arXiv subjects

Z. -N. Xu

Publications and source records attributed to Z. -N. Xu.

4 recordsLinked to original sources

arXiv2026

Distribution amplitudes and functions of ground-state scalar and pseudoscalar charmonia

Charmonia are often supposed to provide simple hydrogen-like ``atomic'' systems that can be used to obtain insights into heavier-quark QCD. We use continuum Schwinger function methods to analyse this hypothesis in connection with ground-state scalar and pseudoscalar charmonia and find that a more complex picture of these states may be necessary. For instance, considering orbital angular momentum, the $χ_{c0}$ is not a simple $P$-wave system; similarly, the $η_c$ wave function contains more than merely $S$-wave contributions. The distribution amplitudes (DAs) and distribution functions (DFs) of these mesons are also nontrivial. For instance, the $χ_{c0}$ DA is not positive definite: owing to QCD symmetries, it possesses domains of balanced negative and positive support. This feature is also expressed in the $χ_{c0}$ DF, but differences between $χ_{c0}$ and $η_c$ DFs diminish under scale evolution. Notably, the light-front momentum fraction carried by glue is the same in both states: it is 10\% less than the in-pion glue momentum fraction. Whilst experimental confirmation of the predictions herein is unlikely, our results should serve as benchmarks for complementary theory attempts to understand local and global structural features of heavier-quark hadrons.

hep-ph↗

arXiv2026

Orbital angular momentum in the pion and kaon: rest-frame and light-front

Orbital angular momentum (OAM) is not a Poincaré invariant quantity; so, its value is observer dependent. Notwithstanding that, in quantum chromodynamics, a Poincaré-invariant theory, OAM is part of every hadron wave function. Using continuum Schwinger function methods, we elucidate both the subjective character of in-hadron OAM and expose some of its impacts on pion and kaon structure and observables. For instance, working with light-front projections of their Bethe-Salpeter wave functions, it is found that the pion is a roughly 50/50 mix of light-front OAM zero and one components and the kaon is a 60/40 system. The overall picture is that (near) Nambu-Goldstone modes are complex bound states, each with significant intrinsic OAM, independent of the observer's reference frame. This feature must be accounted for in the calculation of observables. Inductively, the same is true for all hadrons.

hep-ph↗

arXiv2026

Light-Front Transverse Nucleon Charge and Magnetisation Densities

Nucleon elastic electromagnetic form factors obtained using both the three-body and quark + fully-interacting-diquark pictures of nucleon structure are employed to calculate an array of light-front transverse densities for the proton and neutron and their dressed valence-quark constituents, viz. flavour separations of the proton and neutron results. These two complementary descriptions of nucleon structure deliver mutually compatible predictions, which match expectations based on modern parametrisations of available data, where such are available. Amongst other things, it is found that transverse-plane valence $u$- and $d$-quark Dirac radii are practically indistinguishable; but regarding kindred Pauli radii, the $d$ quark value is roughly 10% greater than that of the $u$-quark. Moreover, magnetically, the valence $d$ quark is far more active than the valence $u$ quark, probably because it has much greater orbital angular momentum. Both pictures of nucleon structure agree in predicting that, in a polarised nucleon, the transverse-plane charge densities are no longer rotationally invariant. Instead, for a $+\hat x$ polarised nucleon, positive charge is displaced in the $+\hat y$ direction, with the opposite effect for negative charge.

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arXiv2025

Distribution Functions of a Radially Excited Pion

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, $π_0$, and its first radial excitation, $π_1$, viz. valence, glue, and sea. Regarding Mellin moments of the valence DFs, the $m=0,1$ moments in both states are identical; but for each $m\geq 2$, that in the $π_0$ is greater than its partner in the $π_1$. Working with such information, pointwise reconstructions of the hadron-scale $π_{0,1}$ valence DFs are developed. The predicted $π_0$ valence DF is consistent with extant results. The $π_1$ 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 $x\approx 0.2,0.8$ and the secondary peaks at $x\approx 0.1,0.9$. Evolution to $ζ=3.2\,$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 $π_{0,1}$ valence DFs remain significant, but analogous differences between glue and sea DFs are far smaller. This analysis shows 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.

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