The emergence of massless (Nambu-Goldstone) bosons in association with a dynamically global broken symmetry is a long known and widespread phenomenon in physics. However, practically nothing is known about the expressions of Nambu–Goldstone boson character on the internal structure of these bound states. Indeed, their structure is often ignored. In strong interactions, pions and kaons are the (would-be) Nambu-Goldstone bosons and experiments underway or planned at existing or anticipated high-energy, high-luminosity facilities will gather data that it is hoped will enable maps to be drawn of their internal structure. Meanwhile, theory and phenomenology find themselves in something of a quagmire. Herein, we provide a snapshot of the current status, highlighting issues under debate and identifying areas that deserve greater attention so that best use can be made of what is likely to be a huge volume of data delivered in the next decade or so.

A reaction model for γ + p → V + p, V=ρ ^0, ϕ , J/ψ , , which exposes the quark–antiquark content of the photon in making the transition where depends on V, and couples the intermediate system to the proton’s valence quarks via Pomeron ( ℙ ) exchange, is used to deliver a unified description of available data – both differential and total cross sections – from near threshold to very high energies, W, for all the V-mesons. For the , this means 10≲ W/GeV≲ 2000. Also provided are predictions for the power-law exponents that are empirically used to characterise the large-W behaviour of the total cross sections and slope parameters characterising the near-threshold differential cross sections. Appealing to notions of vector meson dominance, the latter have been interpreted as vector-meson–proton scattering lengths. The body of results indicates that it is premature to link any γ + p → V + p data with, for instance, in-proton gluon distributions, the quantum chromodynamics trace anomaly, or pentaquark production. Further developments in reaction theory and higher precision data are required before the validity of any such links can be assessed.

The bulk of visible mass is supposed to emerge from nonperturbative dynamics within quantum chromodynamics (QCD). Following years of development and refinement, continuum and lattice Schwinger function methods have recently joined in revealing the three pillars that support this emergent hadron mass (EHM); namely, a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with running masses that take constituent-like values at infrared momenta. One may argue that EHM and confinement are inextricably linked; and theory is now working to expose their manifold expressions in hadron observables and highlight the types of measurements that can be made in order to validate the paradigm. This contribution sketches these ideas via the unified explanation of pion and proton electromagnetic and gravitational form factors.

Using continuum Schwinger function methods, a coherent set of predictions for proton, Λ and Σ^0 distribution functions (DFs) has been made available – both helicity dependent and unpolarised. The results and comparisons between them reveal impacts of diquark correlations and SU(3)-flavour symmetry breaking, some of which are highlighted in this contribution. For instance: in-proton ratios of helicity-dependent/unpolarised valence-quark DFs are presented; it is highlighted that, were it not for the presence of axialvector diquarks in the Σ^0, the valence strange quark would carry none of the Σ^0 spin; and the sign and size of polarised gluon DFs is discussed – at a scale typical of modern measurements, gluon partons carry roughly 40

The profile of the pion valence quark distribution function (DF) remains controversial. Working from the concepts of QCD effective charges and generalised parton distributions, we show that since the pion elastic electromagnetic form factor is well approximated by a monopole, then, at large light-front momentum fraction, the pion valence quark DF is a convex function described by a large-x power law that is practically consistent with expectations based on quantum chromodynamics.

In quantum field theory, the vacuum is popularly considered to be a complex medium populated with virtual particle + antiparticle pairs. To an observer experiencing uniform acceleration, it is generally held that these virtual particles become real, appearing as a gas at a temperature that grows with the acceleration. This is the Unruh effect. However, it has been shown that vacuum complexity is an artifact produced by treating quantum field theory in a manner that does not manifestly enforce causality. Choosing a quantization approach that patently enforces causality, the quantum field theory vacuum is barren, bereft even of virtual particles. We show that acceleration has no effect on a trivial vacuum; hence, there is no Unruh effect in such a treatment of quantum field theory. Since the standard calculations suggesting an Unruh effect are formally consistent, insofar as they have been completed, there must be a canceling contribution that is omitted in the usual analyses. We argue that it is the dynamical action of conventional Lorentz transformations on the structure of an Unruh detector.

