Simultaneous decoupling of bottom and charm quarks

TL;DR

This paper derives precise three-loop relations connecting the parameters and light fields of QCD with heavy bottom and charm quarks to those in an effective theory without these heavy flavours, accounting for their mass ratio.

Contribution

It provides the first three-loop accuracy relations for decoupling parameters and currents in QCD with two heavy quarks, explicitly including the m_c/m_b dependence.

Findings

Explicit three-loop decoupling relations derived.

Exact dependence on m_c/m_b incorporated.

Relations applicable to parameters and bilinear currents.

Abstract

Parameters and light fields of the QCD Lagrangian with two heavy flavours, b and c, are related to those in the low-energy effective theory without these flavours, to three-loop accuracy taking into account the exact dependence on m_c/m_b. Similar relations for bilinear quark currents are also considered.