Euclidean-time sum rules for the nucleon yield rough mass and residue estimates but lack any usable fiducial window because power corrections and continuum contributions introduce larger uncertainties than in Borel sum rules.
A machine-rendered reading of the paper's core claim, the
machinery that carries it, and where it could break.
QCD sum rules extract hadron properties from correlation functions of quark currents. The usual approach applies a Borel transform that suppresses high-energy contributions and creates a window where both the operator-product expansion and the resonance-plus-continuum model can be trusted. The author instead keeps the correlator in coordinate space and studies its dependence on Euclidean time. In the nucleon channel this produces sum rules that still allow a crude extraction of the nucleon mass and its coupling to the current. However, the region where the theoretical and phenomenological sides overlap reliably shrinks to almost nothing once realistic uncertainties in the power corrections and the continuum threshold are included. The comparison therefore highlights that the Borel transform is not merely a technical convenience but an essential stabilizer for the method.
Core claim
A rough estimate of nucleon mass and residue is possible in coordinate space, but such sum rules are much more affected by uncertainties in power corrections and continuum contribution than the Borel ones: the fiducial interval is practically absent.
Load-bearing premise
That the size of the uncertainties assigned to the power corrections and continuum threshold in the Euclidean-time analysis is realistic and not underestimated relative to the Borel case.
read the original abstract
We explore a modification of QCD sum rules where, instead of Borel transforms of current correlators, one considers the correlators in coordinate space as functions of Euclidean time. Taking the nucleon channel as an example, we derive such Euclidean time sum rules and compare them with the traditional Borel sum rules. We show that a rough estimate of nucleon mass and residue is also possible working in coordinate space, but such sum rules are much more affected by the uncertainties in power corrections and continuum contribution than the Borel ones: the fiducial interval is practically absent.
Editorial analysis
A structured set of objections, weighed in public.
Desk editor's note, referee report, simulated authors' rebuttal, and a
circularity audit. Tearing a paper down is the easy half of reading it; the
pith above is the substance, this is the friction.
The abstract supplies no explicit list of free parameters or axioms; the comparison implicitly assumes standard QCD operator-product expansion and a resonance-plus-continuum spectral model whose uncertainties are taken as given.
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