Open research questions in Quantum Chromodynamics and Particle Interactions

What the literature leaves open

• In this paper we focused on correlators involving two bulk operators and one defect operator, constraining the bulk-to-defect couplings of a bulk scalar Φ with both the double-twists [Φ ˆϕ]m1,m2,s or the triple-twists [Φ ˆϕ ˆϕ]m1,m2,s at large transverse spin. The main results for general CFTs are the closed-form expressions (3.19), (3.24), (3.32), and (3.33), while those = 4 SYM are (4.13) and (4.17). The specific to some correlators in d = 4 theories such as straightforward success of this approach leads to some natural directions for future exploration. The appealing feature of the setup we considered here is the simplicity compared to higher-point correlators without defects. The insertion of operators on the defect affects the kinematics in a controlled way. For instance, the defect-channel conformal blocks preserve the factorized structure that was crucial in the derivation of the Lorentzian inversion formula [49] and the dispersion relation [51, 52]. It is therefore natural to ask whether these techniques can be extended to our setup. This would give a rigorous and systematic way to understand the large-spin regime of the theory and it would provide a powerful computational technique for those theories that admit a perturbative expansion with some control over the spectrum of exchanged operators. N Throughout the paper we considered only defects with codimension greater than one. In some respect, the case of codimension-one defects (boundaries or interfaces) should be even simpler because the number of conformal cross ratios is further reduced, see for instance [63]. However, in this case there is no notion of transverse spin and the lightcone limit of the crossing equation should provide information on the defect spectrum at large conformal dimension. We leave a detailed analysis of this case for future work.

  Lightcone bootstrap for multipoint defect correlators · 2026 · DOI

• A Embedding space formalism B Generalized hypergeometric functions C Bulk-channel conformal blocks C.1 Bulk-bulk two-point function C.2 Bulk-bulk-defect three-point function D Large spin expansion of defect-channel blocks 1 6 9 9 14 16 18 22 23 24 25 25 25…

  Lightcone bootstrap for multipoint defect correlators · 2026 · DOI

• CONCLUSION Due to the manner in which stationary-state energies are extracted from matrices of temporal correlations of single- and multi-hadron operators in lattice QCD, the unfortunate possibility exists of flawed spectrum extrac- tions whenever an operator set is insufficient to pro- vide overlaps onto all relevant finite-volume stationary states.

  Investigating the role of tetraquark operators in lattice QCD studies of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:msub> <mml:mi>a</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo stretchy="false">(</mml:mo> <mml:mn>980</mml:mn> <mml:mo stretchy="false">)</mml:mo> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"> <mml:mrow> <mml:mi>κ</mml:mi> </mml:mrow> </mml:math> resonances · 2026 · DOI

• Reduces the open problem to a Lorentzian com- putation of the chiral curvature µ2 χ := ∂2 s B(0) along the JΠ-odd modulus of the saturated Born–Infeld functional, doi:10.

  The Charged-Lepton Koide Relation as a Unit-Dispersion Constraint · 2026 · DOI

• Continuous local gauge freedom, independently variable connection amplitudes, a Yang Mills action, propagating gluons, confinement, running coupling, and physical QCD remain to be derived.

  Paper 114BY: Native Local Color-Facing Transport, Shared-Vertex Link Selection, and Discrete Curvature Specificity in the Repeated Holosphere–QCD Architecture Testing Eight-Direction Adjoint Transport, Plaquette Holonomy, and Native-versus-Scrambled Gluon-Facing Structure After Paper 114BX · 2026 · DOI

• Six open problems are listed in the paper, including a first-principles derivation of β3, quantitative QH=3 production thresholds, and experimental confirmation of the Jeremie anomaly; the companion draft Paper XIX resolves the multi-component Jones-polynomial open problem and reformulates the quark-mass-from-midpoint-breaking open problem, but leaves the others open.

  HopfionSeries Paper XVIII - Preimage Topology and Confinement: Preimage Topology and Confinement: The $Q_H=3$ Sector of the Density-Feedback Hopfion - DRAFT · 2026 · DOI

• The Jeremie anomaly in four-jet BZ angle distributions at m3+m4>10 GeV is consistent with the topologically distinct 4th jet at a discrete predicted deflection angle, though a dedicated experimental analysis confirming this remains an open problem.

