Bottom and Charm Mass determinations from global fits to QQˉQ\bar{Q} bound states at N3^3LO

Nov 15, 2017
41 pages
Published in:
  • JHEP 01 (2018) 122
  • Published: Jan 24, 2018
e-Print:

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Abstract: (Springer)
The bottomonium spectrum up to n = 3 is studied within Non-Relativistic Quantum Chromodynamics up to N3^{3}LO. We consider finite charm quark mass effects both in the QCD potential and the MS \overline{\mathrm{MS}} -pole mass relation up to third order in the Y-scheme counting. The u = 1/2 renormalon of the static potential is canceled by expressing the bottom quark pole mass in terms of the MSR mass. A careful investigation of scale variation reveals that, while n = 1, 2 states are well behaved within perturbation theory, n = 3 bound states are no longer reliable. We carry out our analysis in the n_{ℓ} = 3 and n_{ℓ} = 4 schemes and conclude that, as long as finite mc_{c} effects are smoothly incorporated in the MSR mass definition, the difference between the two schemes is rather small. Performing a fit to bb b\overline{b} bound states we find mb(mb) {\overline{m}}_b\left({\overline{m}}_b\right) = 4.216 ± 0.039 GeV. We extend our analysis to the lowest lying charmonium states finding mc(mc) {\overline{m}}_c\left({\overline{m}}_c\right) = 1.273 ± 0.054 GeV. Finally, we perform simultaneous fits for mb {\overline{m}}_b and αs_{s} finding αs(nf=5)(mZ)=0.1178±0.0051 {\alpha}_s^{\left({n}_f=5\right)}\left({m}_Z\right)=0.1178\pm 0.0051 . Additionally, using a modified version of the MSR mass with lighter massive quarks we are able to predict the uncalculated O(αs4) \mathcal{O}\left({\alpha}_s^4\right) virtual massive quark corrections to the relation between the MS \overline{\mathrm{MS}} and pole masses.
Note:
  • 41 pages, 13 figures and 5 tables. v2: Extended discussion on non-perturbative effects, minor typos corrected, published version
  • Quark Masses and SM Parameters
  • Effective Field Theories
  • Heavy Quark Physics
  • Perturbative QCD
  • bottomonium
  • bottom: mass
  • charmonium
  • charm: mass
  • mass: pole
  • mass: effect