Hadron form factors from sum rules for vacuum-to-hadron correlators

TL;DR

This paper investigates the extraction of hadron form factors using vacuum-to-hadron correlators in QCD sum rules, highlighting challenges in fixing the effective continuum threshold and analyzing the correlator in quantum mechanics.

Contribution

It provides an exact analysis of the correlator in quantum mechanics and examines the difficulties in applying standard sum rule procedures to vacuum-to-hadron correlators.

Findings

Fixing the effective continuum threshold is problematic in sum rule calculations.

Exact quantum mechanical analysis reveals limitations of current sum rule methods.

Challenges in isolating ground-state form factors from vacuum-to-hadron correlators.

Abstract

We analyse the extraction of the bound-state form factor from vacuum-to-hadron correlator, which is the basic object for the calculation of hadron form factors in the method of light-cone sum rules in QCD. We study this correlator in quantum mechanics, calculate it exactly, and derive the corresponding OPE. We then apply the standard procedures of QCD sum rules to isolate the ground-state form factor from this correlator. We demonstrate that fixing the effective continuum threshold, one of the key ingredients of the sum-rule calculation of bound-state parameters, poses a serious problem for sum rules based on vacuum-to-hadron correlators.