  HopfionSeries Paper XVIII - Preimage Topology and Confinement: Preimage Topology and Confinement: The $Q_H=3$ Sector of the Density-Feedback Hopfion - DRAFT · 2026 · DOI

• Two steps remain to be completed in this Goldman bracket argument: the ex- plicit computation on the SU(3) character variety of the hidden-octant torus, and the explicit demonstration that R induces a π/8 rotation of the symplectic form.

  Quarks, the Cabibbo Angle, and the Unified Generation Formula in the Three-Plane Scaffold · 2026 · DOI

• The results suggest that machine learning can provide a complementary contribution to both theoretical and experimental studies in hadron physics, especially by offering useful predictions for hadron states where data are limited, uncertainties are high, or physical properties have not yet been fully established. Additionally, probabilistic models incorporating uncertainty estimation would be valuable for hadron states where experimental measurements are sparse or conflicting.

  Predicting hadron mass and decay width using XGBoost: A unified machine learning framework for baryons and mesons · 2026 · DOI

• Resonance a3(1875) Unusually large width (about 385 MeV) h1(1900) Is probably the same state as h1(1965) a2(1950) Observed on the edge of energy measured in the Crystall Barrell experiment, Reasons of exclusion is therefore very speculative Its mass is not well defined, PDG provides ∼ 2050 MeV π1(2015) An exotic state in the quark model f0(2060) a1(2095) Unusually large width (around 450 MeV) η(2100) ω(2120) f2(2140) Unusually small width (49 ± 28 MeV) η(2190)…

  Hydrogen-Like Symmetry in Regge Spectrum of Light Mesons: Selection of States · 2026 · DOI

• Finally, we identify open issues and outline the discovery potential of future low-energy experiments, such as CBM, in resolving the high-density regime of the phase diagram.

  Exploring the QCD Phase Diagram · 2026 · DOI

• Additional open questions involve the quantitative description of the quark conden- sate mechanism, the strong CP problem and the role of the θ-term, as well as the difficulty in accurately predicting the spectral properties and decay modes of heavy mesons such as the J/ψ 15 [6, 55].

  Time-Dependent 3D Oscillator with Coulomb Interaction: An Alternative Approach for Analyzing Quark-Antiquark Systems · 2026 · DOI

• Future investigations should address the interplay between NLO corrections, target mass effects, and nuclear corrections to achieve a fully consistent description of DIS structure functions across the entire kinematic range.

  Heavy-quark contributions to the DIS structure functions F4 and F5 at NLO in the ACOT scheme · 2026 · DOI

• 1. Derive the Yang-Mills kinetic term − 1 µνF a µν from the recursion field energy density, establishing the gauge field dynamics from E = pr applied to the phase connection fields. 4F a 2. Derive the Weinberg angle θW ≈ 28.17 from the ratio ω2/ω6 at observable density, requiring the R(Dst) calibration of the n = 2 and n = 6 recursion frequencies. 3. Derive the coupling constants e, g, gs from the torsion interval structure and the fine-structure constant α [3]. 4. Derive the symmetry breaking mechanism quantitatively: connect the density- driven phase separation to the observed W and Z masses through the electroweak 6 Gilbert — Gauge Structure of the Standard Model from Torsion Phase Geometry paper’s torsion accumulation account. 5. Extend to the full Standard Model Lagrangian: assemble the gauge-covariant Dirac equation, the Yang-Mills kinetic terms, and the symmetry breaking sector into the complete U(1) × SU(2) × SU(3) Lagrangian.

  Gauge Structure of the Standard Model from Torsion Phase Geometry · 2026 · DOI

• 56 Membrane Thickness and the Proton Saturation Since the membrane’s residual factor is fundamentally defined as α/2, the area is not merely generated by fibers; it is fundamentally limited by the membrane thickness.

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

• 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 fast simulation studies for e+e− → qq collisions and background processes were only performed at √s = 91.2 GeV with IDEA detector response and ISR/FSR selection criteria from LEP. More elaborate studies with simulations for different detector designs are needed to confirm that the main conclusion of obtaining O(10⁹) hadronic events with reasonable purity over √s_had = 20–80 GeV remains valid across detector variations.

