dNdy

dN/dy is a differential quantity used in physics to denote the rate at which a quantity N changes with respect to a variable y, frequently interpreted as a particle yield per unit rapidity in high-energy collisions. In this context, N represents the number of produced particles, and y is rapidity, a kinematic variable related to the particle’s energy and momentum along the beam axis. Rapidities provide a convenient measure because differences in y are invariant under boosts along the beam direction, making dN/dy a useful descriptor of longitudinal particle production.

In collider experiments, dN/dy distributions can reveal the characteristics of the particle production process. For symmetric collisions (such as nucleus-nucleus or proton-proton at equal beams), the distribution is typically symmetric around mid-rapidity y = 0. Central collisions often yield higher multiplicities, reflected in a larger dN/dy near mid-rapidity. The shape of the distribution can indicate whether the system behaves collectively, as in hydrodynamic models, or whether particle production is dominated by other mechanisms.

dN/dy is closely related to dN/dη, the distribution with respect to pseudorapidity η, another angular variable that is easier to measure experimentally. The two are connected by a Jacobian that depends on particle mass and momentum; at high energies, y and η become approximately equivalent for highly relativistic particles, simplifying comparisons between theory and data.

Beyond spectroscopy, integrating dN/dy over y yields the total multiplicity, N, while the distribution’s normalization and energy or centrality dependence help constrain models of Quantum Chromodynamics and the dynamics of the collision system.