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Wolfgang Bietenholz

Publications and source records attributed to Wolfgang Bietenholz.

At least 37 records · Page 2Linked to original sources
arXiv2022

The 3d O(4) model as an effective approach to the QCD phase diagram

The QCD phase diagram is one of the most prominent outstanding puzzles within the Standard Model. Various experiments, which aim at its exploration beyond small baryon density, are operating or in preparation. From the theoretical side, this is an issue of non-perturbative QCD, and therefore of lattice simulations. However, a finite baryon density entails a technical problem (known as the ``sign problem''), which has not been overcome so far. Here we present a study of an effective theory, the O(4) non-linear sigma model. It performs spontaneous symmetry breaking with the same Lie group structure as 2-flavor QCD in the chiral limit, which strongly suggests that they belong to the same universality class. Since we are interested in high temperature, we further assume dimensional reduction to the 3d O(4) model, which implies topological sectors. As pointed out by Skyrme, Wilczek and others, its topological charge takes the rôle of the baryon number. Hence the baryon chemical potential $μ_{B}$ appears as an imaginary vacuum angle, which can be included in the lattice simulation without any sign problem. We present numerical results for the critical line in the chiral limit, and for the crossover in the presence of light quark masses. Their shapes are compatible with other predictions, but up to the value of about $μ_{B} \approx 300~{\rm MeV}$ we do not find the notorious Critical Endpoint (CEP).

hep-lat↗
arXiv2022

Semi-vortices and cluster-vorticity: new concepts in the Berezinskii-Kosterlitz-Thouless phase transition

The Berezinskii-Kosterlitz-Thouless (BKT) essential phase transition in the 2d XY model is revisited. Its mechanism is usually described by the (un)binding of vortex--anti-vortex (V--AV) pairs, which does, however, not provide a clear-cut quantitative criterion for criticality. Known sharp criteria are the divergence of the correlation length and a discontinuity of the helicity modulus. Here we propose and probe a new criterion: it is based on the concepts of semi-vortices and cluster vorticity, which are formulated in the framework of the multi-cluster algorithm that we use to simulate the 2d XY model.

hep-lat↗
arXiv2022

New insight in the 2-flavor Schwinger model based on lattice simulations

We consider the Schwinger model with two degenerate, light fermion flavors by means of lattice simulations. At finite temperature, we probe the viability of a bosonization method by Hosotani et al. Next we explore an analogue to the pion decay constant, which agrees for independent formulations based on the Gell-Mann--Oakes--Renner relation, the 2-dimensional Witten--Veneziano formula and the $δ$-regime. Finally we confront several conjectures about the chiral condensate with lattice results.

hep-lat↗
arXiv2022

The structure of cosmic strings of a $U(1)$ gauge field for the conservation of $B-L$

We consider an extension of the Standard Model, where the difference between the baryon number $B$ and the lepton number $L$ is gauged with an Abelian gauge field, in order to explain the exact conservation of $B-L$. To avoid a gauge anomaly, we add a right-handed neutrino $ν_{\rm R}$ to each fermion generation. Here it is not sterile, so the usual Majorana term is excluded by gauge invariance. We provide a mass term for $ν_{\rm R}$ by adding a non-standard 1-component Higgs field, thus arriving at a consistent extension of the Standard Model, where the conservation of $B-L$ is natural, with a modest number of additional fields. We study the possible formation of cosmic strings by solving the coupled field equations of the two Higgs fields and the non-standard U(1) gauge field. Numerical methods provide the corresponding string profiles, depending on the Higgs winding numbers, such that the appropriate boundary conditions in the string center and far from it are fulfilled.

