Nuclear Theory·nucl-th

Monday·May 4, 2026

11 papers—4 primary·7 cross-listed

05
Baryonic Bound States in the Non-Local NJL Model
Arpan Chatterjee · Stefan Groote
Baryons, as three-quark bound states, require a covariant treatment in the intermediate-energy regime where perturbative QCD is no longer applicable and where nonperturbative correlations dominate. This article reformulates the content of the CERN Baltic Conference 2025 presentation on baryonic bound states in the non-local Nambu--Jona-Lasinio (NJL) model. We review how the relativistic Faddeev approach reduces the three-body quark problem to an effective quark--diquark bound-state problem, describe the scalar and axial-vector diquark channels, and show how the resulting quark--diquark Bethe--Salpeter equation can be written as an eigenvalue problem for the baryon mass. The non-local NJL framework, motivated by QCD-based nonlocal interactions and Dyson--Schwinger considerations, provides a compact description in which baryon masses and form factors are extracted from the numerical solution of coupled integral equations.
↳ hep-phnucl-th0 citations
06
Evidence for Quark Confinement in the Proton
Xiangdong Ji🇨🇳 · Gerald A. Miller🇺🇸 · Chen Yang🇺🇸
The strong interaction is the fundamental force that holds quarks and the gluon force carriers together to form protons and neutrons and also binds the atomic nucleus. The theory governing quark-gluon interactions is Quantum Chromodynamics (QCD). A wide variety of experimental data teaches us that quarks and gluons cannot be observed in isolation, a phenomenon known as confinement that is unique to QCD. But no one has used QCD to mathematically prove confinement. Here we show how to define and measure the force on quarks in the proton using available experimental data. Direct evidence for confinement is obtained because the force is found to be attractive and constant for a wide range of quark positions. This work guides future experimental efforts at future Electron-Ion Colliders aimed at obtaining a rigorous quantitative understanding of confinement and the origin of nuclear mass.
↳ hep-phhep-exhep-latnucl-ex+1Research(2026)·4 citations
07
Twist-2 relations for the twist-3 tensor-polarized distribution function $f_{L T}$ of a spin-1 hadron by the operator-product-expansion method
S. Kumano🇨🇳 · Kenshi Kuroki🇨🇳
In a spin-1 hadron, tensor-polarized parton distribution functions (PDFs) exist. The twist-2 function is $f_{1 LL}$ and a twist-3 one is $f_{L T}$ . Because an experiment is under preparation at the Thomas Jefferson National Accelerator Facility (JLab) to measure the cross section of electron-deuteron deep inelastic scattering with the tensor-polarized deuteron target, these PDFs need to be understood theoretically. Especially, measurements will be done in a relatively low- $Q^{2}$ region at JLab, so that twist-3 contributions could become sizable in the cross section. In a previous work, a twist-2 relation was derived for $f_{L T}$ in terms of $f_{1 LL}$ by using a nonlocal operator, and it corresponds to the Wandzura-Wilczek (WW) relation between $g_{1}$ and $g_{2}$ . In addition, another relation similar to the Burkhardt-Cottingham (BC) sum rule was obtained. It is known that a formal way to derive the WW relation and the BC sum rule is to use the operator product expansion (OPE) with local operators. In this work, the WW-like relation and the BC-like sum rule for $f_{L T}$ are derived by using the local OPE method as a reliable independent way to establish these relations.
↳ hep-phhep-exhep-latnucl-ex+1PLB(2026)·1 citation
08
Maximal mass of neutron stars constrained by neutron star observations
Gábor Kasza🇭🇺 · György Wolf🇭🇺
We investigate constraints on the high-density equation of state (EOS) of neutron star matter by analyzing the probability distributions of the endpoints of mass-radius M(R) sequences within a Bayesian weighting framework. Starting from two representative hadronic baseline EOSs, SFHo and DD2, matched at higher densities to an extended linear sigma model description and constrained to approach perturbative QCD (pQCD) results, we construct families of causal hybrid EOSs spanning a broad range of stiffness at supranuclear densities. Observational constraints from the binary neutron-star merger GW170817, mass-radius measurements from the Neutron Star Interior Composition Explorer (NICER), and candidate low-mass and mass-gap compact objects are incorporated through Bayesian likelihood weighting. This approach allows us to determine probability distributions for the maximum neutron-star mass M $_{TOV}$ and the corresponding radius R $_{TOV}$ , i.e., the endpoints of the M(R) sequences. We find that the maximum-mass distributions are largely determined by observational constraints and show only weak sensitivity to the choice of baseline EOS, favoring values around 2.2-2.3 M $_{⊙}$ when the most robust constraints are applied. In contrast, the corresponding radius distributions exhibit a stronger dependence on the underlying hadronic EOS, with typical preferred values near $12 \pm 1$ km. Additional tidal-deformability constraints further restrict the allowed parameter space and disfavor very stiff EOS realizations when interpreted together with the possible mass-gap neutron-star candidate. Our results demonstrate that endpoint distributions of M(R) sequences provide a sensitive and complementary diagnostic for constraining the high-density behavior of the neutron-star EOS within a multimessenger Bayesian framework.
