The nonperturbative functional renormalization group and its applications

The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for viable ultraviolet completions in fundamental physics. It provides us with a natural framework to study theoretical models where degrees of freedom are correlated over long distances and that may exhibit very distinct behavior on different energy scales. The nonperturbative functional renormalization-group (FRG) approach is a modern implementation of Wilson's RG, which allows one to set up nonperturbative approximation schemes that go beyond the standard perturbative RG approaches. The FRG is based on an exact functional flow equation of a coarse-grained effective action (or Gibbs free energy in the language of statistical mechanics). We review the main approximation schemes that are commonly used to solve this flow equation and discuss applications in equilibrium and out-of-equilibrium statistical physics, quantum many-particle systems, high-energy physics and quantum gravity.

Insights into the emergence of mass from studies of pion and kaon structure

There are two mass generating mechanisms in the standard model of particle physics (SM) One is related to the Higgs boson and fairly well understood The other is embedded in quantum chromodynamics (QCD), the SM's strong interaction piece; and although responsible for emergence of the roughly 1 GeV mass scale that characterises the proton and hence all observable matter, the source and impacts of this emergent hadronic mass (EHM) remain puzzling As bound states seeded by a valence-quark and -antiquark, pseudoscalar mesons present a simpler problem in quantum field theory than that associated with the nucleon Consequently, there is a large array of robust predictions for pion and kaon properties whose empirical validation will provide a clear window onto many effects of both mass generating mechanisms and the constructive interference between them This has now become significant because new-era experimental facilities, in operation, construction, or planning, are capable of conducting such tests and thereby contributing greatly to resolving the puzzles of EHM These aspects of experiment, phenomenology, and theory, along with contemporary successes and challenges, are sketched herein, simultaneously highlighting the potential gains that can accrue from a coherent effort aimed at finally reaching an understanding of the character and structure of Nature's Nambu-Goldstone modes

Insights into the Emergence of Mass from Studies of Pion and Kaon Structure

We study the possible occurrence of the hadron-quark phase transition (PT) during the merging of neutron star binaries by hydrodynamical simulations employing a set of temperature dependent hybrid equations of state (EoSs). Following previous work we describe an unambiguous and measurable signature of deconfined quark matter in the gravitational-wave (GW) signal of neutron star binary mergers including equal-mass and unequal-mass systems of different total binary mass. The softening of the EoS by the PT at higher densities, i.e. after merging, leads to a characteristic increase of the dominant postmerger GW frequency f_peak relative to the tidal deformability Lambda inferred during the premerger inspiral phase. Hence, measuring such an increase of the postmerger frequency provides evidence for the presence of a strong PT. If the postmerger frequency and the tidal deformability are compatible with results from purely baryonic EoS models yielding very tight relations between f_peak and Lambda, a strong PT can be excluded up to a certain density. We find tight correlations of f_peak and Lambda with the maximum density during the early postmerger remnant evolution. These GW observables thus inform about the density regime which is probed by the remnant and its GW emission. Exploiting such relations we devise a directly applicable, concrete procedure to constrain the onset density of the QCD PT from future GW measurements. We point out two interesting scenarios: if no indications for a PT are inferred from a GW detection, our procedure yields a lower limit on the onset density of the hadron quark PT. On the contrary, if a merger event reveals evidence for the occurrence of deconfined quark matter, the inferred GW parameters set an upper limit on the PT onset density. (abridged)

/pdf/constraining-the-onset-density-of-the-hadron-quark-phase-4yc98n1yq2.pdf

Constraining the onset density of the hadron-quark phase transition with gravitational-wave observations

We discuss the QCD phase structure at finite temperature and chemical potential for 2-flavor and $2+1$-flavor QCD. The results are achieved by computing QCD correlation functions within a generalized functional approach that combines Dyson-Schwinger equations (DSE) and the functional renormalization group (fRG). In this setup fRG precision data from [A. K. Cyrol, M. Mitter, J. M. Pawlowski, and N. Strodthoff, Phys. Rev. D 97, 054006 (2018).] for the vacuum quark-gluon vertex and gluon propagator of 2-flavor QCD used as input, and the respective DSEs are expanded about this input. While the vacuum results for other correlation functions serve as a self-consistency check for functional approaches, the results at finite temperature and density are computed, for the first time, without the need of phenomenological infrared parameters.

