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P. Weisz

Publications and source records attributed to P. Weisz.

At least 19 recordsLinked to original sources
arXiv2019

On the rotator Hamiltonian for the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime

We investigate some properties of the standard rotator approximation of the SU$(N)\times\,$SU$(N)$ sigma-model in the delta-regime. In particular we show that the isospin susceptibility calculated in this framework agrees with that computed by chiral perturbation theory up to next-to-next to leading order in the limit $\ell=L_t/L\to\infty\,.$ The difference between the results involves terms vanishing like $1/\ell\,,$ plus terms vanishing exponentially with $\ell\,$. As we have previously shown for the O($n$) model, this deviation can be described by a correction to the rotator spectrum proportional to the square of the quadratic Casimir invariant. Here we confront this expectation with analytic nonperturbative results on the spectrum in 2 dimensions for $N=3\,.$

hep-th↗
arXiv2013

Short Distance Repulsion Among Baryons

We review recent investigations on the short distance behaviors of potentials among baryons, which are formulated through the Nambu-Bethe-Salpeter (NBS) wave function. After explaining the method to define the potentials, we analyze the short distance behavior of the NBS wave functions and the corresponding potentials by combining the operator product expansion and a renormalization group analysis in the perturbation theory of QCD. These analytic results are compared with numerical results obtained in lattice QCD simulations.

hep-lat↗
arXiv2012

Drastic Reduction of Cutoff Effects in 2-d Lattice O(N) Models

We investigate the cutoff effects in 2-d lattice O(N) models for a variety of lattice actions, and we identify a class of very simple actions for which the lattice artifacts are extremely small. One action agrees with the standard action, except that it constrains neighboring spins to a maximal relative angle delta. We fix delta by demanding that a particular value of the step scaling function agrees with its continuum result already on a rather coarse lattice. Remarkably, the cutoff effects of the entire step scaling function are then reduced to the per mille level. This also applies to the theta-vacuum effects of the step scaling function in the 2-d O(3) model. The cutoff effects of other physical observables including the renormalized coupling and the mass in the isotensor channel are also reduced drastically. Another choice, the mixed action, which combines the standard quadratic with an appropriately tuned large quartic term, also has extremely small cutoff effects. The size of cutoff effects is also investigated analytically in 1-d and at N = infinity in 2-d.

hep-lat↗
arXiv2007

Noncompact sigma-models: Large N expansion and thermodynamic limit

Noncompact SO(1,N) sigma-models are studied in terms of their large N expansion in a lattice formulation in dimensions d \geq 2. Explicit results for the spin and current two-point functions as well as for the Binder cumulant are presented to next to leading order on a finite lattice. The dynamically generated gap is negative and serves as a coupling-dependent infrared regulator which vanishes in the limit of infinite lattice size. The cancellation of infrared divergences in invariant correlation functions in this limit is nontrivial and is in d=2 demonstrated by explicit computation for the above quantities. For the Binder cumulant the thermodynamic limit is finite and is given by 2/(N+1) in the order considered. Monte Carlo simulations suggest that the remainder is small or zero. The potential implications for ``criticality'' and ``triviality'' of the theories in the SO(1,N) invariant sector are discussed.

hep-th↗
arXiv2007

Construction and clustering properties of the 2-d non-linear sigma-model form factors: O(3), O(4), large n examples

Multi-particle form factors of local operators in integrable models in two dimensions seem to have the property that they factorize when one subset of the particles in the external states are boosted by a large rapidity with respect to the others. This remarkable property, which goes under the name of form factor clustering, was first observed by Smirnov in the O(3) non-linear sigma-model and has subsequently found useful applications in integrable models without internal symmetry structure. In this paper we conjecture the nature of form factor clustering for the general O(n) sigma-model and make some tests in leading orders of the 1/n expansion and for the special cases n=3,4.

hep-th↗
arXiv2006

Does the XY Model have an integrable continuum limit?

The quantum field theory describing the massive O(2) nonlinear sigma-model is investigated through two non-perturbative constructions: The form factor bootstrap based on integrability and the lattice formulation as the XY model. The S-matrix, the spin and current two-point functions, as well as the 4-point coupling are computed and critically compared in both constructions. On the bootstrap side a new parafermionic super selection sector is found; in the lattice theory a recent prediction for the (logarithmic) decay of lattice artifacts is probed.

hep-lat↗
arXiv2006

Repairing Stevenson's step in the 4d Ising model

In a recent paper Stevenson claimed that analysis of the data on the wave function renormalization constant near the critical point of the 4d Ising model is not consistent with analytical expectations. Here we present data with improved statistics and show that the results are indeed consistent with conventional wisdom once one takes into account the uncertainty of lattice artifacts in the analytical computations.

