Abstract
In the paper, we study the properties of the top-quark $\overline{\rm MS}$ running mass computed from its on-shell mass by using both the four-loop $\overline{\rm MS}$-on-shell relation and the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct magnitude of the strong running coupling of the perturbative series, its prediction avoids the conventional renormalization scale ambiguity, and thus a more precise pQCD prediction can be achieved. After applying the PMC to the four-loop $\overline{\rm MS}$-on-shell relation and taking the top-quark on-shell mass $M_t=172.9\pm0.4$ GeV as an input, we obtain the renormalization scale-invariant $\overline{\rm MS}$ running mass at the scale $m_t$, e.g., $m_t(m_t)\simeq 162.6\pm 0.4$ GeV, in which the error is the squared average of those from $\Delta \alpha_s(M_Z)$, $\Delta M_t$, and the approximate error from the uncalculated five-loop terms predicted by using the Pad\'{e} approximation approach.
Highlights
In quantum chromodynamics (QCD), the quark masses are elementary input parameters of the QCD Lagrangian
We have presented a more accurate prediction of the top-quark MS running mass from the experimentally measured top-quark OS mass by applying the principle of maximum conformality (PMC) to eliminate the conventional renormalization scale ambiguity
Where the errors are squared averages of those from ΔαsðMZÞ, ΔMt, and the uncalculated N5LO-terms predicted by using the Padeapproximation approach (PAA)
Summary
In quantum chromodynamics (QCD), the quark masses are elementary input parameters of the QCD Lagrangian. The direct measurements are based on analysis techniques which use top-pair events provided by Monte Carlo (MC) simulation for different assumed values of the top-quark mass Applying those techniques to data yields a mass quantity corresponding to the top-quark mass scheme implemented in the MC; it is usually referred to as the “MC mass.”. People uses the guessed renormalization scale as the momentum flow of the process and varies it within an arbitrary range to estimate its uncertainty for the pQCD predictions This naive treatment leads to the mismatching of the strong coupling constant with its coefficients, well breaking the renormalization group invariance [25,26,27] and leading to renormalization scale and scheme ambiguities. After adopting the PMC to fix the αs running behavior, the remaining perturbative coefficients of the resultant series match the series of conformal theory, leading to a renormalization scheme independent prediction. The renormalization scaleand-scheme independent series is helpful for estimating the contribution of the unknown higher orders, some examples can be found in Refs. [41,42,43]
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