Using a symmetry preserving treatment of a vector ⊗ vector contact interaction (SCI), results are delivered for the four kaon transverse momentum dependent parton distribution functions (TMDs), viz. helicity-independent (HI) and Boer–Mulders (BM) TMDs for the kaon’s u, s valence degrees of freedom. In completing this analysis, we are able to deliver insights into, amongst other things, the role played by emergent hadron mass (EHM) phenomena in producing these TMDs; the EHM modulating effect of the Higgs-boson coupling that produces the strange quark current mass; the impact of gauge link models on whether predictions satisfy the positivity constraint that bounds the BM function relative to the HI TMD; and the size of the BM shift and effects thereupon of off-diagonal terms in the associated scale-evolution kernel.

Treating baryons as quark + interacting-diquark bound states, a symmetry-preserving formulation of a vector × vector contact interaction (SCI) is used to deliver an extensive, coherent set of predictions for , ^0 baryon unpolarised and polarised distribution functions (DFs) – valence, glue, and four-flavour separated sea – and compare them with those of a like-structured nucleon. , ^0 baryons are strangeness negative-one isospin partners within the SU(3)-flavour baryon octet. This makes such structural comparisons significant. The study reveals impacts of diquark correlations and SU(3)-flavour symmetry breaking on , ^0 structure functions, some of which are significant. For instance, were it not for the presence of axialvector diquarks in the ^0 at the hadron scale, the s quark could carry none of the ^0 spin. The discussion canvasses issues that include helicity retention in hard scattering processes; the sign and size of polarised gluon DFs; and the origin and decomposition of baryon spins. Interpreted judiciously, the SCI analysis delivers an insightful explanation of baryon structure as expressed in DFs.

The Drell–Levy–Yan relation is employed to obtain pion and kaon elementary fragmentation functions (EFFs) from the hadron-scale parton distribution functions (DFs) of these mesons. Two different DF sets are used: that calculated using a symmetry-preserving treatment of a vector $$\times $$ × vector contact interaction (SCI) and the other expressing results obtained using continuum Schwinger function methods (CSMs). Thus determined, the EFFs serve as driving terms in a coupled set of hadron cascade equations, whose solution yields the complete array of hadron-scale fragmentation functions (FFs) for pion and kaon production in high energy reactions. After evolution to scales typical of experiments, the SCI and CSM FF predictions are seen to be in semiquantitative agreement. Importantly, they conform with a range of physical expectations for FF behaviour on the endpoint domains $$z\simeq 0, 1$$ z ≃ 0 , 1 , e.g., nonsinglet FFs vanish at $$z=0$$ z = 0 and singlet FFs diverge faster than 1/ z . Predictions for hadron multiplicities in jets are also delivered. They reveal SU(3) symmetry breaking in the charged-kaon/neutral-kaon multiplicity ratio, whose size diminishes with increasing reaction energy, and show that, with increasing energy, the pion/kaon ratio in $$e^+ e^- \rightarrow h X$$ e + e - → h X diminishes to a value that is independent of hadron masses.

Working with the $29$ available data on the ratio of proton electric and magnetic form factors, $\mu_p G_E^p(Q^2)/ G_M^p(Q^2)$, and independent of any model or theory of strong interactions, we use the Schlessinger point method to objectively address the question of whether the ratio possesses a zero and, if so, its location. Our analysis predicts that, with 50% confidence, the data are consistent with the existence of a zero in the ratio on $Q^2 \leq 10.37\,$GeV$^2$. The level of confidence increases to $99.9$\% on $Q^2 \leq 13.06\,$GeV$^2$. Significantly, the likelihood that existing data are consistent with the absence of a zero in the ratio on $Q^2 \leq 14.49\,$GeV$^2$ is $1/1$-million.