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

• The technical feasibility of operating the FCC-ee at CM energies below the Z pole (√s = 40, 60 GeV) has not been studied with dedicated realistic machine and detector simulations. While parametric accelerator settings simulations support the L ∝ √s luminosity scaling scenario, comprehensive studies accounting for all relevant machine and detector aspects are required before committing to dedicated low-energy runs.

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

• Identification of glueballs -- bound states of gauge bosons in Quantum Chromodynamics (QCD) -- is a very important open question in dynamics of the strong interaction.

  Scalar Glueball in a Top--Down Holographic Approach to QCD · 2015 · DOI

• This is a draft paper with several open problems noted below, two of which are addressed in the companion draft Paper XIX.

  HopfionSeries Paper XVIII - Preimage Topology and Confinement: Preimage Topology and Confinement: The $Q_H=3$ Sector of the Density-Feedback Hopfion - DRAFT · 2026 · DOI

• As such, the 2D system still has to be mapped to 1D, and the representability of the network is limited by the same 1D area law. In practice, size of the wave packets is limited by the combination of the finite system size and the time of the adiabatic ramp.

  Scattering and induced false vacuum decay in the two-dimensional quantum Ising model · 2026 · DOI

• Following the statistical analysis of section 4, an interesting open problem is to derive the asymptotic growth of the independent basis (including equations) analytically.

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

• Hence QCD at high temperature is also in the confining regime and elementary objects are SU (2NF ) symmetric "hadrons" with not yet known properties.

  SU$(2N_F)$ Symmetry of QCD at High Temperature and Its Implications · 2017 · DOI

Most-cited papers in Quantum Chromodynamics and Particle Interactions

• Three ways to decipher the nature of exotic hadrons: Multiplets, three-body hadronic molecules, and correlation functions · Physics Reports · 2024 · 112 citations
• Gravitational Form Factors of the Proton from Lattice QCD · Physical Review Letters · 2024 · 78 citations
• Quantum Simulation of SU(3) Lattice Yang-Mills Theory at Leading Order in Large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>N</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math> Expansion · Physical Review Letters · 2024 · 47 citations
• Heavy-Light Meson Masses in the Framework of Trigonometric Rosen-Morse Potential Using the Generalized Fractional Derivative · East European Journal of Physics · 2022 · 19 citations
• Generalized Parton Distributions from Lattice QCD · Acta Physica Polonica B Proceedings Supplement · 2023 · 14 citations
• Quark-Antiquark Study with Inversely Quadratic Yukawa Potential Using the Nikiforov-Uvarov-Functional-Analysis Method · East European Journal of Physics · 2022 · 13 citations
• Searching for New Physics with \(\bar {\mathcal {B}}(B_{s,d}\to \mu \bar \mu )/\Delta M_{s,d}\) · Acta Physica Polonica B · 2021 · 11 citations
• Effects of Gravitational Field of a Topological Defect on Statistical Properties of Heavy Quark-Antiquark Systems · East European Journal of Physics · 2022 · 11 citations
• "THE EFFECT OF TOPOLOGICAL DEFECT ON THE MASS SPECTRA OF HEAVY AND HEAVY-LIGHT QUARKONIA " · Eurasian Physical Technical Journal · 2022 · 8 citations
• On the Origin of the \(Y(4260)\) · Acta Physica Polonica B · 2020 · 7 citations

Most recent work

• 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
• 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
• Collins-Soper kernel and reduced soft function in lattice QCD · Physical Review D · 2026
• Heavy-quark contributions to the DIS structure functions F4 and F5 at NLO in the ACOT scheme · Journal of High Energy Physics · 2026
• Energy-energy correlator from the AdS Virasoro-Shapiro amplitude · Physical Review D · 2026
• Light baryonium states with exotic quantum numbers · The European Physical Journal C · 2026
• Hidden-charm and -bottom tetraquark states with $$J^{PC}=1^{-+}$$ via QCD sum rules · The European Physical Journal A · 2026
• A Simple Introduction to Soft Resummation · Acta Physica Polonica B · 2026
• Dynamical gluon effects in the three-dimensional structure of the pion · Physical Review D · 2026
• Revisiting the <i>S</i> -wave leptonic decay widths of charmonium and bottomonium via single-photon annihilation using the Bethe–Salpeter approach · International Journal of Modern Physics E · 2026

Related topics in Physics and Astronomy