hep-ph↗
arXiv2021

Conjecture about the QCD phase diagram

We present a phase diagram study of the O(4) model as an effective theory for 2-flavor QCD. In the chiral limit, both theories perform spontaneous symmetry breaking with isomorphic groups, which suggests that they belong to the same universality class. Since we are interested in high temperature, we further assume dimensional reduction to the 3d O(4) model, which implies topological sectors. According to Skyrme and others, the corresponding topological charge represents the baryon number. Hence the baryon chemical potential $μ_{B}$ appears as an imaginary vacuum angle, which can be included in the lattice simulations without any sign problem. We present simulation results for the critical line in the chiral limit, and for the crossover in the presence of light quark masses. The shapes of these lines are compatible with other conjectures, but up to about $μ_{B} \approx 300$ MeV we do not find a Critical Endpoint, although there are indications for it to be near-by.

hep-lat↗
arXiv2021

The Evolution of Lattice Field Theory: a Statistical Study

Researchers working in lattice field theory constitute an established community since the early 1990s, and around the same time the online open-access e-print repository arXiv was created. The fact that this field has a specific arXiv section, hep-lat, provides a unique opportunity for a statistical study of its evolution over the last three decades. We present data for the number of entries, $E$, published papers, $P$, and citations, $C$, in total and separated by nations. We compare them to 6 other arXiv sections, and to socio-economic indices of the nations involved, namely the Gross Domestic Product (GDP) and the Education Index (EI). We present rankings, which are based either on the Hirsch Index $H$, or on the linear combination $Σ= E + P + 0.05 C$. We consider both extensive and intensive national statistics, i.e. absolute and relative to the population or to the GDP.

hep-lat↗
arXiv2021

Finite temperature and delta-regime in the 2-flavor Schwinger model

The Schwinger model is often used as a testbed for conceptual and numerical approaches in lattice field theory. Still, some of its rich physical properties in anisotropic volumes have not yet been explored. For the multi-flavor finite temperature Schwinger model there is an approximate solution by Hosotani et al. based on bosonization. We perform lattice simulations and check the validity of this approximation in the case of two flavors. Next we exchange the rôle of the coordinates to enter the $δ$-regime, and measure the dependence of the residual "pion" mass on the spatial size, at zero temperature. Our results show that universal features, which were derived by Leutwyler, Hasenfratz and Niedermayer referring to quasi-spontaneous symmetry breaking in $d>2$, extend even to $d=2$. This enables the computation of the Schwinger model counterpart of the pion decay constant $F_π$. It is consistent with an earlier determination by Harada et al. who considered the divergence of the axial current in a light-cone formulation, and with analytical results that we conjecture from 2d versions of the Witten--Veneziano formula and the Gell-Mann--Oakes--Renner relation, which suggest $F_π = 1/ \sqrt{2π}$.

hep-lat↗
arXiv2021

From Ramanujan to renormalization: the art of doing away with divergences and arriving at physical results

A century ago, Srinivasa Ramanujan -- the great self-taught Indian genius of mathematics -- died, shortly after returning from Cambridge, UK, where he had collaborated with Godfrey Hardy. Ramanujan contributed numerous outstanding results to different branches of mathematics, like analysis and number theory, with a focus on special functions and series. Here we refer to apparently weird values which he assigned to two simple divergent series, $\sum_{n \geq 1} n$ and $\sum_{n \geq 1} n^{3}$. These values are sensible, however, as analytic continuations, which correspond to Riemann's $ζ$-function. Moreover, they have applications in physics: we discuss the vacuum energy of the photon field, from which one can derive the Casimir force, which has been experimentally measured. We further discuss its interpretation, which remains controversial. This is a simple way to illustrate the concept of renormalization, which is vital in quantum field theory.

physics.hist-ph↗
arXiv2020

The conceptual design of the miniBeBe detector proposed for NICA-MPD

We present the conceptual design for the miniBeBe detector proposed to be installed as a level-0 trigger for the TOF of the NICA-MPD. We discuss the design and the geometrical array of its sensitive parts, the read-out electronics as well as the mechanical support that is envisioned. We also present simulation results for p + p and Bi + Bi collisions to study its capabilities as a function of multiplicity both as a level-0 trigger for the TOF, as well as to serve as a beam-gas interaction veto and to locate the beam-beam interaction vertex.

