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18 pages, 567 KB

Open AccessArticle

Light and Strange Baryons in Medium

by Tanner Massimino, Thomas Klähn and Zoltán Papp

Particles 2026, 9(3), 72; https://doi.org/10.3390/particles9030072 - 9 Jul 2026

Viewed by 347

Abstract

We solve the Goldstone-boson-exchange (GBE) relativistic constituent quark model of light and strange baryons by using the Faddeev approach. The model reproduces the vacuum mass spectrum of light and strange baryons below 2 GeV reasonably well. To test the sensitivity of the model [...] Read more.

We solve the Goldstone-boson-exchange (GBE) relativistic constituent quark model of light and strange baryons by using the Faddeev approach. The model reproduces the vacuum mass spectrum of light and strange baryons below 2 GeV reasonably well. To test the sensitivity of the model to possible medium-induced effects, we vary the masses of the constituent quarks and the exchange bosons, the confinement strength, and the quark–meson coupling constant. In a parametric study, we consider a set of power-law scaling relations for these parameters, including some motivated by constituent quark-level current algebra relations. We find that the baryon spectrum is most sensitive to the quark–meson coupling constant, and generally observe a decrease in baryon mass with decreasing constituent quark mass. We qualitatively estimate the impact of these mass shifts on ideal-gas baryon yields and yield ratios. Absolute yields can already change significantly for mass shifts of a few 10 MeV, whereas yield ratios are strongly modified only when the compared baryons have different constituent quark mass dependence. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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59 pages, 3209 KB

Open AccessArticle

Gauge Symmetry Beyond Perturbation Theory: BRST and Anti-BRST Structure, Background Fields, and Infrared Dynamics of Yang–Mills Theory

by Daniele Binosi

Particles 2026, 9(2), 59; https://doi.org/10.3390/particles9020059 - 19 May 2026

Viewed by 479

Abstract

We present a pedagogical and self-contained account of the functional formulation of non-Abelian gauge theories, aimed at the construction of a process-independent effective charge for Yang–Mills theory. Starting from the path integral quantization of gauge fields, we review gauge fixing and the emergence [...] Read more.

We present a pedagogical and self-contained account of the functional formulation of non-Abelian gauge theories, aimed at the construction of a process-independent effective charge for Yang–Mills theory. Starting from the path integral quantization of gauge fields, we review gauge fixing and the emergence of Faddeev–Popov ghosts, illustrating how gauge invariance is preserved at the quantum level through Becchi–Rouet–Stora–Tyutin (BRST) symmetry. We then develop the BRST and anti-BRST formalisms and show how their simultaneous implementation leads to powerful functional identities that severely constrain the ghost and gluon sectors. Background field gauges are introduced as a natural framework in which these symmetries manifest themselves through Abelian-like Ward identities, allowing for a transparent separation between quantum and background degrees of freedom. This structure makes it possible to define renormalization group-invariant combinations of Green functions that generalize the QED effective charge to the non-Abelian case. The resulting effective charge is shown to be unique, gauge-invariant, and process-independent, providing a unified description of the theory from the ultraviolet down to the infrared. The interplay between functional identities, Dyson–Schwinger equations, and lattice results is discussed in detail, highlighting how dynamical mass generation and infrared saturation naturally emerge within this framework. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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24 pages, 2939 KB

Open AccessArticle

Getting a Handle on Correlation Functions

by Gernot Eichmann

Particles 2026, 9(2), 52; https://doi.org/10.3390/particles9020052 - 12 May 2026

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Abstract

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing [...] Read more.

The central objects in a quantum field theory are its n-point correlation functions and matrix elements. Their structure is determined by Lorentz invariance and leads to tensor decompositions, the Lorentz-invariant coefficient functions of which encode the physics of the process. For growing n, the complexity of these objects may increase considerably and make it challenging to deal with them. Here, we give a pedagogical introduction to the topic and provide some tools to manage this complexity, and we will show how symmetries can be used as organizing principles. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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13 pages, 8112 KB

Open AccessArticle

Searching for Stable States in the T_DD1 Systems Based on a Chiral Quark Model

by Yuheng Wu, Linkai Li, Yuheng Xing, Xinxing Wu and Yue Tan

Particles 2026, 9(2), 35; https://doi.org/10.3390/particles9020035 - 2 Apr 2026

Viewed by 596

Abstract

Experimentally, the

1^{+}

state

X (3872)

was first discovered, and subsequently, its partner state

Y (4260)

, with the same quark content

(c \bar{q} q \bar{c})

and quantum number

1^{-}

was also observed. [...] Read more.

