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15 pages, 6504 KiB

Open AccessArticle

Chaos in QCD? Gap Equations and Their Fractal Properties

by Thomas Klähn, Lee C. Loveridge and Mateusz Cierniak

Particles 2023, 6(2), 470-484; https://doi.org/10.3390/particles6020026 - 11 Apr 2023

Viewed by 1436

Abstract

In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or [...] Read more.

In this study, we discuss how iterative solutions of QCD-inspired gap-equations at the finite chemical potential demonstrate domains of chaotic behavior as well as non-chaotic domains, which represent one or the other of the only two—usually distinct—positive mass gap solutions with broken or restored chiral symmetry, respectively. In the iterative approach, gap solutions exist which exhibit restored chiral symmetry beyond a certain dynamical cut-off energy. A chirally broken, non-chaotic domain with no emergent mass poles and hence with no quasi-particle excitations exists below this energy cut-off. The transition domain between these two energy-separated domains is chaotic. As a result, the dispersion relation is that of quarks with restored chiral symmetry, cut at a dynamical energy scale, and determined by fractal structures. We argue that the chaotic origin of the infrared cut-off could hint at a chaotic nature of confinement and the deconfinement phase transition. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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14 pages, 3171 KiB

Open AccessArticle

Precision Storage Rings for Electric Dipole Moment Searches: A Tool En Route to Physics Beyond-the-Standard-Model

by Hans Ströher, Sebastian M. Schmidt, Paolo Lenisa and Jörg Pretz

Particles 2023, 6(1), 385-398; https://doi.org/10.3390/particles6010020 - 2 Mar 2023

Cited by 1 | Viewed by 1972

Abstract

Electric Dipole Moments (EDM) of particles (leptons, nucleons, and light nuclei) are currently deemed one of the best indicators for new physics, i.e., phenomena which lie outside the Standard Model (SM) of elementary particle physics—so-called physics “Beyond-the-Standard-Model” (BSM). Since EDMs of the SM [...] Read more.

Electric Dipole Moments (EDM) of particles (leptons, nucleons, and light nuclei) are currently deemed one of the best indicators for new physics, i.e., phenomena which lie outside the Standard Model (SM) of elementary particle physics—so-called physics “Beyond-the-Standard-Model” (BSM). Since EDMs of the SM are vanishingly small, a finite permanent EDM would indicate charge-parity (CP) symmetry violation in addition to the well-known sources of the SM, and could explain the baryon asymmetry of the Universe, while an oscillating EDM would hint at a possible Dark Matter (DM) field comprising axions or axion-like particles (ALPs). A new approach exploiting polarized charged particles (proton, deuteron, ³He) in precision storage rings offers the prospect to push current experimental EDM upper limits significantly further, including the possibility of an EDM discovery. In this paper, we describe the scientific background and the steps towards the realization of a precision storage ring, which will make such measurements possible. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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22 pages, 1551 KiB

Open AccessArticle

Masses of Compact (Neutron) Stars with Distinguished Cores

by Rico Zöllner, Minghui Ding and Burkhard Kämpfer

Particles 2023, 6(1), 217-238; https://doi.org/10.3390/particles6010012 - 2 Feb 2023

Cited by 6 | Viewed by 2496

Abstract

In this paper, the impact of core mass on the compact/neutron-star mass-radius relation is studied. Besides the mass, the core is parameterized by its radius and surface pressure, which supports the outside one-component Standard Model (SM) matter. The core may accommodate SM matter [...] Read more.

In this paper, the impact of core mass on the compact/neutron-star mass-radius relation is studied. Besides the mass, the core is parameterized by its radius and surface pressure, which supports the outside one-component Standard Model (SM) matter. The core may accommodate SM matter with unspecified (or poorly known) equation-of-state or several components, e.g., consisting of admixtures of Dark Matter and/or Mirror World matter etc. beyond the SM. Thus, the admissible range of masses and radii of compact stars can be considerably extended. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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9 pages, 357 KiB

Open AccessArticle

Experimental Determination of the QCD Effective Charge α_g1(Q)

by Alexandre Deur, Volker Burkert, Jian-Ping Chen and Wolfgang Korsch

Particles 2022, 5(2), 171-179; https://doi.org/10.3390/particles5020015 - 31 May 2022

Cited by 22 | Viewed by 8925

Abstract

The QCD effective charge

α_{g_{1}} (Q)

is an observable that characterizes the magnitude of the strong interaction. At high momentum Q, it coincides with the QCD running coupling

α_{s} (Q)

. At low Q, [...] Read more.

