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Observations of debris disks have significantly improved over the past decades, both in terms of sensitivity and spatial resolution. At near-infrared wavelengths, new observing strategies and post-processing algorithms allow us to drastically improve the final images, revealing faint structures in the disks. These structures inform us about the properties and spatial distribution of the small dust particles. We present new $H$-band observations of the disk around HD 129590, which display an intriguing arc-like structure in total intensity but not in polarimetry, and propose an explanation for the origin of this arc. Assuming geometric parameters for the birth ring of planetesimals, our model provides the positions of millions of particles of different sizes to compute scattered light images. We demonstrate that if the grain size distribution is truncated or strongly peaks at a size larger than the radiation pressure blow-out size we are able to produce an arc quite similar to the observed one. If the birth ring is radially narrow, given that particles of a given size have similar eccentricities, they will have their apocenters at the same distance from the star. Since this is where the particles will spend most of their time, this results in a "apocenter pile-up" that can look like a ring. Due to more efficient forward scattering this arc only appears in total intensity observations and remains undetected in polarimetric data. This scenario requires sharp variations either in the grain size distribution or for the scattering efficiencies $Q_\mathrm{sca}$. Alternative possibilities such as a wavy size distribution and a size-dependent phase function are interesting candidates to strengthen the apocenter pile-up. We also discuss why such arcs are not commonly detected in other systems, which can mainly be explained by the fact that most parent belts are usually broad., Accepted for publication in A&A, abstract shortened