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20 pages, 359 KiB

Open AccessArticle

Neutrino Oscillations in Finite Time Path Out-of-Equilibrium Thermal Field Theory

by Ivan Dadić and Dubravko Klabučar

Symmetry 2023, 15(11), 1970; https://doi.org/10.3390/sym15111970 - 24 Oct 2023

Cited by 1 | Viewed by 1163

Abstract

We demonstrate that the Finite-Time-Path Field Theory is an adequate tool for calculating neutrino oscillations. We apply this theory using a mass-mixing Lagrangian which involves the correct Dirac spin and chirality structure and a Pontecorvo–Maki–Nakagawa–Sakata (PMNS)-like mixing matrix. The model is exactly solvable. [...] Read more.

We demonstrate that the Finite-Time-Path Field Theory is an adequate tool for calculating neutrino oscillations. We apply this theory using a mass-mixing Lagrangian which involves the correct Dirac spin and chirality structure and a Pontecorvo–Maki–Nakagawa–Sakata (PMNS)-like mixing matrix. The model is exactly solvable. The Dyson–Schwinger equations transform propagators of the input free (massless) flavor neutrinos into a linear combination of oscillating (massive) neutrinos. The results are consistent with the predictions of the PMNS matrix while allowing for extrapolation to early times. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

10 pages, 329 KiB

Open AccessEditor’s ChoiceArticle

Dynamical Chiral Symmetry Breaking in Quantum Chromo Dynamics: Delicate and Intricate

by Reinhard Alkofer

Symmetry 2023, 15(9), 1787; https://doi.org/10.3390/sym15091787 - 18 Sep 2023

Cited by 5 | Viewed by 1249

Abstract

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator [...] Read more.

Dynamical chiral symmetry breaking (D

χ

SB) in quantum chromo dynamics (QCD) for light quarks is an indispensable concept for understanding hadron physics, i.e., the spectrum and the structure of hadrons. In functional approaches to QCD, the respective role of the quark propagator has been evident since the seminal work of Nambu and Jona-Lasinio has been recast in terms of QCD. It not only highlights one of the most important aspects of D

χ

SB, the dynamical generation of constituent quark masses, but also makes plausible that D

χ

SB is a robustly occurring phenomenon in QCD. The latter impression, however, changes when higher n-point functions are taken into account. In particular, the quark–gluon vertex, i.e., the most elementary n-point function describing the full, non-perturbative quark–gluon interaction, plays a dichotomous role: It is subject to D

χ

SB as signalled by its scalar and tensor components but it is also a driver of D

χ

SB due to the infrared enhancement of most of its components. Herein, the relevant self-consistent mechanism is elucidated. It is pointed out that recently obtained results imply that, at least in the covariant gauge, D

χ

SB in QCD is located close to the critical point and is thus a delicate effect. In addition, requiring a precise determination of QCD’s three-point functions, D

χ

SB is established, in particular in view of earlier studies, by an intricate interplay of the self-consistently determined magnitude and momentum dependence of various tensorial components of the gluon–gluon and the quark–gluon interactions. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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11 pages, 408 KiB

Open AccessFeature PaperArticle

Cancellation of the Sigma Mode in the Thermal Pion Gas by Quark Pauli Blocking

by David Blaschke, Alexandra Friesen and Yuri Kalinovsky

Symmetry 2023, 15(3), 711; https://doi.org/10.3390/sym15030711 - 13 Mar 2023

Viewed by 1246

Abstract

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the

σ

- and

ϱ

-meson resonances. The repulsive phase shift

δ_{0}^{2}

is taken from [...] Read more.