The QCD effective charge

α_{g_{1}} (Q)

is an observable that characterizes the magnitude of the strong interaction. At high momentum Q, it coincides with the QCD running coupling

α_{s} (Q)

. At low Q, it offers a nonperturbative definition of the running coupling. We have extracted

α_{g_{1}} (Q)

from measurements carried out at Jefferson Lab that span the very low to moderately high Q domain,

0.14 \leq Q \leq 2.18

GeV. The precision of the new results is much improved over the previous extractions and the reach in Q at the lower end is significantly expanded. The data show that

α_{g_{1}} (Q)

becomes Q-independent at very low Q. They compare well with two recent predictions of the QCD effective charge based on Dyson–Schwinger equations and on the AdS/CFT duality. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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Review

Jump to: Research

18 pages, 1479 KiB

Open AccessReview

Impact of Multiple Phase Transitions in Dense QCD on Compact Stars

by Armen Sedrakian

Particles 2023, 6(3), 713-730; https://doi.org/10.3390/particles6030044 - 14 Jul 2023

Cited by 5 | Viewed by 1464

Abstract

This review covers several recent developments in the physics of dense QCD with an emphasis on the impact of multiple phase transitions on astrophysical manifestations of compact stars. To motivate the multi-phase modeling of dense QCD and delineate the perspectives, we start with [...] Read more.

This review covers several recent developments in the physics of dense QCD with an emphasis on the impact of multiple phase transitions on astrophysical manifestations of compact stars. To motivate the multi-phase modeling of dense QCD and delineate the perspectives, we start with a discussion of the structure of its phase diagram and the arrangement of possible color-superconducting and other phases. It is conjectured that pair-correlated quark matter in

β

-equilibrium is within the same universality class as spin-imbalanced cold atoms and the isospin asymmetrical nucleonic matter. This then implies the emergence of phases with broken space symmetries and tri-critical (Lifshitz) points. The beyond-mean-field structure of the quark propagator and its non-trivial implications are discussed in the cases of two- and three-flavor quark matter within the Eliashberg theory, which takes into account the frequency dependence (retardation) of the gap function. We then construct an equation of state (EoS) that extends the two-phase EoS of dense quark matter within the constant speed of sound parameterization by adding a conformal fluid with a speed of sound

c_{conf .} = 1 / \sqrt{3}

at densities

\geq 10 n_{sat}

, where

n_{sat}

is the saturation density. With this input, we construct static, spherically symmetrical compact hybrid stars in the mass–radius diagram, recover such features as the twins and triplets, and show that the transition to conformal fluid leads to the spiraling-in of the tracks in this diagram. Stars on the spirals are classically unstable with respect to the radial oscillations but can be stabilized if the conversion timescale between quark and nucleonic phases at their interface is larger than the oscillation period. Finally, we review the impact of a transition from high-temperature gapped to low-temperature gapless two-flavor phase on the thermal evolution of hybrid stars. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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31 pages, 750 KiB

Open AccessReview

Several Topics on Transverse Momentum-Dependent Fragmentation Functions

by Kai-Bao Chen, Tianbo Liu, Yu-Kun Song and Shu-Yi Wei

Particles 2023, 6(2), 515-545; https://doi.org/10.3390/particles6020029 - 27 Apr 2023

Cited by 8 | Viewed by 2253

Abstract

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features [...] Read more.

The hadronization of a high-energy parton is described by fragmentation functions which are introduced through QCD factorizations. While the hadronization mechanism per se remains uknown, fragmentation functions can still be investigated qualitatively and quantitatively. The qualitative study mainly concentrates on extracting genuine features based on the operator definition in quantum field theory. The quantitative research focuses on describing a variety of experimental data employing the fragmentation function given by the parameterizations or model calculations. With the foundation of the transverse-momentum-dependent factorization, the QCD evolution of leading twist transverse-momentum-dependent fragmentation functions has also been established. In addition, the universality of fragmentation functions has been proven, albeit model-dependently, so that it is possible to perform a global analysis of experimental data in different high-energy reactions. The collective efforts may eventually reveal important information hidden in the shadow of nonperturbative physics. This review covers the following topics: transverse-momentum-dependent factorization and the corresponding QCD evolution, spin-dependent fragmentation functions at leading and higher twists, several experimental measurements and corresponding phenomenological studies, and some model calculations. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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24 pages, 7008 KiB

Open AccessReview

Nucleon Resonance Electroexcitation Amplitudes and Emergent Hadron Mass

by Daniel S. Carman, Ralf W. Gothe, Victor I. Mokeev and Craig D. Roberts

Particles 2023, 6(1), 416-439; https://doi.org/10.3390/particles6010023 - 15 Mar 2023

Cited by 17 | Viewed by 2502

Abstract

Understanding the strong interaction dynamics that govern the emergence of hadron mass (EHM) represents a challenging open problem in the Standard Model. In this paper we describe new opportunities for gaining insight into EHM from results on nucleon resonance (

N^{*}

) [...] Read more.

