Charm Effects in the $\bar{MS}$ Bottom Quark Mass from $\Upsilon$ Mesons

TL;DR

This paper investigates how a non-zero charm quark mass influences the $ar{MS}$ bottom quark mass determination from $$psilon mesons, revealing a shift of about -20 MeV and highlighting uncertainties from higher order corrections.

Contribution

It provides a detailed analysis of charm mass effects on bottom quark mass extraction, emphasizing the importance of non-analytic terms and higher order uncertainties.

Findings

Charm mass causes approximately -20 MeV shift in bottom quark mass.

Incomplete cancellation of non-analytic terms affects mass determination.

Uncertainty in higher order corrections could significantly alter the shift.

Abstract

We study the shift in the $\Upsilon$ mass due to a non-zero charm quark mass. This shift affects the value of the $\bar{\rm MS}$ $b$-quark mass extracted from the $\Upsilon$ system by about -20 MeV, due to an incomplete cancellation of terms that are non-analytic in the charm quark mass. The precise size of the shift depends on unknown higher order corrections, and might have a considerable uncertainty if they are large.