In this study, we calculate the pressure of the interacting pion gas using the Beth–Uhlenbeck approach to the relativistic virial expansion with Breit–Wigner phase shifts for the

σ

- and

ϱ

-meson resonances. The repulsive phase shift

δ_{0}^{2}

is taken from the quark interchange model of Barnes and Swanson, which is in very good agreement with the experimental data. In this work we show that the cancellation of the attractive (I = 0) and repulsive (I = 2) isospin channel contributions to the scalar

π π

interaction in the low-energy region that is known for the vacuum phase shifts also takes place at a finite temperature. This happens despite the strong medium dependence of these phase shifts that enters our model by the temperature dependence of the

σ

-meson and constituent quark masses, because for these masses the relation

M_{σ} (T) \approx 2 m_{q} (T)

holds and the scattering length approximation is valid as long as the strong decay channel

σ \to π π

is open. Exploiting the Nambu–Jona-Lasinio model for describing the dynamical breaking of chiral symmetry in the vacuum and its restoration at a finite temperature, we justify with our approach that the

σ

-meson should be absent from the hadron resonance gas description at low temperatures because the above cancellation holds. However, since this cancellation breaks down in the vicinity of the hadronization transition, where due to chiral symmetry restoration the decay channel

σ \to π π

closes and the

σ

-meson becomes a good resonance, the latter should be included into the statistical model description of chemical freeze-out in heavy-ion collisions. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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11 pages, 1127 KiB

Open AccessArticle

How to Determine the Branch Points of Correlation Functions in Euclidean Space II: Three-Point Functions

by Markus Q. Huber, Wolfgang J. Kern and Reinhard Alkofer

Symmetry 2023, 15(2), 414; https://doi.org/10.3390/sym15020414 - 3 Feb 2023

Cited by 2 | Viewed by 1260

Abstract

The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation functions for purely space-like momenta has reached a high [...] Read more.

The analytic structure of elementary correlation functions of a quantum field is relevant for the calculation of masses of bound states and their time-like properties in general. In quantum chromodynamics, the calculation of correlation functions for purely space-like momenta has reached a high level of sophistication, but the calculation at time-like momenta requires refined methods. One of them is the contour deformation method. Here we describe how to employ it for three-point functions. The basic mechanisms are discussed for a scalar theory, but they are the same for more complicated theories and are thus relevant, e.g., for the three-gluon or quark-gluon vertices of quantum chromodynamics. Their inclusion in existing truncation schemes is a crucial step for investigating the analytic structure of elementary correlation functions of quantum chromodynamics and the calculation of its spectrum from them. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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16 pages, 6091 KiB

Open AccessFeature PaperArticle

Two-Real-Singlet-Model Benchmark Planes

by Tania Robens

Symmetry 2023, 15(1), 27; https://doi.org/10.3390/sym15010027 - 22 Dec 2022

Cited by 9 | Viewed by 1272

Abstract

In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a

Z_{2} \otimes Z_{2}^{'}

symmetry. In this model, all fields [...] Read more.

In this manuscript, I briefly review the Benchmark Planes in the Two-Real-Singlet Model (TRSM), a model that enhances the Standard Model (SM) scalar sector by two real singlets that obey a

Z_{2} \otimes Z_{2}^{'}

symmetry. In this model, all fields acquire a vacuum expectation value, such that the model contains in total three CP-even neutral scalars that can interact with each other. All interactions with SM-like particles are inherited from the SM-like doublet via mixing. I remind the readers of the previously proposed benchmark planes and briefly discuss possible production at future Higgs factories, as well as regions in a more generic scan of the model. For these, I also discuss the use of the W-boson mass as a precision observable to determine allowed/excluded regions in the models’ parameter space. This work is an extension of a white paper submitted to the Snowmass process. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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8 pages, 307 KiB

Open AccessFeature PaperArticle

Thermodynamical Aspects of the LGGR Approach for Hadron Energy Spectra

by Tamás S. Biró and Zoltán Néda

Symmetry 2022, 14(9), 1807; https://doi.org/10.3390/sym14091807 - 31 Aug 2022

Cited by 3 | Viewed by 1395

Abstract

The local growth global reset (LGGR) dynamical model is reviewed and its performance in describing the hadron energy spectra in relativistic collisions is demonstrated. It is shown that even for dynamical processes a temperature-like quantity can be defined and distributions resembling statistical equilibrium [...] Read more.

