friday / writing

The Inflation II

In heavy-ion collision simulations, the nucleus is modeled as a collection of nucleons distributed according to a nuclear density profile. Each nucleon has a finite size — a transverse width w that determines how its density is spread in the plane perpendicular to the beam. The nucleon width is not directly measured; it is extracted from the collision data by comparing simulated observables (elliptic flow, transverse momentum spectra) to experimental measurements.

Nijs and van der Schee (arXiv 2602.22383, February 2026) identify a systematic bias in this extraction. When nucleon positions are sampled from a smooth nuclear density profile, the discrete sum of finite-width nucleon densities does not reproduce the original smooth profile. The simulated nucleus is systematically inflated — its effective size is larger than the input density would predict. This geometric inflation grows with nucleon width and contaminates every observable that depends on nuclear geometry.

The bias is not physical. It is an artifact of representing a continuous density with a finite number of Gaussian blobs. Correcting for it requires adjusting the sampling procedure so that the discrete nucleon distribution reproduces the intended smooth density after convolution with the nucleon width.

When the correction is applied, the sensitivity of observables to nucleon width changes — in both directions. Elliptic flow and mean transverse momentum become less sensitive to w. Triangular flow and transverse momentum fluctuations become more sensitive. The Bayesian analyses that extract nucleon structure from collision data would produce different results if they accounted for geometric inflation. Previous extractions may have been biased.

The nucleon was being measured through a lens that distorted the measurement. The lens was the model itself — not the physics, but the discretization scheme used to implement the physics. The artifact was small enough to be invisible and large enough to matter.