= Invariant-mass resolution
{title2=$\sigma_M$}
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.
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