The local growth global reset (LGGR) dynamical model is reviewed and its performance in describing the hadron energy spectra in relativistic collisions is demonstrated. It is shown that even for dynamical processes a temperature-like quantity can be defined and distributions resembling statistical equilibrium can be reached. With appropriate growth and reset rates the LGGR model is capable of describing the right energy spectra. These findings draw a certain picture of quark–gluon plasma development with random hadronization and re-swallowing steps and signals the fact that observing an exponential spectrum does not necessarily prove thermal equilibrium in the experiment. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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11 pages, 308 KiB

Open AccessFeature PaperArticle

Using a Strongly Intense Observable to Study the Formation of Quark-Gluon String Clusters in pp Collisions at LHC Energies

by Svetlana Belokurova and Vladimir Vechernin

Symmetry 2022, 14(8), 1673; https://doi.org/10.3390/sym14081673 - 12 Aug 2022

Cited by 3 | Viewed by 1478

Abstract

Within the framework of the model with quark-gluon strings (color flux tubes) as sources, the properties of the strongly intense variable

Σ

, which characterizes the correlations between the number of particles in two observation windows separated in rapidity, are studied. It is [...] Read more.

Within the framework of the model with quark-gluon strings (color flux tubes) as sources, the properties of the strongly intense variable

Σ

, which characterizes the correlations between the number of particles in two observation windows separated in rapidity, are studied. It is shown that, in pp collisions at LHC energies, string fusion effects leading to the formation of string clusters have a significant effect on the behavior of this observable. The experimentally observed changes in this variable with the initial energy and centrality of the pp collision can only be explained by taking into account the formation of string clusters consisting of an increasing number of merged strings. It is demonstrated that the study of the behavior of the

Σ

observable as a function of the rapidity distance between the centers of the observation windows and the width of these windows with variable experimental conditions using different energies and centralities of pp-collisions makes it possible to extract the parameters of string clusters from the experimental data. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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7 pages, 407 KiB

Open AccessArticle

The Partonic Origin of Multiplicity Scaling in Heavy and Light Flavor Jets

by Zoltán Varga and Róbert Vértesi

Symmetry 2022, 14(7), 1379; https://doi.org/10.3390/sym14071379 - 5 Jul 2022

Cited by 1 | Viewed by 1348

Abstract

Research shows that Koba–Nielsen–Olesen (KNO)-like scaling is fulfilled inside the jets, which indicates that KNO scaling is violated by complex vacuum quantum chromodynamics (QCD) processes outside the jet development, such as single and double parton scattering or softer multiple parton interactions. In the [...] Read more.

Research shows that Koba–Nielsen–Olesen (KNO)-like scaling is fulfilled inside the jets, which indicates that KNO scaling is violated by complex vacuum quantum chromodynamics (QCD) processes outside the jet development, such as single and double parton scattering or softer multiple parton interactions. In the current work, we investigated the scaling properties of heavy-flavor jets using Monte-Carlo simulations. We found that while jets from leading-order flavor-creation processes exhibit flavor-dependent patterns, heavy-flavor jets from production in parton showers follow inclusive-jet patterns. This suggests that KNO-like scaling is driven by initial hard parton production and not by processes in the later stages of the reaction. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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12 pages, 1259 KiB

Open AccessFeature PaperArticle

Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum

by Ismail Zahed

Symmetry 2022, 14(5), 932; https://doi.org/10.3390/sym14050932 - 4 May 2022

Cited by 2 | Viewed by 1409

Abstract

We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum [...] Read more.

We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji

^{'} s

invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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7 pages, 782 KiB

Open AccessConference Report

Analogies between Lattice QCD and the Truncated Nambu–Jona-Lasinio Model

by Mitja Rosina

Symmetry 2024, 16(5), 607; https://doi.org/10.3390/sym16050607 - 14 May 2024

Viewed by 611

Abstract

A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the [...] Read more.

A modified Nambu–Jona-Lasinio Model with lattice structure is very instructive. It shows several similar problems and their solutions as the Lattice QCD. We study the limits of the large box size, small cell size and realistic pion mass. In particular, we study the relation of the discrete (bound state) solutions to the physical scattering states, for example the pion–pion scattering. Full article

(This article belongs to the Special Issue Selected Papers from ACHT 2021: Perspectives in Particle, Cosmo- and Astroparticle Theory)

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