On the difference between FOPT and CIPT for hadronic tau decays.

Area of Science:

• Theoretical Physics
• Quantum Chromodynamics

Background:

• Discrepancies in Borel representations of hadronic spectral function moments from CIPT and FOPT methods have caused significant theoretical uncertainties.
• These uncertainties impact precise determinations of the strong coupling constant from hadronic tau decays.

Purpose of the Study:

• To review and explain the differences between the Borel representations of hadronic spectral function moments obtained using the CIPT and FOPT methods.
• To investigate the impact of these differences on theoretical uncertainties in strong coupling determinations.

Main Methods:

• Focus on the large- flavor expansion approximation for closed-form expressions.
• Comment on the generalization to full Quantum Chromodynamics (QCD).

Main Results:

• The study explains the discrepancy in the behavior of FOPT and CIPT series, a long-standing issue in the literature.
• It is found that Operator Product Expansion (OPE) corrections differ for FOPT and CIPT.
• OPE corrections for CIPT do not follow the standard form.

Conclusions:

• The findings reconcile previous discussions on FOPT and CIPT series behavior.
• The results provide a clearer understanding of theoretical uncertainties in strong coupling determinations.
• The non-standard form of OPE corrections for CIPT is highlighted.