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Bernd A. Berg

Publications and source records attributed to Bernd A. Berg.

At least 19 recordsLinked to original sources
arXiv2019

Topological charge and cooling scales in pure SU(2) lattice gauge theory

Using Monte Carlo simulations with overrelaxation, we have equilibrated lattices up to $β=2.928$, size $60^4$, for pure SU(2) lattice gauge theory with the Wilson action. We calculate topological charges with the standard cooling method and find that they become more reliable with increasing $β$ values and lattice sizes. Continuum limit estimates of the topological susceptibility $χ$ are obtained of which we favor $χ^{1/4}/T_c=0.643\,(12)$, where $T_c$ is the SU(2) deconfinement temperature. Differences between cooling length scales in different topological sectors turn out to be too small to be detectable within our statistical errors.

hep-lat↗
arXiv2017

Estimates of Scaling Violations for Pure SU(2) LGT

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining transition, Luescher's gradient flow, and the cooling flow to set the scale. Of those, the cooling flow turns out to be computationally most efficient. We explore systematic errors due to use of three different energy observables and two distinct reference values for the flow time, the latter obtained by matching initial scaling behavior of some energy observables to that of the deconfining transition. Another important source of systematic errors are distinct fitting forms for the approach to the continuum limit. Besides relying in the conventional way on ratios of masses, we elaborate on a form introduced by Allton, which incorporates asymptotic scaling behavior. Ultimately we find that, though still small, our systematic errors are considerably larger than our statistical errors. ~

hep-lat↗
arXiv2016

Deconfinement, gradient and cooling scales for pure SU(2) lattice gauge theory

We investigate the approach of pure SU(2) lattice gauge theory with the Wilson action to its continuum limit using the deconfining phase transition, the gradient flow and the cooling flow to set the scale. For the gradient and cooling scales we explore three different energy observables and two distinct reference values for the flow time. When the aim is to follow scaling towards the continuum limit, one gains at least a factor of 100 in computational efficiency by relying on the gradient instead of the deconfinement scale. Using cooling instead of the gradient flow one gains another factor of at least 34 in computational efficiency on the gradient flow part without any significant loss in the accuracy of scale setting. Concerning our observables, the message is to keep it simple. The Wilson action itself performs as well as or even better than the other two observables explored. Two distinct fitting forms for scaling are compared of which one connects to asymptotic scaling. Differences of the obtained estimates show that systematic errors of length ratios, though only about 1%, can be considerably larger than statistical errors of the same observables.

hep-lat↗
arXiv2016

Least square fitting with one parameter less

It is shown that whenever the multiplicative normalization of a fitting function is not known, least square fitting by $χ^2$ minimization can be performed with one parameter less than usual by converting the normalization parameter into a function of the remaining parameters and the data.

physics.data-an↗
arXiv2015

Asymptotic scaling and continuum limit of pure SU(3) lattice gauge theory

Recently the Yang-Mills gradient flow of pure SU(3) lattice gauge theory has been calculated in the range from $β=6/g_0^2=6.3$ to~7.5 (Asakawa et al.), where $g_0^2$ is the bare coupling constant of the SU(3) Wilson action. Estimates of the deconfining phase transition are available from $β=5.7$ to~6.8 (Francis et al.). Here it is shown that the entire range from 5.7 to 7.5 is well described by a power series of the lattice spacing $a$ times the lambda lattice mass scale $Λ_L$, using asymptotic scaling in the 2-loop and 3-loop approximations for $aΛ_L$. In both cases identical ratios for gradient flows versus deconfinement observables are obtained. Differences in the normalization constants with respect to $Λ_L$ give a handle on their systematic errors.

hep-lat↗
arXiv2015

Status of the Lambda Lattice Scale for the SU(3) Wilson gauge action

With the emergence of the Yang-Mills gradient flow technique there is renewed interest in the issue of scale setting in lattice gauge theory. Here I compare for the SU(3) Wilson gauge action non-perturbative scale functions of Edwards, Heller and Klassen (EHK), Necco and Sommer (NS), both relying on Sommer's method using the quark potential, and the scale function derived by Bazavov, Berg and Velytsky (BBV) from a deconfining phase transition investigation by the Bielefeld group. It turns out that the scale functions are based on mutually inconsistent data, though the BBV scale function is consistent with the EHK data when their low $β$ ($β=5.6$) data point is removed. Besides, only the BBV scale function is consistent with three data points calculated from the gradient flow by Lüscher. In the range for which data exist the discrepancies between the scale functions are only up to $\pm 2$\% of their values, but clearly visible within the statistical accuracy.

hep-lat↗
arXiv2014

Detection of a small shift in a broad distribution

Statistical methods for the extraction of a small shift in broad data distributions are examined by means of Monte Carlo simulations. This work was originally motivated by the CERN neutrino beam to Gran Sasso (CNGS) experiment for which the OPERA detector collaboration reported a time shift in a broad distribution with an accuracy of $\pm 7.8\,$ns, while the fluctuation of the average time turns with $\pm 23.8\,$ns out to be much larger. Although the physical result of a big shift has been withdrawn, statistical methods that make an identification in a broad distribution with such a small error possible remain of interest.