/pdf/qcd-phase-structure-from-functional-methods-x03bxudc5c.pdf

QCD phase structure from functional methods

Chiral phase structure and critical end point in QCD

The reconstruction of the spectral function from the correlation function in Euclidean space is a challenging task. In this paper, we employ the machine learning techniques in terms of the radial basis functions networks to reconstruct the spectral function from a finite number of correlation data. To test our method, we first generate one type of correlation data using a mock spectral function by mixing several Breit-Wigner propagators. We found that compared with other traditional methods, e.g., truncated singular value decomposition, Tikhonov, and maximum entropy methods, our approach gives a continuous and unified reconstruction for both positive definite and negative spectral functions, which is especially useful for studying the QCD phase transition. Moreover, our approach has considerably better performance in the low-frequency region. This has advantages for the extraction of transport coefficients which are related to the zero frequency limit of the spectral function. With the mock data generated through a model spectral function of stress energy tensor, we find our method gives a precise and stable extraction of the transport coefficients.

Application of radial basis functions neutral networks in spectral functions

With analyzing the mass function obtained by solving Dyson-Schwinger Equations, we propose a cut-off independent definition of quark condensate beyond chiral limit. With this well-defined condensate, we then analyze the evolution of the condensate and its susceptibility with the current quark mass. The susceptibility shows a critical mass in the neighborhood of the s-quark current mass, which defines a transition boundary for internal hadron dynamics.

New insight on the quark condensate beyond the chiral limit

We implement the Dyson-Schwinger equation approach to study the mass dependence of pseudocritical temperature of QCD crossover at zero chemical potential. For the quark-gluon vertex, we take simply the rainbow approximation, while for the gluon propagator, we make use of various dressing functions. We analyze the scaling behavior with these different gluon models and obtain the critical exponent consistent with the mean field value for 3D O(4) universality class, which means the rainbow truncation will lead to the mean field result, regardless of the gluon dressing model. The size of critical region is up to ${m}_{0}\ensuremath{\le}1--2\text{ }\text{ }\mathrm{MeV}$ in this mean field approximation, which sets naturally an upper bound of the critical region since the fluctuations beyond mean field usually diminish the critical region. The pseudocritical temperature corresponds to the maximum value of the chiral susceptibility, and for the chiral susceptibility of a certain percentage of its maximum value, the corresponding temperature might be mass independent. We analyze this percentage and studied the pion mass range in which the corresponding temperature remain constant. The results show that this percentage and the pion mass range depend on the details of interaction kernel, which differs in gluon models.

Mass dependence of pseudocritical temperature in mean field approximation

Handle everyday research tasks with reliable, citation-backed results

Your personal Research Agent to handle research tasks with citation-backed results

Popular Tasks used by Researchers

How can I help with your research?

Meet SciSpace

Get more enhanced response by uploading the PDFs you want me to reference.

No relevant PDFs in your library

SciSpace is the AI research assistant for academics. Run systematic literature reviews on 280M+ papers, and write papers with cited sources. Trusted by 1M+ students, PhDs & researchers.

SciSpace | AI for Research

Analyze PDFs

Code & Manuscripts

Funding & Grants

Literature & Patents

Medical & Clinical Data

Systematic Review

Visualize & Present

Web & Data

Build a Google Scholar-like website for your research.

Build a website

Create charts and images for your research

Create a Chart

Write a paper for submission to a journal

Draft a manuscript

Patent Search

Design eye-catching scientific posters in minutes.

Scientific Poster Generation

Systematic Literature Review

One task is running at the moment. Your messages will be shown right after.

Drag and drop or click here to browse

Loved by <highlight>1 million+</highlight> researchers

Extract a list of specific topics and their sources from unstructured text

Topics

Compare and analyze relevant papers that matches with your search

Papers

Get insights from PDFs and bookmarked papers from your library

My library

Recent searches

Try searching for:

Catch AI-generated content in scholarly and non-scholarly content

{ai} Detector

Ai Writer

Get PDF Summaries, highlighted text explanations 

Chat with PDF

Effortlessly create in-text citations and bibliographies in APA and 2,500 other formats

Citation generator

Get explanations, summaries, and answers on academic papers

Ease up your research workflow with {scispace}'s cohort of exciting AI tools

Elevate your academic writing skills and convey your ideas the way you want

Paraphraser

Explore our range of reading and writing tools

Your file is being prepared and should be ready in a few minutes. If it's a large file, it might take a bit longer. You can close this window, and we'll email you the file when it's done.

You have reached a maximum limit of <strong>{limit}</strong> columns in the table. Remove at least <strong>1</strong> column to add or create another one.

Fei Gao

Author Tools

Chat about Author