Light Fermion Finite Mass Effects in Non-relativistic Bound States

Dolors Eiras; Joan Soto

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Light Fermion Finite Mass Effects in Non-relativistic Bound States

Dolors Eiras, Joan Soto

High Energy Physics - Phenomenology · Submitted 8 May 2000

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim 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.

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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, \Upsilon (1s) and t\bar{t} production near threshold are briefly discussed.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	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.	contribution 0.94	0.95	0.69	asserted 1.00
s1	Applications to exotic atoms, \Upsilon (1s) and t\bar{t} production near threshold are briefly discussed.	contribution 0.71	0.56	0.07	asserted 0.80

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The paper

Original 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, \Upsilon (1s) and t\bar{t} production near threshold are briefly discussed.

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References

Forward citations

Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

The bottom quark mass from the $\Upsilon(1S)$ system at NNNLO
hep-ph 2014-07 conditional novelty 6.0 of 10

Using the full NNNLO Upsilon(1S) mass expression and an improved leading-renormalon normalization Nm = 0.563(26), the bottom MS-bar mass is determined to be 4201(43) MeV.
Precision calculation of threshold pi^- d scattering, pi N scattering lengths, and the GMO sum rule
nucl-th 2011-07 accept novelty 6.0 of 10

A detailed chiral calculation shows that feared infrared enhancements in the pion-deuteron scattering length cancel, yielding a few-percent prediction and improved pion-nucleon scattering lengths.
Roy-Steiner-equation analysis of pion-nucleon scattering
hep-ph 2015-10 accept novelty 5.0 of 10

Solving Roy-Steiner equations for pion-nucleon scattering with pionic-atom scattering lengths imposed as constraints yields a pion-nucleon sigma-term of 59.1 +/- 3.5 MeV, about 14 MeV above the long-quoted canonical value.
Hadronic atoms
hep-ph 2024-12 unverdicted novelty 1.0 of 10

A pedagogical survey of non-relativistic effective field theory for hadronic atoms, restating the known next-to-leading-order formulas for the pionic hydrogen energy shift and width.

How the literature uses it

11 arXiv papers cite this in 25 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 12 sentences without a confident label

Uses its method or tool 1 paper

More easily, the same goal may be achieved, using e.g. the methods described in Ref. [ref] (see also Refs. [ref] ).

Hadronic atoms in QCD + QED · Vacuum polarization due to electrons · 0.98

Uses its data or values 3 papers

For example, in the ground state, the correction amounts to $δ_1^vac=0.31 ·10^-2$ [ref] .

Hadronic atoms in QCD + QED · DGBT formula and numerical analysis · 0.94
The $ε^2$ correction has been calculated in Ref. [ref] , for arbitrary quantum numbers, and in the $$ scheme it reads :

Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$ bound states at N$^3$LO · Finite Charm Mass Effects on Bottomonium · 0.93
In Eq. ([ref]) we have $δ_^D^vac=2δΨ_D(0)/Ψ_D(0)=0.51%$ [ref] , $K_D=2α(1-logα)μ_D a_π^- d$, and $μ_D$ as the $πD$ reduced mass.

Precision calculation of the pi^- deuteron scattering length and its impact on threshold pi-N scattering · Pionic atoms · 0.88

Compares with it 2 papers

As we have mentioned before, the way a finite electron mass affects muonic hydrogen is similar to the way a finite charm quark mass affects bottomonium [ref] .

Non-relativistic bound states at finite temperature (II): the muonic hydrogen · Discussion and Conclusions · 0.80
Furthermore, the energy levels $e_N,m_c^(1)$ as well as the wave function $f_1,m_c^(1)$ are in numerical agreement with [ref] .

The bottom-quark mass from non-relativistic sum rules at NNNLO · Single insertions · 1.00

Cites it as support 1 paper

It turns out that, while the effects of the finiteness of $m_c$ cannot be neglected in the relation between $m_b$ and $_b$, Eqs. ([ref])-([ref]), these effects can be safely neglected in the binding energy $E_b b̅(N_f=3)$; cf. Ref. [ref] based on Refs. [ref] .

Calculation of binding energies and masses of quarkonia in analytic QCD models · Bottom mass extraction · 0.96

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