  We applied the approach of K.-Y. Yang, T. M. Rice and F.-Ch. Zhang (YRZ) to
analyze the high resolution angular resolved photo-emission spectroscopy
(ARPES) data in BiSCO obtained recently at Brookhaven. In the YRZ ansatz a
constant RVB gap is assumed which leads to Luttinger zeros along the
antiferromagnetic Brillouin zone (AFBZ) and four Fermi pockets centered on the
nodal directions. We relax the assumption of a constant RVB gap function,
treating it as a Ising order parameter accompanied by thermal fluctuations. If
these thermal fluctuations are very strong leading to strictly short range
correlations in the spatial dependence of the RVB gap, then the reconstruction
of the Fermi surface into pockets will not survive. We examined the
intermediate case of critical fluctuations leading to a power law falloff of
the RVB gap correlations. To this end we followed the analysis recently
developed by two of us to treat the effect of the power law correlations in the
antiferromagnetic 2-dimensional xy model on the single electron Green's
function. The partial truncation of the Fermi surface to form pockets survives
in the presence of power law correlations. The linewidth of the quasiparticle
peaks increases with the exponent of the power law correlations. If this
exponent is set at the value of critical fluctuations in the 2-dimensional
Ising model a relatively small linewidth is obtained. If this exponent is
doubled, a linewidth comparable to the values found in recent ARPES experiments
on underdoped BiSCO (Tc = 65 K) at T = 140K was obtained. The anisotropic
suppression of the quasiparticle peak around the Fermi pockets hides the back
side of the pockets closest to the AFBZ to give essentially Fermi arcs seen
experimentally.