↳ astro-ph.HEhep-phnucl-thJ.Subatomic Part.Cosmol.(2026)·1 citation
09
Nuclear structure and saturation effects from diffractive vector meson production
Heikki Mäntysaari🇫🇮 · Hendrik Roch🇫🇮 · Björn Schenke🇺🇸 · Chun Shen🇺🇸 · Wenbin Zhao🇨🇳
We study exclusive vector meson production in ultraperipheral collisions (UPCs) of a wide range of nuclei, and assess the potential of measurements to constrain the small- $x$ structure of oxygen and neon nuclei. We employ an impact-parameter-dependent color glass condensate framework incorporating JIMWLK evolution, with parameters constrained by a recent global Bayesian analysis of $γ + p$ and $γ + Pb$ data. We present predictions for coherent and incoherent $J / ψ$ production in $O + O$ and $Ne + Ne$ UPCs at LHC energies, and quantify theoretical uncertainties using posterior samples from the calibration. We employ several nuclear structure models and find that $t$ -differential observables are sensitive to the chosen model. We further study the mass-number dependence of saturation effects through nuclear suppression factors for coherent and incoherent vector meson production. Saturation-induced suppression increases systematically with both nuclear mass number and energy. Our results provide a unified framework for the systematic study of the onset of gluon saturation and nuclear structure at high energy, accessible in future UPC measurements at the LHC and at the Electron-Ion Collider.
↳ hep-phnucl-thPRD(2026)·3 citations
10
MuDirac 1.3.0: A Sustainable Software Tool for Calculating Ground State Nuclear Properties Using Muonic X-Ray Measurements
Leandro Liborio · Milan Kumar · Subindev Devadasan · Philip Jones · Martin Plummer · Adrian Hillier · Albert Bartok
The nuclear charge radius is one of the most fundamental quantities of the atomic nucleus. It can be deduced from a combination of experimental measurements of muonicX-raytransitionenergieswithmodellingofthoseX-raytransitionenergies. In thisworkwepresentMuDirac (1.3.0), whichisanopen, publiclyavailable, sustainable and computationally efficient software tool that will be at put the disposal of the negative muon community. With MuDirac (1.3.0), the community will be able to accurately and efficiently estimate nuclear properties, such as the nuclear charge radius, by assuming a 2-parameter Fermi distribution of the nuclear charge.
↳ physics.comp-phnucl-thphysics.atom-ph1 citation
11
Stability of parton distributions at high $x$ : impact of nuclear and power corrections
C. Cocuzza🇺🇸 · W. Melnitchouk🇺🇸 · N. Sato🇺🇸 · A. W. Thomas🇦🇺
We present a comprehensive new global QCD analysis of unpolarized parton distribution functions (PDFs) based upon proton, deuteron and $A = 3$ data, including the latest inclusive deep-inelastic scattering (DIS) measurements from Jefferson Lab at high Bjorken- $x$ . Using the JAM Bayesian Monte Carlo framework, we systematically explore the stability of the PDFs with respect to variations in the cuts on the invariant mass $W$ of the DIS final state, the implementation of target mass and higher twist corrections, as well as on the nuclear wave functions for the $A = 2$ and 3 data. We find the $u$ and $d$ quark PDFs (and the $d / u$ ratio) are relatively stable up to $x \approx 0.8$ , and able to describe DIS data down to $W^{2} = 3.5$ GeV $^{2}$ and $Q^{2} = m_{c}^{2}$ . Within the collinear factorization framework, the fitted higher twist corrections to DIS are found to be positive, and largely isospin independent. The description of the nuclear data also requires nonzero isoscalar and isovector nucleon off-shell PDF contributions, which gives specific predictions for the ratio, $R_{D}$ , of deuteron to isoscalar nucleon structure functions.
↳ hep-phhep-exnucl-th5 citations

Affiliations

first authorsco-authorsvia INSPIRE

Baryonic Bound States in the Non-Local NJL Model

Evidence for Quark Confinement in the Proton

Twist-2 relations for the twist-3 tensor-polarized distribution function fLT​ of a spin-1 hadron by the operator-product-expansion method

Maximal mass of neutron stars constrained by neutron star observations

Nuclear structure and saturation effects from diffractive vector meson production

MuDirac 1.3.0: A Sustainable Software Tool for Calculating Ground State Nuclear Properties Using Muonic X-Ray Measurements

Stability of parton distributions at high x: impact of nuclear and power corrections

Affiliations

Twist-2 relations for the twist-3 tensor-polarized distribution function $f_{L T}$ of a spin-1 hadron by the operator-product-expansion method

Stability of parton distributions at high $x$ : impact of nuclear and power corrections