Understanding the strong interaction dynamics that govern the emergence of hadron mass (EHM) represents a challenging open problem in the Standard Model. In this paper we describe new opportunities for gaining insight into EHM from results on nucleon resonance (

N^{*}

) electroexcitation amplitudes (i.e.,

γ_{v} p N^{*}

electrocouplings) in the mass range up to 1.8 GeV for virtual photon four-momentum squared (i.e., photon virtualities

Q^{2}

) up to 7.5 GeV

^{2}

available from exclusive meson electroproduction data acquired during the 6-GeV era of experiments at Jefferson Laboratory (JLab). These results, combined with achievements in the use of continuum Schwinger function methods (CSMs), offer new opportunities for charting the momentum dependence of the dressed quark mass from results on the

Q^{2}

-evolution of the

γ_{v} p N^{*}

electrocouplings. This mass function is one of the three pillars of EHM and its behavior expresses influences of the other two, viz. the running gluon mass and momentum-dependent effective charge. A successful description of the

Δ (1232) 3 / 2^{+}

and

N (1440) 1 / 2^{+}

electrocouplings has been achieved using CSMs with, in both cases, common momentum-dependent mass functions for the dressed quarks, for the gluons, and the same momentum-dependent strong coupling. The properties of these functions have been inferred from nonperturbative studies of QCD and confirmed, e.g., in the description of nucleon and pion elastic electromagnetic form factors. Parameter-free CSM predictions for the electrocouplings of the

Δ (1600) 3 / 2^{+}

became available in 2019. The experimental results obtained in the first half of 2022 have confirmed the CSM predictions. We also discuss prospects for these studies during the 12-GeV era at JLab using the CLAS12 detector, with experiments that are currently in progress, and canvass the physics motivation for continued studies in this area with a possible increase of the JLab electron beam energy up to 22 GeV. Such an upgrade would finally enable mapping of the dressed quark mass over the full range of distances (i.e., quark momenta) where the dominant part of hadron mass and

N^{*}

structure emerge in the transition from the strongly coupled to perturbative QCD regimes. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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52 pages, 2842 KiB

Open AccessReview

Gauge Sector Dynamics in QCD

by Mauricio Narciso Ferreira and Joannis Papavassiliou

Particles 2023, 6(1), 312-363; https://doi.org/10.3390/particles6010017 - 15 Feb 2023

Cited by 34 | Viewed by 2741

Abstract

The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of [...] Read more.

The dynamics of the QCD gauge sector give rise to non-perturbative phenomena that are crucial for the internal consistency of the theory; most notably, they account for the generation of a gluon mass through the action of the Schwinger mechanism, the taming of the Landau pole, the ensuing stabilization of the gauge coupling, and the infrared suppression of the three-gluon vertex. In the present work, we review some key advances in the ongoing investigation of this sector within the framework of the continuum Schwinger function methods, supplemented by results obtained from lattice simulations. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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35 pages, 1247 KiB

Open AccessReview

Generalised Parton Distributions in Continuum Schwinger Methods: Progresses, Opportunities and Challenges

by Cédric Mezrag

Particles 2023, 6(1), 262-296; https://doi.org/10.3390/particles6010015 - 8 Feb 2023

Cited by 7 | Viewed by 2259

Abstract

This paper review the modelling efforts regarding Generalised Parton Distributions (GPDs) using continuum techniques relying on Dyson–Schwinger and Bethe–Salpeter equations. The definition and main properties of the GPDs are first recalled. Then, we detail the strategies developed in the last decade in the [...] Read more.

This paper review the modelling efforts regarding Generalised Parton Distributions (GPDs) using continuum techniques relying on Dyson–Schwinger and Bethe–Salpeter equations. The definition and main properties of the GPDs are first recalled. Then, we detail the strategies developed in the last decade in the meson sector, highlighting that observables connected to the pion GPDs may be measured at future colliders. We also highlight the challenges one will face when targeting baryons in the future. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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64 pages, 5437 KiB

Open AccessEditor’s ChoiceReview

Emergence of Hadron Mass and Structure

by Minghui Ding, Craig D. Roberts and Sebastian M. Schmidt

Particles 2023, 6(1), 57-120; https://doi.org/10.3390/particles6010004 - 11 Jan 2023

Cited by 44 | Viewed by 23123

Abstract

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale-invariant. Thus, if the Standard Model is truly a [...] Read more.

Visible matter is characterised by a single mass scale; namely, the proton mass. The proton’s existence and structure are supposed to be described by quantum chromodynamics (QCD); yet, absent Higgs boson couplings, chromodynamics is scale-invariant. Thus, if the Standard Model is truly a part of the theory of Nature, then the proton mass is an emergent feature of QCD; and emergent hadron mass (EHM) must provide the basic link between theory and observation. Nonperturbative tools are necessary if such connections are to be made; and in this context, we sketch recent progress in the application of continuum Schwinger function methods to an array of related problems in hadron and particle physics. Special emphasis is given to the three pillars of EHM—namely, the running gluon mass, process-independent effective charge, and running quark mass; their role in stabilising QCD; and their measurable expressions in a diverse array of observables. Full article

(This article belongs to the Special Issue Strong Interactions in the Standard Model: Massless Bosons to Compact Stars)

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