Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Bottom and Charm Mass determinations from global fits to $Q\bar{Q}$
  bound states at N$^3$LO   The bottomonium spectrum up to $n = 3$ is studied within Non-Relativistic
Quantum Chromodynamics up to N$^3$LO. We consider finite charm quark mass
effects both in the QCD potential and the $\overline{\mathrm{MS}}$-pole mass
relation up to third order in the $\Upsilon$-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 $n_\ell = 3$ and $n_\ell = 4$ 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
$b\bar{b}$ bound states we find $\overline{m}_b(\overline{m}_b) = 4.216\pm
0.039$ GeV. We extend our analysis to the lowest lying charmonium states
finding $\overline{m}_c(\overline{m}_c)=1.273 \pm 0.054$ GeV. Finally, we
perform simultaneous fits for $\overline{m}_b$ and $\alpha_s$ finding
$\alpha_s^{(n_f=5)}(m_Z)=0.1178\pm 0.0051$. Additionally, using a modified
version of the MSR mass with lighter massive quarks we are able to predict the
uncalculated $\mathcal{O}(\alpha_s^4)$ virtual massive quark corrections to the
relation between the $\overline{\mathrm{MS}}$ and pole masses.

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The categories of this paper are: physics
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
2
The categories of this paper are: math
35
The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
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The categories of this paper are: nucl-th
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: bayes-an
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The categories of this paper are: cs