Systematic uncertainties of hadron parameters obtained with QCD sum rules

Understand

We study the uncertainties of the determination of the ground-state parameters from Shifman-Vainshtein-Zakharov (SVZ) sum rules, making use of the harmonic-oscillator potential model as an example.

• In this case, one knows the exact solution for the polarization operator $\Pi(\mu)$, which allows one to obtain both the OPE to any order and the spectrum of states.
• We start with the OPE for $\Pi(\mu)$ and analyze the extraction of the square of the ground-state wave function, $R\propto|\Psi_0(\vec r=0)|^2$, from an SVZ sum rule, setting the mass of the ground state $E_0$ equal to its known value and treating the effective continuum threshold as a fit parameter.
• We show that in a limited ``fiducial'' range of the Borel parameter there exists a solution for the effective threshold which precisely reproduces the exact $\Pi(\mu)$ for any value of $R$ within the range $0.7 \le R/R_0 \le 1.15$ ($R_0$ is the known exact value).