Pion and Kaon Structure at the Electron-Ion Collider

TL;DR

The paper argues that most hadron mass arises from emergent QCD dynamics, especially dynamical chiral symmetry breaking, and contrasts this with the small explicit mass from the Higgs mechanism in Nambu–Goldstone bosons like the pion. It advocates a coordinated program combining phenomenology, continuum QCD, lattice QCD, and high-luminosity experiments at the Electron–Ion Collider to access pion and kaon structure via Sullivan processes, form factors, PDFs, GPDs, and fragmentation. It outlines five high-impact measurements that can map the mass budget and internal distributions in the pion and kaon, constrain the gluon content, and probe the trace anomaly’s role in mass generation. The work highlights strong synergy with lattice QCD and continuum approaches to interpret data and to illuminate how mass emerges in the Standard Model and governs the evolution of the Universe.

Abstract

Understanding the origin and dynamics of hadron structure and in turn that of atomic nuclei is a central goal of nuclear physics. This challenge entails the questions of how does the roughly 1 GeV mass-scale that characterizes atomic nuclei appear; why does it have the observed value; and, enigmatically, why are the composite Nambu-Goldstone (NG) bosons in quantum chromodynamics (QCD) abnormally light in comparison? In this perspective, we provide an analysis of the mass budget of the pion and proton in QCD; discuss the special role of the kaon, which lies near the boundary between dominance of strong and Higgs mass-generation mechanisms; and explain the need for a coherent effort in QCD phenomenology and continuum calculations, in exa-scale computing as provided by lattice QCD, and in experiments to make progress in understanding the origins of hadron masses and the distribution of that mass within them. We compare the unique capabilities foreseen at the electron-ion collider (EIC) with those at the hadron-electron ring accelerator (HERA), the only previous electron-proton collider; and describe five key experimental measurements, enabled by the EIC and aimed at delivering fundamental insights that will generate concrete answers to the questions of how mass and structure arise in the pion and kaon, the Standard Model's NG modes, whose surprisingly low mass is critical to the evolution of our Universe.

Figures (12)

• Figure 1: Twist-two parton distribution amplitudes at a resolving scale $\zeta=2 \,$GeV$=:\zeta_2$. A solid (green) curve – pion $\Leftarrow$ emergent mass generation is dominant; B dot-dashed (blue) curve – $\eta_c$ meson $\Leftarrow$ Higgs mechanism is the primary source of mass generation; C solid (thin, purple) curve -- asymptotic profile, 6x(1 - x); and D dashed (black) curve – "heavy-pion", i.e. a pion-like pseudo-scalar meson in which the valence-quark current masses take values corresponding to a strange quark $\Leftarrow$ the boundary, where emergent and Higgs-driven mass generation are equally important.
• Figure 2: Lattice-QCD computations of the pion’s electromagnetic charge radius (green circles Wang:2018pii, red down-triangle Chambers:2017tuf, cyan cross Koponen:2017fvm) as a function of $m_\pi^2$, compared with a continuum theory prediction Chen:2018rwz (blue curve within bands, which indicate response to reasonable parameter variation). The continuum analysis establishes $f_\pi r_\pi \approx\,$constant, from which it follows that the size of a Nambu-Goldstone mode decreases in inverse proportion to the active strength of the dominant mass generating mechanism. The empirical value of $r_\pi$ is marked by the gold star.
• Figure 3: Sullivan processes. In these examples, a nucleon's pion cloud is used to provide access to the pion's (a) elastic form factor and (b) parton distribution functions. $t = –(k-k^\prime)^2$ is a Mandelstam variable and the intermediate pion, $\pi^\ast(P=k-k^\prime)$, $P^2= –t$, is off-shell.
• Figure 4: Virtuality-dependence of pion twist-two PDA. Solid (blue) curve: $v_\pi =0$ result; and dot-dashed (green) curve, PDA at $v_\pi=31$. Even this appreciable virtuality only introduces a modest rms relative-difference between the computed PDAs; namely, 13%. Measured equivalently, the zero virtuality result differs by 34% from that appropriate to QCD's asymptotic limit (dotted, red curve).
• Figure 5: Geometric acceptances for detection of leading neutrons and the decay products of $\Lambda$ and $\Sigma$ particles in the integrated JLEIC detector concept, to tag the pion and kaon Sullivan processes.