Experimentally, the

1^{+}

state

X (3872)

was first discovered, and subsequently, its partner state

Y (4260)

, with the same quark content

(c \bar{q} q \bar{c})

and quantum number

1^{-}

was also observed. Inspired by this pattern, we systematically investigate the newly discovered

1^{+}

state

T_{c c}

and its possible

1^{-}

partner, the

T_{D D_{1}}

system with the same quark content

(c \bar{q} c \bar{q})

. Within the framework of the chiral quark model, we perform a comprehensive study of the bound and resonance states of

T_{D D_{1}}

using the Gaussian expansion method (GEM). Two quark configurations, the molecular structure and the diquark structure, are considered in our calculations. Our results indicate the existence of a shallow bound state dominated by the

D D_{1}^{*}

channel, which is analogous to the experimentally observed

T_{c c}

, as well as two compact resonant states with narrow widths around 4.5 GeV. To avoid the influence of model parameters on the results, we additionally fitted a new set of parameters and obtained consistent conclusions. According to our calculation results, although the color-octet and diquark configurations have relatively high energies, the channel-coupling effects induced by them play a crucial role in the formation of these stable states. We strongly encourage experimental efforts to search for the stable states predicted in the

T_{D D_{1}}

system. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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18 pages, 1790 KB

Open AccessArticle

The Kaon Off-Shell Generalized Parton Distributions and Transverse Momentum Dependent Parton Distributions

by Jin-Li Zhang

Particles 2025, 8(4), 85; https://doi.org/10.3390/particles8040085 - 25 Oct 2025

Cited by 2 | Viewed by 1284

Abstract

We investigate the off-shell generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) of kaons within the framework of the Nambu–Jona-Lasinio model, employing proper time regularization. Compared to the pion case, the off-shell effects in kaons are of similar magnitude, modifying [...] Read more.

We investigate the off-shell generalized parton distributions (GPDs) and transverse momentum dependent parton distributions (TMDs) of kaons within the framework of the Nambu–Jona-Lasinio model, employing proper time regularization. Compared to the pion case, the off-shell effects in kaons are of similar magnitude, modifying the GPDs by about 10–

25 %

, which is notable. The absence of crossing symmetry leads to odd powers in the x-moments of the off-shell GPDs, giving rise to new off-shell form factors. We analyze the relations among these kaon off-shell form factors by analogy with electromagnetic form factors. Our results extend the off-shell GPDs from pions to kaons and simultaneously address the associated off-shell form factors. We also compare the off-shell and on-shell gravitational form factors of the kaon. In addition, the off-shell kaon TMD shows a stronger dependence on the momentum fraction x than its on-shell counterpart. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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11 pages, 285 KB

Open AccessArticle

Diquark Study in Quark Model

by Xinmei Zhu, Hongxia Huang and Jialun Ping

Particles 2025, 8(4), 83; https://doi.org/10.3390/particles8040083 - 2 Oct 2025

Cited by 1 | Viewed by 1479

Abstract

To investigate diquark correlation in baryons, the baryon spectra with different light–heavy quark combinations are calculated using Gaussian expansion method within both the naive quark model and the chiral quark model. By computing the diquark energies and separations between any two quarks in [...] Read more.

To investigate diquark correlation in baryons, the baryon spectra with different light–heavy quark combinations are calculated using Gaussian expansion method within both the naive quark model and the chiral quark model. By computing the diquark energies and separations between any two quarks in baryons, we analyze the diquark effect in the

u d

-q/Q,

u s

-Q,

s s

-q/Q, and

Q Q

-q/Q systems (where

q = u, d

, or s;

Q = c, b

). The results show that diquark correlations exist in baryons. In particular, for

q q

-Q and

Q Q

-q systems, the same type of diquark exhibits nearly identical energy and size across different baryons. In the orbital ground states of baryons, scalar–isoscalar diquarks have lower energy and a smaller size compared to vector–isovector diquark, which qualifies them as “good diquarks”. In

Q Q

-q systems, a larger mass of Q leads to a smaller diquark separation and a more pronounced diquark effect. In

q q

-Q systems, the separation between the two light quarks remains larger than that between a light and a heavy quark, indicating that the internal structure of such diquarks must be taken into account. A comparison between the naive quark model and the chiral quark model reveals that the introduction of meson exchange slightly increases the diquark size in most systems. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

Review

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27 pages, 1438 KB

Open AccessReview

Understanding Transversely Polarized Quarks Inside Longitudinally Polarized Nucleons

by Hui Li, Xiaoyu Wang and Zhun Lu

Particles 2026, 9(3), 80; https://doi.org/10.3390/particles9030080 - 5 Aug 2026

Viewed by 116

Abstract

We review the current understanding of transversely polarized quarks inside longitudinally polarized nucleons from the perspective of the longi-transversity distribution function and transverse-momentum-dependent (TMD) factorization. Employing the recently developed TMD evolution formalism for the unpolarized and longi-transversity distribution functions, we present the theoretical [...] Read more.

