Invariant-mass resolution (${\sigma }_M$)

The simulation separates a stipulated physical distribution from measurement broadening. Its Cauchy distribution is only a convenient resonance-shaped input, not a complete quantum scattering model. Spatial resolution, magnetic field calibration, Multiple Coulomb scattering, stopping power and incorrect daughter identities all propagate into the measured invariant mass. Instrumental broadening must be understood before interpreting an observed width as a lifetime.

Selection also changes the shape. A momentum threshold can remove low-invariant mass pairs; a fit that fixes the candidate parent's mass would artificially concentrate that same mass and cannot supply an independent search distribution. Compare accepted simulated events with the input distribution, vary justified selection criteria, and check neighboring invariant mass intervals. A peak supported only by one untested selection is weaker evidence than a structure that survives calibration and background checks. The smooth background in the figure is a stipulated control component, not a claim that every physical background is smooth.