Using available information from Drell-Yan data on pion and kaon structure functions, an approach is described which enables the development of pointwise profiles for all pion and kaon parton distribution functions (DFs) without reference to theories of hadron structure. The key steps are construction of structure-function-constrained probability-weighted ensembles of valence DF replicas and use of an evolution scheme for parton DFs that is all-orders exact. The DFs obtained express qualitatively sound features of light-meson structure, e.g., the effects of Higgs boson couplings into QCD and the size of heavy-quark momentum fractions in light hadrons. In order to improve the results, additional and more precise data on the u-quark-in-kaon, u^K, to u-quark-in-pion, u^π, DF ratio would be necessary. Of greater value would be extraction of u^K alone, thereby avoiding inference from the ratio: currently, the data-based form of u^K is materially influenced by results for u^π.

A symmetry-preserving analysis of strong interaction quantum field equations is used to complete a unified treatment of pion, kaon, and nucleon electromagnetic and gravitational form factors. Findings include a demonstration that the pion near-core pressure is roughly twice that in the proton, so both are significantly greater than that of a neutron star; parton species separations of the nucleon’s three gravitational form factors, in which, inter alia, the glue-to-quark ratio for each form factor is seen to take the same constant value, independent of momentum transfer; and a determination of proton radii orderings, with the mechanical (normal force) radius being less than the mass-energy radius, which is less than the proton charge radius. This body of predictions should prove useful in an era of experiments that will enable them to be tested.

The Circular Electron-Positron Collider (CEPC), a proposed next-generation Higgs factory, provides new opportunities to explore physics beyond the Standard Model (SM). With its clean electron-positron collision environment and the ability to collect large samples of Higgs, W, and Z bosons, the CEPC enables precision measurements and searches for new physics. This white paper outlines the CEPC's discovery potential, including studies of exotic decays of the Higgs, Z, and top quarks, dark matter and dark sector phenomena, long-lived particles, supersymmetry, and neutrino-related signatures. Advanced detector technologies and reconstruction techniques, such as one-to-one correspondence reconstruction and jet origin identification, significantly improve sensitivity to rare and weakly interacting processes. The CEPC is particularly well suited to probe the electroweak phase transition and test models of electroweak baryogenesis and dark sector interactions. In addition, global fit analyses highlight the CEPC's complementary role in constraining a wide range of new physics scenarios. These features position the CEPC as a powerful tool for exploring the next frontier in fundamental particle physics in the post-Higgs discovery era.

A unified set of predictions for pion, kaon and nucleon gravitational form factors is obtained using a symmetry-preserving truncation of each relevant quantum field equation. A crucial aspect of the study is the self-consistent characterization of the dressed quark-graviton vertices, applied when probing each quark flavor inside mesons or nucleons. The calculations reveal that each hadron's mass radius is smaller than its charge radius, matching available empirical inferences; moreover, core pressures are significantly greater than those in neutron stars. This set of predictions is expected to be instrumental as forthcoming experiments provide opportunities for validation.

Working with a Poincaré-covariant quark + diquark, q(qq), Faddeev equation approach to nucleon structure, a refined symmetry preserving current for electron + nucleon elastic scattering is developed. The parameters in the interaction current are chosen to ensure that the q(qq) picture reproduces selected results from contemporary 3-body analyses of nucleon elastic electromagnetic form factors. Although the subset of fitted results is small, the q(qq) picture reproduces almost all the 3-body predictions and often results in better agreement with available data. Notably, the q(qq) framework predicts a zero in G_E^p/G_M^p, the absence of such a zero in G_E^n/G_M^n, and a zero in the proton's d-quark Dirac form factor. Derived q(qq) results for proton flavour-separated light-front-transverse number and anomalous magnetisation densities are also discussed. With the q(qq) framework thus newly benchmarked, one may proceed to comparisons with a broader array of 3-body results. This may enable new steps to be made toward answering an important question, viz. is the quark + fully-interacting diquark picture of baryon structure only a useful phenomenology or does it come close to expressing robust features of baryon structure?

