This paper argues that a known geometric effect, called spectator shadowing, can produce the same signature that some experiments have taken as evidence for a change in the collision medium. The authors show that the observed breaking of constituent quark number (NCQ) scaling of elliptic flow at low beam energies can arise because passing nucleons — the “spectators” — sit near the collision zone and absorb or deflect particles before they escape.

NCQ scaling is the empirical observation that the elliptic flow of different hadrons (particles made of quarks) lines up when you divide transverse momentum and the flow by the number of constituent quarks. Many researchers have taken good NCQ scaling as a sign that hadrons formed by quark coalescence, which in turn suggests a deconfined, partonic stage in the collision. Recent low-energy measurements show that this scaling breaks down, and that was interpreted by some as a hint that the partonic stage disappears at low energy.

The authors introduce a simple, test framework that adds the effect of spectator shadowing to the usual coalescence picture. They model hadrons forming from nearby quarks in a narrow-coalescence limit, and they model the bypassing spectators with a ballistic Glauber picture. The key point is that the probability for a produced particle to escape without further absorption depends on the emission angle. This escape probability multiplies the source emission pattern, so the measured flow is the sum of the intrinsic source anisotropy and a shadowing contribution. The authors also outline a way, using a Fourier decomposition of the escape probability, to subtract the shadowing part and recover the underlying source flow.

Using a toy calculation, the paper shows that spectator shadowing grows stronger at lower collision energies because the spectators spend more time near the fireball. The model produces a split in the elliptic flow of different hadron species that looks qualitatively like the NCQ-scaling breaking seen by the STAR-FXT measurements. The shadowing effect depends on species through effective absorption cross sections and on hadron mass through particle velocity. When the authors subtract the modeled shadowing contribution, the original NCQ scaling is restored by construction in their setup.