The $l=1$ Hyperfine Splitting in Bottomium as a Precise Probe of the QCD Vacuum.

Abstract

By relating fine and hyperfine spittings for l=1 states in bottomium we can factor out the less tractable part of the perturbative and nonperturbative effects. Reliable predictions for one of the fine splittings and the hyperfine splitting can then be made calculating in terms of the remaining fine splitting, which is then taken from experiment; perturbative and nonperturbative corrections to these relations are under full control. The method (which produces reasonable results even for the $c\bar{c}$ system) predicts a value of 1.5 MeV for the $(s=1)-(s=0)$ splitting in $b\bar{b}$, opposite in sign to that in $c\bar{c}$. For this result the contribution of the gluon condensate $<{\alpha }_s{G}^2>$ is essential, as any model (in particular potential models) which neglects this would give a negative $b\bar{b}$ hyperfine splitting.

12 pages, 2 postscript figures, typeset with ReVTeX

References in corpus (1)

• Rigourous QCD Evaluation of Spectrum and Ground State Properties of Heavy Quarkonium Systems; with a Precision Determination of the bottom quark mass and of the eta-b mass

Cited by in corpus (21)

• QCD and strongly coupled gauge theories: challenges and perspectives
• The QCD Running Coupling
• Bottom quark mass and alpha_s from the Upsilon system
• Next-to-leading nonperturbative calculation in heavy quarkonium
• Determination of Alpha_s(1 GeV) from the charmonium fine structure
• Strong coupling constant from bottomonium fine structure
• Long-distance behavior of the quark-antiquark static potential. Application to light-quark mesons and heavy quarkonia
• Semi-inclusive radiative decays of Upsilon 1S
• The 1P quarkonium fine splittings at NLO
• Soft, collinear and non-relativistic modes in radiative decays of very heavy quarkonium
• Generalized screened potential model
• Chi_b(3P) splitting predictions in potential models
• A plausible explanation of ${\rm Y}(10860)$
• Nonperturbative hyperfine contribution to the $b_1$ and $h_1$ meson masses
• Super-heavy Quarkonia and the Gluon Condensate
• Heavy Quarkonium and nonperturbative corrections
• The gluonic condensate from the hyperfine splitting $M_{\mathrm{cog}}({\chi }_{cJ})-M(h_c)$ in charmonium
• Radiative decays in bottomonium beyond the long wave length approximation
• Nonperturbative Effects in Quarkonia Associated with Large Orders in Perturbation Theory
• Super-heavy Quarkonia as a probe of the QCD Vacuum
• Heavy quark potential from QCD-related effective coupling