Open research questions in Quantum Chromodynamics and Particle Interactions

What the literature leaves open

• The complexity of hadronic two-photon interactions at electron-positron colliders, requiring a flexible and accurate tool for modeling. The need to generate events with exact leading-order QED coupling and a flat phase space decay of the hadronic state. The challenge of simulating the decay of the hadronic system into multiple final-state particles.

  HadroTOPS: A Monte Carlo Event Generator For Hadron Production In Two-Photon Scattering In Electron Positron Collisions · 2026 · DOI

• The lack of suitable simulation tools for the study of multi-hadron production, - The need for a Monte Carlo generator capable of modeling the complex hadronic processes involved in the fusion mechanism, - The code requires quadruple precision floating point numbers to ensure numerical stability

  HadroTOPS: A Monte Carlo Event Generator For Hadron Production In Two-Photon Scattering In Electron Positron Collisions · 2026 · DOI

• further experimental measurements of magnetic moments of mesons, - more precise calculations of photon momenta, - extension of our approach to other hadronic states

  Systematic study of light and charm meson M1 radiative transitions · 2026 · DOI

• Precise experimental measurement of magnetic moment of mesons is absent to date. The extremely short lifetimes of vector mesons pose difficulties to their magnetic moment measurements using standard techniques. Theoretical models have significant uncertainty in predicting the magnetic moments of hadronic states.

  Systematic study of light and charm meson M1 radiative transitions · 2026 · DOI

• Further study of the non-perturbative large N vacuum - Investigation of the trans-series corrections - Analysis of the formal series in γ through their explicit Borel transforms

  Anatomy of the simplest renormalon · 2026 · DOI

• The coefficients Kα specify phase space and color–spin–flavor recoupling for a stated normalization, while the physical channel-dependent coupling remains to be calculated.

  Compact $cs\bar{s}\bar{s}$ Tetraquarks in the Charm--Strange Sector: Mass Spectra, Rearrangement Decays and Regge Trajectories with $D_s$ Threshold Inputs · 2026

• However, the resulting increase in the $χ^2$-statistic of the fit warrants further examination into the physical uncertainty of the valence quark model, which is a work in progress.

  Constraining Proton Spin at Small $x$ with Valence Quark Model · 2026

• 6223); (iii) index, SHA-256 manifest of the files in this record, status README and list of open questions; (iv) Python scripts of the computations and a Blender geometry script.

  INDYNA-STATIK: Law Register L1–L386, Prediction Ledger (27), Index, Manifest and Scripts — Master Data for INDYNA Notes 16–34, the Capstone and the Tamura Companion Note · 2026 · DOI

• Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions.

  QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State · 2025 · DOI

• However, its exact spin, whether 1/2 or 3/2, remains undetermined in both experimental and theoretical studies.

  Deciphering Hypertriton and Antihypertriton Spins from Their Global Polarizations in Heavy-Ion Collisions · 2025 · DOI

• The paper identifies a gap in our understanding of the fundamental laws of physics, particularly with regards to the three fermion generations and the strong CP problem. The paper notes that prior work has failed to provide a satisfactory solution to these problems.

  Particle Physics from Vacuum Coherence: Six Problems Resolved Without New Particles · 2026 · DOI

• Lack of detailed QCD studies in e+e- collisions at low center-of-mass energies √s ≈ 20-80 GeV. Need for large event samples for QCD analyses.

  Physics case for low-$\sqrt{s}$ QCD studies at FCC-ee · 2026 · DOI

• Dedicated studies are required to investigate the achievable luminosity at √s = 40 GeV and 60 GeV using realistic FCC-ee beam parameters without further modifications to the baseline Z-pole machine configuration. The current parametric simulations need validation against detailed lattice and beam dynamics calculations to confirm the 1-month operation timeline for collecting O(10⁹) HFS events.

  Physics case for low-$\sqrt{s}$ QCD studies at FCC-ee · 2026 · DOI

• The challenge of determining a dynamically independent basis of operators within a truncated space. The difficulty of efficiently constructing the complete set of loop equations.

  Direct and indirect loop equations in lattice Yang-Mills theory · 2026 · DOI

• Experimental verification of the IFD framework. Development of new technologies and experimental designs based on the IFD framework.

  Deterministic Decay of Exotic Hadrons: A Phase-Vector Analysis of Mass Synchronization and Geometric Equilibrium · 2026 · DOI

• The current understanding of subatomic decay is based on probabilistic principles. The IFD framework challenges this understanding by proposing a deterministic mechanism.

