### Abstract

We derive a formula which relates the QCD potentials in momentum space and in position space in terms of the β function of the renormalization-group equation for the potential. This formula is used to study the theoretical uncertainties in the potential and in particular in its application to the determination of the pole mass m_{b} when we use perturbative expansions. We demonstrate the existence of these uncertainties for the Richardson potential explicitly and then discuss the limited theoretical accuracy in the perturbative QCD potential. We conclude that a theoretical uncertainty of m_{b} much below 100 MeV would not be achievable within perturbative QCD.

Original language | English |
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Pages (from-to) | 352-358 |

Number of pages | 7 |

Journal | Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics |

Volume | 428 |

Issue number | 3-4 |

DOIs | |

Publication status | Published - 1998 Jun 4 |

### ASJC Scopus subject areas

- Nuclear and High Energy Physics

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## Cite this

Jezabek, M., Peter, M., & Sumino, Y. (1998). Relation between QCD potentials in momentum and position space.

*Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics*,*428*(3-4), 352-358. https://doi.org/10.1016/S0370-2693(98)00418-3