Bjorken) x behavior is derived. Structure functions in the special case of the n=3 model are accurately computed over the whole x range for $-q^2/M^2<10^5$, and some moments are compared with results from renormalized perturbation theory. Some results concerning the structure functions in the 1/n approximation are also presented.

hep-th↗

arXiv2004

String excitation energies in SU(N) gauge theories beyond the free-string approximation

In the presence of a static quark--antiquark pair, the spectrum of the low-lying states in SU($N$) gauge theories is discrete and likely to be described, at large quark separations $r$, by an effective string theory. The expansion of the excitation energies in powers of $1/r$, which derives from the latter, involves an increasing number of unknown couplings that characterize the string self-interactions. Using open--closed string duality, we show that the possible values of the couplings are constrained by a set of algebraic relations. In particular, the corrections of order $1/r^2$ must vanish, while the $1/r^3$ terms (which we work out for the few lowest levels) depend on a single adjustable coupling only.

hep-th↗

arXiv2004

Structure functions of 2d integrable asymptotically free models

We investigate structure functions in the 2--dimensional (asymptotically free) non--linear O$(n) σ$--models using the non--perturbative S--matrix bootstrap program. In particular the {\it exact small (Bjorken) $x$ behavior is exhibited}; the structure is rather universal and is probably the same in a wide class of (integrable) asymptotically free models. Structurally similar universal formulae may also hold for the small $x$ behavior of QCD in 4--dimensions. Structure functions in the special case of the $n=3$ model are accurately computed over the whole $x$ range for $-q^2/M^2<10^5$, and some moments are compared with results from renormalized perturbation theory. Some remarks concerning the structure functions in the $1/n$ approximation are also made.

hep-th↗

arXiv2003

Lattice QCD in the epsilon-regime and random matrix theory

In the epsilon-regime of QCD the main features of the spectrum of the low-lying eigenvalues of the (euclidean) Dirac operator are expected to be described by a certain universality class of random matrix models. In particular, the latter predict the joint statistical distribution of the individual eigenvalues in any topological sector of the theory. We compare some of these predictions with high-precision numerical data obtained from lattice QCD for a range of lattice spacings and volumes. While no complete matching is observed, the results agree with theoretical expectations at volumes larger than about 5 fm^4.

hep-lat↗

arXiv2002

Quark confinement and the bosonic string

Using a new type of simulation algorithm for the standard SU(3) lattice gauge theory that yields results with unprecedented precision, we confirm the presence of a $γ/r$ correction to the static quark potential at large distances $r$, with a coefficient $γ$ as predicted by the bosonic string theory. In both three and four dimensions, the transition from perturbative to string behaviour is evident from the data and takes place at surprisingly small distances.

hep-lat↗

arXiv2001

Locality and exponential error reduction in numerical lattice gauge theory

In non-abelian gauge theories without matter fields, expectation values of large Wilson loops and loop correlation functions are difficult to compute through numerical simulation, because the signal-to-noise ratio is very rapidly decaying for increasing loop sizes. Using a multilevel scheme that exploits the locality of the theory, we show that the statistical errors in such calculations can be exponentially reduced. We explicitly demonstrate this in the SU(3) theory, for the case of the Polyakov loop correlation function, where the efficiency of the simulation is improved by many orders of magnitude when the area bounded by the loops exceeds 1 fm^2.

hep-lat↗

arXiv2001

First results on the running coupling in QCD with two massless flavours

We report on the non-perturbative computation of the running coupling of two-flavour QCD in the Schr"odinger functional scheme. The corresponding Lambda-parameter, which describes the coupling strength at high energy, is related to a low energy scale which still remains to be connected to a hadronic ``experimentally'' observable quantity. We find the non-perturbative evolution of the coupling indispensable to avoid untolerable errors in the estimated Lambda-parameter.

hep-lat↗

arXiv2001

Two Loop Computation of the Schroedinger Functional in Lattice QCD

We compute the Schroedinger functional (SF) for the case of lattice QCD with Wilson fermions (with and without SW improvement) at two-loop order in lattice perturbation theory. This allows us to extract the three-loop beta-function in the SF-scheme. These results are required to compute the running coupling, the Lambda-parameter and quark masses by finite size techniques with negligible systematic errors. In addition our results enable the implementation of two-loop O(a) improvement in SF-simulations.

hep-lat↗

arXiv2001

O(a) improved twisted mass lattice QCD

Lattice QCD with Wilson quarks and a chirally twisted mass term (tmQCD) has been introduced in refs. [1,2]. We here apply Symanzik's improvement programme to this theory and list the counterterms which arise at first order in the lattice spacing a. Based on the generalised transfer matrix, we define the tmQCD Schrodinger functional and use it to derive renormalized on-shell correlation functions. By studying their continuum approach in perturbation theory we then determine the new O(a) counterterms of the action and of a few quark bilinear operators to one-loop order.

hep-lat↗

arXiv2001

Lattice QCD with a chirally twisted mass term

Lattice QCD with Wilson quarks and a chirally twisted mass term represents a promising alternative regularization of QCD, which does not suffer from unphysical fermion zero modes. We show how the correlation functions of the renormalized theory are related to the theory with a standard parameterization of the mass term. In particular we discuss the conditions under which these relations take the same form as obtained from naive continuum considerations. We discuss in detail some applications and comment on potential benefits and problems of this framework.

hep-lat↗

arXiv1999

A local formulation of lattice QCD without unphysical fermion zero modes

The problem of unphysical zero modes in lattice QCD with Wilson fermions can be solved in a clean way by including a mass term proportional to $i \psibar γ_5 τ^3 ψ$ in the standard lattice theory with Nf=2 mass degenerate Wilson quarks. We argue that up to cutoff effects, this lattice theory is equivalent to standard lattice QCD, for suitable choices of the mass parameters and with a natural re-interpretation of observables. On-shell O(a) improvement can be implemented in a straightforward way.

hep-lat↗

arXiv1999

Comparison of the O(3) Bootstrap $σ$-Model with the Lattice Regularization at Low Energies

The renormalized coupling $\gr$ defined through the connected 4-point function at zero external momentum in the non-linear O(3) sigma-model in two dimensions, is computed in the continuum form factor bootstrap approach with estimated error $\sim 0.3%$. New high precision data are presented for $\gr$ in the lattice regularized theory with standard action for nearly thermodynamic lattices $L/ξ\sim 7$ and correlation lengths $ξ$ up to $\sim 122$ and with the fixed point action for correlation lengths up to $\sim 12$. The agreement between the form factor and lattice results is within $\sim 1%$. We also recompute the phase shifts at low energy by measuring the two-particle energies at finite volume, a task which was previously performed by Lüscher and Wolff using the standard action, but this time using the fixed point action. Excellent agreement with the Zamolodchikov S-matrix is found.

hep-lat↗

arXiv1998

The running quark mass in the SF scheme and its two-loop anomalous dimension

The non-perturbatively defined running quark mass introduced by the ALPHA collaboration is based on the PCAC relation between correlation functions derived from the Schrödinger functional (SF). In order to complete its definition it remains to specify a number of parameters, including the ratio of time to spatial extent, $T/L$, and the angle $θ$ which appears in the spatial boundary conditions for the quark fields. We investigate the running mass in perturbation theory and propose a choice of parameters which attains two desired properties: firstly the two-loop anomalous dimension $\d1SF$ is reasonably small. This is needed in order to ease matching with the non-perturbative computations and to achieve a precise determination of the renormalization group invariant quark mass. Secondly, to one-loop order of perturbation theory, cut-off effects in the step-scaling function are small in O($a$) improved lattice QCD.

hep-lat↗