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Bottom and charm mass determinations from global fits to QQ¯ $$ Q\overline{Q} $$ bound states at N3LO
oleh: Vicent Mateu, Pablo G. Ortega
Format: | Article |
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Diterbitkan: | SpringerOpen 2018-01-01 |
Deskripsi
Abstract The bottomonium spectrum up to n = 3 is studied within Non-Relativistic Quantum Chromodynamics up to N3LO. 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 m 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 m¯bm¯b $$ {\overline{m}}_b\left({\overline{m}}_b\right) $$ = 4.216 ± 0.039 GeV. We extend our analysis to the lowest lying charmonium states finding m¯cm¯c $$ {\overline{m}}_c\left({\overline{m}}_c\right) $$ = 1.273 ± 0.054 GeV. Finally, we perform simultaneous fits for m¯b $$ {\overline{m}}_b $$ and α s finding αsnf=5mZ=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 Oαs4 $$ \mathcal{O}\left({\alpha}_s^4\right) $$ virtual massive quark corrections to the relation between the MS¯ $$ \overline{\mathrm{MS}} $$ and pole masses.