Light fermion finite mass effects in non-relativistic bound states

Abstract

We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, Υ(1s) and tt production near threshold are briefly discussed.

Bottom quark mass from $ \varUpsilon $ sum rules to $ \mathcal{O}\left( {\alpha_s^3} \right) $

“…Since its mass m c is not much smaller than the soft scale, the charm quark mass effect on the effective potential and the bound state dynamics may not be negligible [58,59]. This effect has been analyzed in the context of Υ sum rules through the NNLO [60].…”

Spectrum and decays of kaonic hydrogen

“…in Ref. [27], in the same approach as used in the present paper (see also [13,28] for the related discussion). At the order of accuracy we are working, these contributions do not depend on the total angular momentum j.…”

The rare decay $K_{\mathrm{L}} \rightarrow\pi^{0} \mu^{ + } \mu^{-}$ within the SM

“…In particular, the lifetime of pionium was studied by the use of the Bethe-Salpeter equation [19] and in the framework of the quasipotential-constraint theory approach [20]. The width of the π + π − atom has also been analyzed within a non-relativistic effective field theory [21,22,23], which was originally developed for bound states in QED by Caswell and Lepage [24]. The non-relativistic framework has proven to be a very efficient method to evaluate bound state characteristics.…”