There is an enormous interest in renormalization of quasi-particle (qp) dispersion relation of cuprate superconductors both below and above the critical temperature Tc because it enables determination of the fluctuation spectrum to which the qps are coupled. A remarkable discovery by angle-resolved photoemission spectroscopy (ARPES) is a sharp low energy feature (LEF) in qp spectra well below the superconducting energy gap but with its energy increasing in proportion to Tc and its intensity increasing sharply below Tc. This unexpected feature needs to be reconciled with d-wave superconductivity. Here, we present a quantitative analysis of ARPES data from Bi2Sr2CaCu2O 8+δ (Bi2212) using Eliashberg equations to show that the qp scattering rate due to the forward scattering impurities far from the Cu-O planes is modified by the energy gap below Tc and shows up as the LEF. This is also a necessary step to analyze ARPES data to reveal the spectrum of fluctuations promoting superconductivity.PACS numbers: 74.20.-z, 74.25.-q, 74.72.-h The accumulated high resolution ARPES data on the Bi-cuprate (BSCCO) over a wide doping and temperature range have revealed a sharp feature in the spectral function [1][2][3][4][5][6]. This occurs below about 10 meV along the nodal (0, 0) − (π, π) direction in the Brillouin zone. Further investigations revealed that the energy of the feature tracks T c regardless of the families of BSCCO or doping concentration, that its position is much smaller than the maximum energy gap ∆ 0 , and that its strength is sharply enhanced below T c . Here, we show that all these aspects of LEF can be explained by the forward scattering impurities located off the Cu-O planes. We substantiate this by combining computation of the selfenergy using the Eliashberg equations and analysis of the momentum distribution curve (MDC) of the ultra high resolution laser based ARPES intensity from Bi2212 in terms of the self-energy [7,8]. The off-plane impurity parameters from fitting the LEF in the superconducting (SC) state agree well with the normal state scattering rate determined independently as discussed below. This means that the qp scattering rate due to the off-plane impurities is modified by the energy gap below T c and remarkably shows up as the LEF in the d-wave SC state. The idea that forward scattering in d-wave superconductors may lead to unusual spectroscopic feature in SC state was already pointed out by Zhu, Hirschfeld and Scalapino [9][10][11][12]. Here, we quantitatively show the relevance of the idea by analyzing the ARPES experiments at various angles and temperatures to producing the low energy feature. We also compare the off-plane impurity idea with the proposal that the LEF may be due to scattering from acoustic phonons [13].The qp scattering rate Γ measured by ARPES in the normal state depends on direction on the Fermi surface and is significantly larger than k B T c , but this scattering does not show up in the resistivity [14]. This led to the proposal that it is due to dopant impurities wh...