Steve Sharpe's fourth lecture contradicts some of the points of my
fourth lecture. Here I make a few comments on these issues. I'll
plan to edit this file if we resolve some of these questions. I
believe we agree that the picture on Steve's slide 41 is exactly what
generates the relevant additive mass shift around which the
controversy revolves.
A particular problem is that the 28/3 scaling appearing in Steve's
fourth lecture, slides 42-46 is not correct. In my lecture 2, slides
13-17, I discuss in continuum language how non-trivial topology gives
the eta prime its mass, which is expected to be of order lambda qcd.
This gives us a handle on how the topology depends on cutoff. Then in
my lecture 4 slides 16-18 I discuss how this implies the semiclassical
arguments on the scaling give the wrong answer. If the topological
effects are as suppressed as the semiclassical argument suggests, then
the eta prime will not get its large mass. My slides 10 and 11 of
lecture 4 are meant to indicate that the uncertainty in the quark mass
and the eta prime mass are intimately entwined.
As for using partially quenched fermions to determine the mass,
with only one sea quark there is no reason for the partially quenched
pion to become massless. As psibar psi behaves smoothly for the sea quark,
there cannot be an accumulation of small complex zeros of the Dirac operator.
As the valence quarks use the same propagator, one doesn't expect
the condensation required to get a Goldstone boson. The valence
chiral symmetry should remain unbroken in this case.
At a general level, as only the up quark mass passes through zero,
every conventional physical process shows no structure. This includes
all particle masses and scattering amplitudes. It seems absurd to me
that some complicated abstract theoretical construction such as
topological susceptibility could reveal something new. Indeed, even
the correlator of ffdual with ffdual at another point (known to be
negative) should behave smoothly in m_up. The conventionally claimed
zero in topological susceptibility can only be subtly hidden in the
contact term. This seems very bizarre and physically unnecessary.
Finally, it is unclear to me why there should be the a^2 decrease in
the spurious cuts on Steve's backup slide 56. At least naively the
scaling should be the same as the physical cuts since we are just
taking different quark combinations.