Systematic uncertainties of hadron parameters obtained with QCD sum rules

Abstract

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). Thus, the value of $R$ extracted from the sum rule is determined to a great extent by the contribution of the hadron continuum. Our main finding is that in the cases where the hadron continuum is not known and is modeled by an effective continuum threshold, the systematic uncertainties of the sum-rule procedure cannot be controlled.

Revtex 9 pages, typoes corrected, version to be published in Phys. Rev. D

References in corpus (5)

• New Results on B->pi, K, eta Decay Formfactors from Light-Cone Sum Rules
• f_B and f_B_s from QCD sum rules
• Quark-hadron duality and hadron properties from correlators of pseudoscalar and axial currents
• Heavy-to-light form factors: sum rules on the light cone and beyond
• Correspondence between QCD sum rules and constituent quark models

Cited by in corpus (49)

• The $XYZ$ states: experimental and theoretical status and perspectives
• QCD Sum Rules Approach to the $X,Y$ and $Z$ States
• Bottom Baryons
• Radiative Decays of the Heavy Flavored Baryons in Light Cone QCD Sum Rules
• Doubly heavy spin--1/2 baryon spectrum in QCD
• Analysis of the ${\frac{3}{2}}^{+}$ heavy and doubly heavy baryon states with QCD sum rules
• Light Scalar Tetraquark Mesons in the QCD Sum Rule
• The effective continuum threshold in dispersive sum rules
• OPE, charm-quark mass, and decay constants of D and D_s mesons from QCD sum rules
• Decay constants of heavy pseudoscalar mesons from QCD sum rules
• Decay constants of the charmed vector mesons $D^{\ast }$ and $D_s^{\ast }$ from QCD sum rules
• Mass-splittings of doubly heavy baryons in QCD
• Extraction of ground-state decay constant from dispersive sum rules: QCD vs potential models
• Can one control systematic errors of QCD sum rule predictions for bound states?
• Pion form factor at spacelike momentum transfers from local-duality QCD sum rule
• Accuracy of bound-state form factors extracted from dispersive sum rules
• Hadron form factors from sum rules for vacuum-to-hadron correlators
• Effective continuum threshold for vacuum-to-bound-state correlators
• Accurate bottom-quark mass from Borel QCD sum rules for $f_B$ and $f_{B_s}$
• Pion elastic and $({\pi }^0,\eta ,{\eta }^{\prime })\to \gamma {\gamma }^{\ast }$ transition form factors in a broad range of momentum transfers
• Bound-state parameters from dispersive sum rules for vacuum-to-vacuum correlators
• SVZ sum rules : 30 + 1 years later
• Analysis of the ${\Sigma }_Q$ baryons in the nuclear matter with the QCD sum rules
• The puzzle of the π-> γγ* transition form factor
• Extraction of bound-state parameters from dispersive sum rules
• Accurate decay-constant ratios $f_{B^{\ast }}/f_B$ and $f_{B_s^{\ast }}/f_{B_s}$ from Borel QCD sum rules
• Exotic B_c-like molecules in QCD Sum Rules
• Mass spectrum of the axial-vector hidden charmed and hidden bottom tetraquark states
• Analysis of the doubly heavy baryons in the nuclear matter with the QCD sum rules
• Accuracy of the pion elastic form factor extracted from a local-duality sum rule
• The ${\gamma }^{\ast }{\gamma }^{\ast }\to {\eta }_c$ transition form factor
• Isospin breaking in the decay constants of heavy mesons from QCD sum rules
• Weinberg like sum rules revisited
• Local-duality QCD sum rules for strong isospin breaking in the decay constants of heavy-light mesons
• Precise Ratios of Decay Constants of Vector over Pseudoscalar $B_{(s)}$ Mesons
• Pion form factor from local-duality QCD sum rule
• Charmed Pseudoscalar and Vector Mesons: a Comprehensive QCD Sum-Rule View of Their Decay Constants
• Heavy-Meson Decay Constants: QCD Sum-Rule Glance at Isospin Breaking
• Advances in QCD sum rule calculations
• Heavy-Meson Decay Constants: Isospin Breaking from QCD Sum Rules
• Strong Isospin Breaking in the Decay Constants of Heavy-Light Mesons from Local-Duality QCD Sum Rules
• On properties of the exotic hadrons from QCD sum rules
• Bound-state properties from field-theory correlators
• QCD Sum Rules for Heavy-Meson Decay Constants: Impact of Renormalization Scale and Scheme
• Constraining ${\lambda }_{B_s}$ by $B_s\to {\gamma }^{\ast }$ and $B_s\to \varphi$ form factors
• Quark-Hadron Duality and Effective Continuum Thresholds in Dispersive Sum Rules
• On the description of exotic hadron states within QCD sum rules
• How reliable are bound-state parameters obtained from QCD sum rules?
• Extracting Hadron Parameters from Dispersive Sum Rules