Developing an understanding of phenomena driven by the emergence of hadron mass (EHM) is one of the most challenging problems in the Standard Model. This discussion focuses on the impact of results on nucleon resonance (N*) electroexcitation amplitudes (or γvpN* electrocouplings) obtained from experiments during the 6 GeV era in Hall B at Jefferson Lab on understanding EHM. Analyzed using continuum Schwinger function methods (CSMs), these results have revealed new pathways for the elucidation of EHM. A good description of the Δ(1232)3/2+, N(1440)1/2+, and Δ(1600)3/2+ electrocouplings, achieved by CSM analyses that express a realistic dressed quark mass function, sheds light on the strong interaction dynamics underlying EHM. Extensions to N* studies for higher-mass states are outlined, as well as experimental results anticipated in the 12 GeV era at Jefferson Lab and those that would be enabled by a further increase in the beam energy to 22 GeV.

The bulk of visible mass is supposed to emerge from nonperturbative dynamics within quantum chromodynamics (QCD) -- the strong interaction sector of the Standard Model. Following years of development and refinement, continuum and lattice Schwinger function methods have recently joined in revealing the three pillars that support this emergent hadron mass (EHM); namely, a nonzero gluon mass-scale, a process-independent effective charge, and dressed-quarks with constituent-like masses. One may argue that EHM and confinement are inextricably linked; and theory is now working to expose their manifold expressions in hadron observables and highlight the types of measurements that can be made in order to validate the paradigm. This contribution sketches the role played by EHM in shaping hadron electromagnetic and gravitational form factors, exciting nucleon resonances, and moulding hadron parton distributions.

Abstract A symmetry preserving treatment of a vector $$\otimes $$ ⊗ vector contact interaction (SCI) is used as the basis for calculations of the two pion transverse momentum dependent parton distribution functions (TMDs); namely, that for unpolarised valence degrees-of-freedom and the analogous Boer–Mulders (BM) function. Amongst other things, the analysis enables the following themes to be addressed: the quark current mass dependence of pion TMDs; the impact of the gauge link model on the positivity constraint that bounds the BM function relative to the unpolarised TMD; the equivalence of direct diagrammatic and light-front wave function TMD calculations; and the size of the BM shift. Interpreted astutely, these SCI results enable one to draw insightful pictures of pion TMDs.

A nonperturbatively-improved, symmetry-preserving approximation to the quantum field equations relevant in calculations of meson masses and interactions is used to deliver predictions for all distribution functions (DFs) of the ground state pion, $$\pi _0$$ π 0 , and its first radial excitation, $$\pi _1$$ π 1 , viz. valence, glue, and sea. Regarding Mellin moments of the valence DFs, the $$m=0,1$$ m = 0 , 1 moments in both states are identical; but for each $$m\ge 2$$ m ≥ 2 , that in the $$\pi _0$$ π 0 is greater than its partner in the $$\pi _1$$ π 1 . Working with such information, pointwise reconstructions of the hadron-scale $$\pi _{0,1}$$ π 0 , 1 valence DFs are developed. The predicted $$\pi _0$$ π 0 valence DF is consistent with extant results. The $$\pi _1$$ π 1 valence DF is novel: it possesses three-peaks, with the central maximum partnered by secondary peaks on either side, each separated from the centre by a zero: the zeroes lie at $$x\approx 0.2,0.8$$ x ≈ 0.2 , 0.8 and the secondary peaks at $$x\approx 0.1,0.9$$ x ≈ 0.1 , 0.9 . Evolution to $$\zeta =3.2\,$$ ζ = 3.2 GeV, a typical scale for nonperturbative calculations, is accomplished using an evolution scheme for parton DFs that is all-orders exact. At this higher scale, differences between the $$\pi _{0,1}$$ π 0 , 1 valence DFs remain significant, but analogous differences between glue and sea DFs are far smaller. This analysis confirms that, owing to constraints imposed by chiral symmetry and the pattern by which it is broken in Nature, there are noticeable differences between the structural properties of the pion ground state and its radial excitations.

A light-front holographic model is used to illustrate an algebraic scheme for constructing a representation of a hadron's zero-skewness generalised parton distribution (GPD) from its valence-quark distribution function (DF) and electromagnetic form factor, FH, without reference to deeply virtual Compton scattering data. The hadron's mass distribution gravitational form factor, AH, calculated from this GPD is harder than FH; and, for each hadron, the associated mass-density profile is more compact than the analogous charge profile, with each pion near-core density being larger than that of its proton partner. These features are independent of the scheme employed.