https://doi.org/10.1140/epjc/s10052-020-7967-x
Regular Article - Theoretical Physics
The heavy quarkonium inclusive decays using the principle of maximum conformality
Department of Physics, Chongqing University, Chongqing, 401331, People’s Republic of China
* e-mail: wuxg@cqu.edu.cn
Received:
20
January
2020
Accepted:
24
April
2020
Published online:
6
May
2020
The next-to-next-to-leading order (NNLO) pQCD correction to the inclusive decays of the heavy quarkonium 
(Q being c or b) has been done in the literature within the framework of nonrelativistic QCD. One may observe that the NNLO decay width still has large conventional renormalization scale dependence due to its weaker pQCD convergence, e.g. about 
for 
and 
for 
, by varying the scale within the range of 
. The principle of maximum conformality (PMC) provides a systematic way to fix the 
-running behavior of the process, which satisfies the requirements of renormalization group invariance and eliminates the conventional renormalization scheme and scale ambiguities. Using the PMC single-scale method, we show that the resultant PMC conformal series is renormalization scale independent, and the precision of the inclusive decay width can be greatly improved. Taking the relativistic correction 
into consideration, the ratios of the 
decays to light hadrons or 
are: 
and 
, respectively. Here the errors are for 
. As a step forward, by applying the Pad
approximation approach (PAA) over the PMC conformal series, we obtain approximate NNNLO predictions for those two ratios, e.g. 
and 
. The 
ratio agrees with the latest PDG value 
, indicating the necessity of a strict calculation of NNNLO terms.
© The Author(s), 2020