physics.ins-det↗
arXiv2019

Meron- and Semi-Vortex-Clusters as Physical Carriers of Topological Charge and Vorticity

In O($N$) non-linear $σ$-models on the lattice, the Wolff cluster algorithm is based on rewriting the functional integral in terms of mutually independent clusters. Through improved estimators, the clusters are directly related to physical observables. In the $(N-1)$-d O($N$) model (with an appropriately constrained action) the clusters carry an integer or half-integer topological charge. Clusters with topological charge $\pm 1/2$ are denoted as merons. Similarly, in the 2-d O(2) model the clusters carry pairs of semi-vortices and semi-anti-vortices (with vorticity $\pm 1/2$) at their boundary. Using improved estimators, meron- and semi-vortex-clusters provide analytic insight into the topological features of the dynamics. We show that the histograms of the cluster-size distributions scale in the continuum limit, with a fractal dimension $D$, which suggests that the clusters are physical objects. We demonstrate this property analytically for merons and non-merons in the 1-d O(2) model (where $D=1$), and numerically for the 2-d O(2), 2-d O(3), and 3-d O(4) model, for which we observe fractal dimensions $D < d$. In the vicinity of a critical point, a scaling law relates $D$ to a combination of critical exponents. In the 2-d O(3) model, meron- and multi-meron-clusters are responsible for a logarithmic ultraviolet divergence of the topological susceptibility.

hep-lat↗
arXiv2019

A beam-beam monitoring detector for the MPD experiment at NICA

The Multi-Purpose Detector (MPD) is to be installed at the Nuclotron Ion Collider fAcility (NICA) of the Joint Institute for Nuclear Research (JINR). Its main goal is to study the phase diagram of the strongly interacting matter produced in heavy-ion collisions. These studies, while providing insight into the physics of heavy-ion collisions, are relevant for improving our understanding of the evolution of the early Universe and the formation of neutron stars. In order to extend the MPD trigger capabilities, we propose to include a high granularity beam-beam monitoring detector (BE-BE) to provide a level-0 trigger signal with an expected time resolution of 30 ps. This new detector will improve the determination of the reaction plane by the MPD experiment, a key measurement for flow studies that provides physics insight into the early stages of the reaction. In this work, we use simulated Au+Au collisions at NICA energies to show the potential of such a detector to determine the event plane resolution, providing further redundancy to the detectors originally considered for this purpose namely, the Fast Forward Detector (FFD) and the Hadron Calorimeter (HCAL). We also show our results for the time resolution studies of two prototype cells carried out at the T10 beam line at the CERN PS complex.

physics.ins-det↗
arXiv2019

Time resolution studies for scintillating plastics coupled to silicon photo-multipliers

We present results for time resolution studies performed on three different scintillating plastics and two silicon photo-multipliers. These studies are intended to determine whether scintillating plastic/silicon photo-multiplier systems can be employed to provide a fast trigger signal for NICA's Multi Purpose Detector (MPD). Our results show that such a system made of cells with transverse dimensions of order of a few cm, coupled to silicon photo-multipliers, provides a time resolution of about 50 ps, which can be even further improved to attain the MPD trigger requirements of 20 ps.

physics.ins-det↗
arXiv2018

Topological Susceptibility of the 2d O(3) Model under Gradient Flow

The 2d O(3) model is widely used as a toy model for ferromagnetism and for Quantum Chromodynamics. With the latter it shares --- among other basic aspects --- the property that the continuum functional integral splits into topological sectors. Topology can also be defined in its lattice regularised version, but semi-classical arguments suggest that the topological susceptibility $χ_{\rm t}$ does not scale towards a finite continuum limit. Previous numerical studies confirmed that the quantity $χ_{\rm t}\, ξ^{2}$ diverges at large correlation length $ξ$. Here we investigate the question whether or not this divergence persists when the configurations are smoothened by the Gradient Flow (GF). The GF destroys part of the topological windings; on fine lattices this strongly reduces $χ_{\rm t}$. However, even when the flow time is so long that the GF impact range --- or smoothing radius --- attains $ξ/2$, we do still not observe evidence of continuum scaling.