hep-lat↗
arXiv2004

A strategy to study the role of the charm quark in explaining the Delta{I}=1/2 rule

We present a strategy designed to separate several possible origins of the well-known enhancement of the Delta{I}=1/2 amplitude in non-leptonic kaon decays. In particular, we seek to disentangle the contribution of physics at the typical QCD scale (soft-gluon exchange) from the effects at the scale of the charm quark mass. This is achieved by considering QCD with an unphysically light charm quark, so that the theory possesses an approximate SU(4)_L x SU(4)_R chiral symmetry. By computing the relevant operator matrix elements and monitoring their values as the charm quark mass departs from the SU(4)-symmetric situation, the role of the charm quark can be assessed. We study the influence of the charm quark mass in Chiral Perturbation Theory. First results from lattice simulations in the SU(4)-symmetric limit are also discussed.

hep-lat↗
arXiv2004

Correlation functions at small quark masses with overlap fermions

We report on recent work on the determination of low-energy constants describing Delta{S}=1 weak transitions, in order to investigate the origins of the Delta{I}=1/2 rule. We focus on numerical techniques designed to enhance the statistical signal in three-point correlation functions computed with overlap fermions near the chiral limit.

hep-lat↗
arXiv2004

Low-energy couplings of QCD from current correlators near the chiral limit

We investigate a new numerical procedure to compute fermionic correlation functions at very small quark masses. Large statistical fluctuations, due to the presence of local ``bumps'' in the wave functions associated with the low-lying eigenmodes of the Dirac operator, are reduced by an exact low-mode averaging. To demonstrate the feasibility of the technique, we compute the two-point correlator of the left-handed vector current with Neuberger fermions in the quenched approximation, for lattices with a linear extent of L~1.5 fm, a lattice spacing a~0.09 fm, and quark masses down to the epsilon-regime. By matching the results with the corresponding (quenched) chiral perturbation theory expressions, an estimate of (quenched) low-energy constants can be obtained. We find agreement between the quenched values of F extrapolated from the p-regime and extracted in the epsilon-regime.

hep-lat↗
arXiv2004

Low-energy couplings of QCD from topological zero-mode wave functions

By matching 1/m^2 divergences in finite-volume two-point correlation functions of the scalar or pseudoscalar densities with those obtained in chiral perturbation theory, we derive a relation between the Dirac operator zero-mode eigenfunctions at fixed non-trivial topology and the low-energy constants of QCD. We investigate the feasibility of using this relation to extract the pion decay constant, by computing the zero-mode correlation functions on the lattice in the quenched approximation and comparing them with the corresponding expressions in quenched chiral perturbation theory.

hep-lat↗
arXiv2003

Test of asymptotic freedom and scaling hypothesis in the 2d O(3) sigma model

The 7--particle form factors of the fundamental spin field of the O(3) nonlinear $σ$--model are constructed. We calculate the corresponding contribution to the spin--spin correlation function, and compare with predictions from the spectral density scaling hypothesis. The resulting approximation to the spin--spin correlation function agrees well with that computed in renormalized (asymptotically free) perturbation theory in the expected energy range. Further we observe simple lower and upper bounds for the sum of the absolute square of the form factors which may be of use for analytic estimates.

hep-th↗
arXiv2001

Two loop lattice expansion of the Schroedinger functional coupling in improved QCD

The contributions of the improved fermion action of Sheikholeslami and Wohlert to the two loop coefficient of the expansion of the Schroedinger functional coupling in terms of the lattice coupling are calculated for the gauge group SU(3). These coefficients are required for the second order relation of lattice data to the MSbar-coupling. By taking into account all improvement coefficients we are able to improve the Schroedinger functional to two loop order.

hep-lat↗
arXiv2000

The Intrinsic Coupling in Integrable Quantum Field Theories

The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and to high accuracy from the form factors of an (integrable) QFT. The technique is illustrated and tested with the Ising model, the XY-model and the O(3) nonlinear sigma-model. The results are compared to those from high precision lattice simulations.

hep-th↗
arXiv1998

Two-Loop Computation of the Schroedinger Functional in Pure SU(3) Lattice Gauge Theory

We compute the Schroedinger functional (SF) for the case of pure SU(3) gauge theory 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, we can now implement two-loop O(a) improvement in simulations and extend and study series in alternative ("tadpole-improved") bare couplings.

hep-lat↗
arXiv1997

Non-perturbative quark mass renormalization

We show that the renormalization factor relating the renormalization group invariant quark masses to the bare quark masses computed in lattice QCD can be determined non-perturbatively. The calculation is based on an extension of a finite-size technique previously employed to compute the running coupling in quenched QCD. As a by-product we obtain the $Λ$--parameter in this theory with completely controlled errors.

hep-lat↗