Low-energy renormalization of the electron dispersion of high-Tcsuperconductors

High-resolution angle-resolved photoemission spectroscopy studies in cuprates have detected low-energy changes in the dispersion and absorption of quasiparticles at low temperatures, in particular, in the superconducting state. Based on a $1/N$ expansion of the $t-J$-Holstein model, which includes collective antiferromagnetic fluctuations already in leading order, we argue that the observed low-energy structures are mainly caused by phonons and not by spin fluctuations, at least, in the optimal and overdoped regime.