QCD sum rules on the complex Borel plane

Abstract

Borel transformed QCD sum rules conventionally use a real valued parameter (the Borel mass) for specifying the exponential weight over which hadronic spectral functions are averaged. In this paper, it is shown that the Borel mass can be generalized to have complex values and that new classes of sum rules can be derived from the resulting averages over the spectral functions. The real and imaginary parts of these novel sum rules turn out to have damped oscillating kernels and potentially contain a larger amount of information on the hadronic spectrum than the real valued QCD sum rules. As a first practical test, we have formulated the complex Borel sum rules for the phi meson channel and have analyzed them using the maximum entropy method, by which we can extract the most probable spectral function from the sum rules without strong assumptions on its functional form. As a result, it is demonstrated that, compared to earlier studies, the complex valued sum rules allow us to extract the spectral function with a significantly improved resolution and thus to study more detailed structures of the hadronic spectrum than previously possible.

22 pages, 10 figures

References in corpus (10)

• Maximum Entropy Analysis of the Spectral Functions in Lattice QCD
• QCD Sum Rules for Skeptics
• World Summary of ${\alpha }_s$ (2012)
• SU(2) chiral perturbation theory low-energy constants from 2+1 flavor staggered lattice simulations
• The V-A sum rules and the Operator Product Expansion in complex q^2-plane from tau-decay data
• Charmonium spectra at finite temperature from QCD sum rules with the maximum entropy method
• A Bayesian approach to QCD sum rules
• Thermal modification of bottomonium spectra from QCD sum rules with the maximum entropy method
• Parity projection of QCD sum rules for the nucleon
• A Bayesian analysis of the nucleon QCD sum rules

Cited by in corpus (8)

• Exotic Hadrons with Heavy Flavors -X, Y, Z and Related States-
• Constraining the strangeness content of the nucleon by measuring the $\varphi$ meson mass shift in nuclear matter
• Heavy meson spectroscopy under strong magnetic field
• Bayesian inference of real-time dynamics from lattice QCD
• Negative-parity nucleon excited state in nuclear matter
• Relativistic self-energy decomposition of nuclear symmetry energy and equation of state of neutron matter within QCD sum rules
• Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion, sum rules and the maximum entropy method
• Charmonium ground and excited states at finite temperature from complex Borel sum rules