Polarization selection rules and superconducting gap anisotropy in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$

We discuss polarization selection rules for angle-resolved photoemission spectroscopy in Bi2212. Using these we show that the hump in the superconducting gap observed in the X quadrant in our earlier work is not on the main ${\mathrm{CuO}}_2$ band, but rather on an umklapp band arising from the structural superlattice. The intrinsic gap is most likely quite small over a range of ±10° about the diagonal directions.