Journal Article

QCD sum rules on the complex Borel plane

Ken-Ji Araki, Keisuke Ohtani, Philipp Gubler and Makoto Oka

in Progress of Theoretical and Experimental Physics

Published on behalf of The Physical Society of Japan

Volume 2014, issue 7
Published online July 2014 | e-ISSN: 2050-3911 | DOI:

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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 complex Borel sum rules for the [math]-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.

Keywords: D32; B67

Journal Article.  8229 words.  Illustrated.

Subjects: Nuclear Physics ; Particles and Fields

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