  Deterministic Decay of Exotic Hadrons: A Phase-Vector Analysis of Mass Synchronization and Geometric Equilibrium · 2026 · DOI

• Further study of the QCD axion mass using the introduced isospin symmetry violating condensate component. Application of the result to other areas of physics.

  Isospin symmetry breaking and the mass of the QCD axion in a three-flavor linear sigma model · 2026 · DOI

• The need for a transparent analytical computation of the isospin symmetry breaking effect on the QCD axion mass. The lack of introduction of an isospin symmetry violating condensate component in previous models.

  Isospin symmetry breaking and the mass of the QCD axion in a three-flavor linear sigma model · 2026 · DOI

• The study is limited to 1+1-dimensional SU(2) lattice gauge theory with dynamical fermions. The emergence of random matrix behavior is observed, but the study does not provide a complete understanding of the underlying mechanisms. The study uses exact diagonalization, which may not be feasible for larger systems.

  Eigenstate thermalization in ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-dimensional SU(2) lattice gauge theory coupled with dynamical fermions · 2026 · DOI

• The study of the eigenstate thermalization hypothesis in 1+1-dimensional SU(2) lattice gauge theory with dynamical fermions is a new direction. The inclusion of dynamical fermions is a significant step forward. The emergence of random matrix behavior is not well understood.

  Eigenstate thermalization in ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> )-dimensional SU(2) lattice gauge theory coupled with dynamical fermions · 2026 · DOI

• Determining the values of the reduced system, such as the bound state with definite radius, energy, shell maximum, and mode frequency. Proving the full backreacted nonlinear stability of the complete integrated field. Exploring the implications of the integrated topological-amplitude-gauge field for the development of new technologies and materials.

  Integrated Topological-Amplitude-Gauge Field · 2026 · DOI

• The recurrent failure of simpler models to sustain simultaneously a stable topological carrier, a non-orphan current, and genuine higher-order composite closure. The lack of a formal substrate for DIFT that does not collapse it into ordinary field theory. The need for a dimensionless reduction logic to compress the parameter space into a smaller set of control ratios.

  Integrated Topological-Amplitude-Gauge Field · 2026 · DOI

• Further analysis of the orbital angular momentum content of other hadrons. Investigation of the implications of orbital angular momentum for hadronic observables.

  Orbital angular momentum in the pion and kaon: Rest-frame and light-front · 2026 · DOI

• where n is a lightlike 4-vector, n2 = 0, n · k⊥ = 0, and n · P = −m5 in the meson rest frame. The superscript in Eq. (15) indicates the light-front orbital angular momentum projection: L = 0 =↑↓=↓↑ means the LFWF has the light-front spins of the valence constituents antialigned; and L = 1 =↑↑=↓↓ has them aligned. We take this opportunity to again highlight the frame- 5 (rest-frame S - 5 (rest-frame P-wave) contribute to the light-front 5 (rest-frame P-wave) is the sole con- 5 term is higher twist dependence of OAM. Regarding Eq. (15), X 2 wave) and X 3 OAM L = 0 term and X 4 tributor to light-front L = 1. Since the X 1, it makes no contribution to ψ5(x, k2 ⊥). In comparison with the BSWF, a bound-state’s LFWF does have a probability interpretation. Consequently, its normalisation is guaranteed by an identity like that in nonrelativistic quantum mechanics: (cid:90) (cid:90) dx d2k⊥ (cid:104) |ψ0 5(x, k2 ⊥)|2 + k2 ⊥|ψ1 5(x, k2 ⊥)|2(cid:105). (16) 1 = 1 (2π)3 In this case, it is straightforward to identify the relative strength of the different light-front OAM components. We list the results in Table 4, obtained by using the procedure in Ref. to project the Bethe-Salpeter wave functions onto the light-front. Three important observations are signalled by Table 4. (i) Since Eq (16) is equivalent to ensuring unit electric charge for pseudoscalar mesons, then L = 1 components of all states considered herein are crucial parts of their LFWFs. They may be ignored only with foresight and careful compensation, and exploiting the results in Ref.. (ii) The relative strength of the L = 1 light-front OAM component diminishes with increasing quark current mass and the L = 0 contribution grows to compensate. (iii) The EHM-improved bRL Bethe-Salpeter kernel leads to a material enhancement of L = 1 components in pseudoscalar meson LFWFs. Indeed, the ground-state pion is roughly an equal mixture of L = 0 and L = 1 light-front OAM 7 The “proton spin crisis” has made the orbital angular momentum content of hadron bound states into a much debated topic. In these discussions, a variety of issues are often overlooked; so, we reiterate a few here. (a) Orbital angular momentum (OAM) is not a Poincaré invariant quantity; so, it is frame (hence, observer) dependent. (b) In QCD, a relativistic quantum field theory, like the degrees of freedom amongst which it is distributed, OAM depends on the energy scale of the probe used to infer its frame-dependent value. Herein, using continuum Schwinger function methods (CSMs), we focused on (a), elucidating aspects of the subjective character of in-hadron OAM by exposing its structural impacts within Nature’s most fundamental (near) Nambu- Goldstone (NG) bosons, viz. pions and kaons. (In the CSM context, elements of (b) are sketched elsewhere.) The analysis revealed and stressed the following points.