hep-lat↗
arXiv2018

Theoretical High Energy Physics in Latin America from 1990 to 2012: a Statistical Study

We present a statistical overview of the publications in theoretical high energy physics (HEP), which emerged in Latin America (LA) in the period from 1990 to 2012. Our study captures the eight Latin American nations, which are dominant in this field of research: Brazil, Mexico, Argentina, Chile, Colombia, Venezuela, Uruguay and Cuba. As an intercontinental benchmark, we compare them with India, Canada, South Korea, Belgium and South Africa. We consider the productivity of research papers in specialized high-impact journals, and the corresponding numbers of citations. The goal is to document the efforts in LA to catch up with the most wealthy countries, in a field of research without direct practical benefits. The restriction to theoretical HEP excludes large international collaborations, which enables a fair evaluation of national achievements. We further investigate how these records are correlated with three socio-economic indices: the Gross Domestic Product (GDP), the Human Development Index (HDI) and the Education Index (EI). Despite some progress, there remains a backlog of LA compared to the dominant countries, which cannot be explained solely by economic deficiency. In general, a detailed correlation between the socio-economic and scientific evolution is not obvious.

physics.soc-ph↗
arXiv2017

Topological Susceptibility under Gradient Flow

We study the impact of the Gradient Flow on the topology in various models of lattice field theory. The topological susceptibility $χ_{\rm t}$ is measured directly, and by the slab method, which is based on the topological content of sub-volumes ("slabs") and estimates $χ_{\rm t}$ even when the system remains trapped in a fixed topological sector. The results obtained by both methods are essentially consistent, but the impact of the Gradient Flow on the characteristic quantity of the slab method seems to be different in 2-flavour QCD and in the 2d O(3) model. In the latter model, we further address the question whether or not the Gradient Flow leads to a finite continuum limit of the topological susceptibility (rescaled by the correlation length squared, $ξ^{2}$). This ongoing study is based on direct measurements of $χ_{\rm t}$ in $L \times L$ lattices, at $L/ξ\simeq 6$.

hep-lat↗
arXiv2017

Topology in the 2d Heisenberg Model under Gradient Flow

The 2d Heisenberg model --- or 2d O(3) model --- is popular in condensed matter physics, and in particle physics as a toy model for QCD. Along with other analogies, it shares with 4d Yang-Mills theories, and with QCD, the property that the configurations are divided in topological sectors. In the lattice regularisation the topological charge $Q$ can still be defined such that $Q \in \mathbb{Z}$. It has generally been observed, however, that the topological susceptibility $χ_{\rm t} = \langle Q^2 \rangle / V$ does not scale properly in the continuum limit, i.e. that the quantity $χ_{\rm t} ξ^2$ diverges for $ξ\to \infty$ (where $ξ$ is the correlation length in lattice units). Here we address the question whether or not this divergence persists after the application of the Gradient Flow.

hep-lat↗
arXiv2017

Berezinskii-Kosterlitz-Thouless Transition and the Haldane Conjecture: Highlights of the Physics Nobel Prize 2016

The 2016 Physics Nobel Prize honors a variety of discoveries related to topological phases and phase transitions. Here we sketch two exciting facets: the groundbreaking works by John Kosterlitz and David Thouless on phase transitions of infinite order, and by Duncan Haldane on the energy gaps in quantum spin chains. These insights came as surprises in the 1970s and 1980s, respectively, and they have both initiated new fields of research in theoretical and experimental physics.

physics.pop-ph↗