Collider-quality positron acceleration in plasma
In plain words
The usual plasma wake focuses electrons but pushes positrons apart, so positrons cannot be accelerated in it with good quality. A collider needs both, and no scheme yet works for positrons in experiment.
Precise statement
In the nonlinear blowout regime, plasma electrons are expelled and the ion column focuses electrons but defocuses positrons. Find a wake configuration (hollow channel, finite-radius plasma, electron filament, magnetized wake, quasi-linear wake) that simultaneously gives gradient above $1e7\,\mathrm{eV}/\mathrm{cm}$, energy-transfer efficiency above 30 percent, rms energy spread below 1 percent and collider-level emittance preservation. An answer is a demonstrated configuration or a proof that the requirements are incompatible.
What would settle it
An experiment accelerating a positron bunch meeting all four metrics simultaneously.
Status in the literature
Unverified note
Several schemes meet subsets of the requirements in simulation (2023-2026, e.g. magnetized wakes, arXiv:2608.30455); none meets all in experiment.