We review the current understanding of transversely polarized quarks inside longitudinally polarized nucleons from the perspective of the longi-transversity distribution function and transverse-momentum-dependent (TMD) factorization. Employing the recently developed TMD evolution formalism for the unpolarized and longi-transversity distribution functions, we present the theoretical formalism for the relevant physical observables, namely the

A_{L L}^{\cos 2 ϕ}

asymmetry in the Drell–Yan process and the

A_{U L}^{\sin 2 ϕ_{h}}

asymmetry in the semi-inclusive deep inelastic scattering process. The phenomenological results are presented numerically. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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22 pages, 750 KB

Open AccessReview

A Step-by-Step Introduction to Generalised Parton Distributions

by Cédric Mezrag

Particles 2026, 9(3), 69; https://doi.org/10.3390/particles9030069 - 29 Jun 2026

Cited by 1 | Viewed by 509

Abstract

These notes comprise the material I presented during the International Workshop and School on Hadron Structure & Strong Interactions which took place in Nanjing in 2025. The aim of the lectures was to introduce and motivate the study of Generalised Parton Distributions (GPDs) [...] Read more.

These notes comprise the material I presented during the International Workshop and School on Hadron Structure & Strong Interactions which took place in Nanjing in 2025. The aim of the lectures was to introduce and motivate the study of Generalised Parton Distributions (GPDs) for an audience of Master and Ph.D. students in hadron physics, with little to no background regarding the description of exclusive processes at high virtuality. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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16 pages, 644 KB

Open AccessReview

Radiative Decays of Hadronic Molecules: From Confusion to Inspiration

by Feng-Kun Guo, Christoph Hanhart and Alexey Nefediev

Particles 2026, 9(2), 46; https://doi.org/10.3390/particles9020046 - 28 Apr 2026

Viewed by 628

Abstract

Radiative decays of hadronic states provide an essential source of information that can facilitate deciphering their nature and properties. However, a lot of confusion concerning radiative decays of hadronic molecules and their interpretation can be found in the literature. In this paper, we [...] Read more.

Radiative decays of hadronic states provide an essential source of information that can facilitate deciphering their nature and properties. However, a lot of confusion concerning radiative decays of hadronic molecules and their interpretation can be found in the literature. In this paper, we briefly review several types of such decays and pinpoint similarities and essential differences between them. In particular, we emphasise the crucial role played by the hierarchy of the scales relevant to the studied system and the resulting necessity of employing an approach that considers them appropriately. We illustrate the situation with several instructive examples. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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43 pages, 1772 KB

Open AccessReview

Symmetry- Preserving Contact Interaction Approaches: An Overview of Meson and Diquark Form Factors

by Laura Xiomara Gutiérrez-Guerrero and Roger José Hernández-Pinto

Particles 2026, 9(2), 45; https://doi.org/10.3390/particles9020045 - 24 Apr 2026

Cited by 1 | Viewed by 690

Abstract

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the [...] Read more.

We present an updated overview of the symmetry-preserving contact interaction model in hadronic physics, which was developed a little over a decade ago to describe the mass spectrum and internal structure of mesons and diquarks composed of light and heavy quarks. Over the years, the contact interaction model has evolved into a framework capable of treating both ground and excited states, providing a simple yet consistent approach to nonperturbative QCD. In this review, we examine the mass spectrum and elastic form factors of forty mesons with different spins and parities, together with their corresponding diquark partners. Importantly, we update the comparison of contact interaction predictions using recent results from the literature, offering a fresh perspective on the model’s performance, strengths, and limitations. The analysis presented here refines previous conclusions and supports the contact interaction model as a practical tool for hadron structure studies, with potential applications to baryons and multiquark states. We also present comparisons with other theoretical models and approaches, including lattice quantum chromodynamics, and comment on future prospects in view of ongoing and planned experimental programs regarding hadron structure. In particular, forthcoming measurements at FAIR together with future studies at Jefferson Lab and the Electron Ion Collider are expected to provide key insights into hadron structure, with FAIR offering indirect constraints via hadron spectroscopy, hadronic interactions, and in-medium properties; high-precision data on meson structure and form factors from Jefferson Lab and the Electron Ion Collider will provide valuable benchmarks with which to confront predictions based on the contact interaction model. Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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Other

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51 pages, 1443 KB

Open AccessTutorial

Introduction to Transverse Momentum Imaging

by Andrea Signori

Particles 2026, 9(3), 75; https://doi.org/10.3390/particles9030075 - 15 Jul 2026

Viewed by 244

Abstract

This set of notes complements the lectures and recitation sessions discussed in the following graduate schools: Hampton University Graduate Summer Program (HUGS) at Jefferson Lab (years 2018, 2019, 2021), the International School and Workshop on Probing Hadron Structure at the Electron-Ion Collider at [...] Read more.

This set of notes complements the lectures and recitation sessions discussed in the following graduate schools: Hampton University Graduate Summer Program (HUGS) at Jefferson Lab (years 2018, 2019, 2021), the International School and Workshop on Probing Hadron Structure at the Electron-Ion Collider at International Centre for Theoretical Sciences (ICTS) (2024), Frontiers in Nuclear and Hadronic Physics at The Galileo Galilei Institute for Theoretical Physics (GGI) (2025), and the International Workshop and School on Hadron Structure and Strong Interactions at Nanjing University (2025). Full article

(This article belongs to the Special Issue Strong QCD and Hadron Structure)

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