  Orbital angular momentum in the pion and kaon: Rest-frame and light-front · 2026 · DOI

• Future research could focus on applying the paper's framework to other complex systems. Future research could focus on experimental verification of the paper's predictions. Future research could focus on further developing the paper's geometric theory of physics.

  Geometric Theory of Physics: The ${}^{6}\Pi_4$ Model - Technical Compendium \& Empirical Evidence · 2026 · DOI

Most-cited papers in Quantum Chromodynamics and Particle Interactions

• Chiral perturbation theory for heavy hadrons and chiral effective field theory for heavy hadronic molecules · Physics Reports · 2023 · 240 citations
• Nonmagnetic Ground State in RuO 2 Revealed by Muon Spin Rotation · Physical Review Letters · 2024 · 167 citations
• Lattice calculation of the short and intermediate time-distance hadronic vacuum polarization contributions to the muon magnetic moment using twisted-mass fermions · Physical review. D/Physical review. D. · 2023 · 159 citations
• Determining the gluonic gravitational form factors of the proton · Nature · 2023 · 127 citations
• Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions · Physics Reports · 2024 · 112 citations
• Hadron spectra and quarks · American Journal of Physics · 1981 · 103 citations
• Gravitational Form Factors of the Proton from Lattice QCD · Physical Review Letters · 2024 · 78 citations
• Two-step QCA revisited: the necessity of context conditions · Quality & Quantity · 2018 · 75 citations
• A review of integrated QCA and statistical analyses · Quality & Quantity · 2016 · 68 citations
• Escape from S− · Learning and Motivation · 1971 · 62 citations

Most recent work

• Exclusive photoproduction of light and heavy vector mesons: thresholds to very high energies · The European Physical Journal C · 2026
• One-Octonion Brane-Bulk Framework — Methodological Audit Package v2.4 (a0 MOND chain traced end-to-end; section 9.3 and 12.4 flags discharged) · Zenodo (CERN European Organization for Nuclear Research) · 2026
• Study of hidden-charm, doubly-strange pentaquarks in $$\Lambda _b\rightarrow J/\psi \Xi ^- K^+$$ and $$\Xi _b\rightarrow J/\psi \Xi ^- \pi ^+$$ · The European Physical Journal C · 2026
• Pion physics with dressed quark-gluon vertices · The European Physical Journal C · 2026
• Electromagnetic characteristics as probes into the inner structures of the predicted $$\Xi _c^{(',*)}D^{(*)}_s$$ molecular states · The European Physical Journal C · 2026
• The $$\Lambda _{b} \rightarrow \Lambda $$ transition form factors in perturbative QCD approach · The European Physical Journal C · 2026
• Hidden-charm pentaquarks: electromagnetic structure in a diquark–diquark–antiquark model · The European Physical Journal C · 2026
• Electromagnetic form factors: a window into the $$D\Lambda _c$$, $$D^*\Lambda _c$$, and $$D\Lambda _c^*$$ molecular structure · The European Physical Journal C · 2026
• Analysis of the hidden-charm pentaquark candidates in the $$J/\psi p$$ mass spectrum with QCD sum rules · The European Physical Journal C · 2026
• Erratum Compendium (June 2026): Papers XIII, LVIII, LXXII, LXXX, CXV and Supplement Rev. 2 - with Paper LXXX v2 (Photon Sphere as Critical-Coherence Surface) · Zenodo (CERN European Organization for Nuclear Research) · 2026

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