hep-ph↗
arXiv2013

SU(3) deconfining phase transition with finite volume corrections due to a confined exterior

Using the geometry of a double-layered torus we investigate the deconfining phase transition of pure SU(3) lattice gauge theory by Markov chain Monte Carlo simulations. In one layer, called "outside", the temperature is set below the deconfining temperature and in the other, called "inside", it is iterated to a pseudo-transition temperature. Lattice sizes are chosen in a range suggested by the physical volumes achieved in relativistic heavy ion collisions and both temperatures are kept close enough to stay in the SU(3) scaling region. Properties of the transition are studied as function of the volume for three outside temperatures. When compared with infinite volume extrapolations, small volume corrections of the deconfining temperature and width become competitive with those found by including quarks. Effective finite size scaling exponents of the specific and Polyakov loop susceptibilities are also calculated.

hep-lat↗
arXiv2012

Fisher zeros and conformality in lattice models

Fisher zeros are the zeros of the partition function in the complex beta=2N_c/g^2 plane. When they pinch the real axis, finite size scaling allows one to distinguish between first and second order transition and to estimate exponents. On the other hand, a gap signals confinement and the method can be used to explore the boundary of the conformal window. We present recent numerical results for 2D O(N) sigma models, 4D U(1) and SU(2) pure gauge and SU(3) gauge theory with N_f=4 and 12 flavors. We discuss attempts to understand some of these results using analytical methods. We discuss the 2-lattice matching and qualitative aspects of the renormalization group (RG) flows in the Migdal-Kadanoff approximation, in particular how RG flows starting at large beta seem to move around regions where bulk transitions occur. We consider the effects of the boundary conditions on the nonperturbative part of the average energy and on the Fisher zeros for the 1D O(2) model.

hep-lat↗
arXiv2012

On the energy momentum dispersion in the lattice regularization

For a free scalar boson field and for U(1) gauge theory finite volume (infrared) and other corrections to the energy-momentum dispersion in the lattice regularization are investigated calculating energy eigenstates from the fall off behavior of two-point correlation functions. For small lattices the squared dispersion energy defined by $E_{\rm dis}^2=E_{\vec{k}}^2-E_0^2-4\sum_{i=1}^{d-1}\sin(k_i/2)^2$ is in both cases negative ($d$ is the Euclidean space-time dimension and $E_{\vec{k}}$ the energy of momentum $\vec{k}$ eigenstates). Observation of $E_{\rm dis}^2=0$ has been an accepted method to demonstrate the existence of a massless photon ($E_0=0$) in 4D lattice gauge theory, which we supplement here by a study of its finite size corrections. A surprise from the lattice regularization of the free field is that infrared corrections do {\it not} eliminate a difference between the groundstate energy $E_0$ and the mass parameter $M$ of the free scalar lattice action. Instead, the relation $E_0=\cosh^{-1} (1+M^2/2)$ is derived independently of the spatial lattice size.

hep-lat↗
arXiv2012

Vector boson mass generation without new fields

Previously a model of only vector fields with a local U(2) symmetry was introduced for which one finds a massless U(1) photon and a massive SU(2) vector boson in the lattice regularization. Here it is shown that quantization of its classical continuum action leads to perturbative renormalization difficulties. But, non-perturbative Monte Carlo calculations favor the existence of a quantum continuum limit.

hep-lat↗
arXiv2011

Two exercises about neutrino departure times at CERN

Two simple exercises are solved, which educators can use to awake interest of their students in subtleties of the CERN Neutrino beam to Grand Sasso (CNGS) experiment. The first one is about the statistical error of the average departure time of neutrinos from CERN. The second one about a hypothetical bias in the departure times.

physics.pop-ph↗
arXiv2011

Finite Volume Corrections to the SU(3) Deconfining Temperature due to a Confined Exterior

Deconfined regions in relativistic heavy ion collisions are limited to small volumes surrounded by a confined exterior. Using the geometry of a double layered torus, we keep an outside temperature slightly lower than the inside temperature, so that both regions are in the SU(3) scaling region. Deconfined volume sizes are chosen to be in a range typical for such volumes created at the BNL RHIC. Even with small temperature differences a dependence of the (pseudo) deconfining temperature on a colder surrounding temperature is clearly visible. For temporal lattice sizes Ntau=4, 6 and 8 we find consistency with SU(3) scaling behavior for the measured transition temperature signals.

hep-lat↗
arXiv2010

Deconfined SU(2) vector fields at zero temperature

Markov chain Monte Carlo simulations of pure SU(2)xU(1) lattice gauge theory show a (zero temperature) deconfining phase transition in the SU(2) gluon sector when a term is added to the SU(2) and U(1) Wilson actions, which requires joint U(2) gauge transformations of the SU(2) and U(1) vector fields. Investigations of this deconfined phase are of interest as it could provide an alternative to the Higgs mechanism.

hep-lat↗
arXiv2009

Lagrangian with U(1)-SU(2) mixing

Principal axis transformation is performed for a Lagrangian with a U(1)-SU(2) mixing term, that can cause a SU(2) deconfining transition.

hep-th↗