QCD corrections of $e^+e^- \to J/\psi+c+\bar{c}$ using the principle of maximum conformality

TL;DR

This paper calculates the cross sections for $e^+e^- o J/mbda+c+ar{c}$ at B factories using NLO corrections and applies the Principle of Maximum Conformality to improve the pQCD series, resulting in more precise predictions that align better with experimental data.

Contribution

It introduces the application of the Principle of Maximum Conformality to NLO QCD calculations of $e^+e^- o J/mbda+c+ar{c}$, enhancing the precision of theoretical predictions.

Findings

More accurate prompt total cross section after PMC application.

Improved agreement with Belle experimental measurements.

Quantified uncertainties including uncalculated NNLO contributions.

Abstract

In this paper, we compute the total and differential cross sections for $e^+e^- \to J/\psi+c+\bar{c}$ at the $B$ factories up to next-to-leading order (NLO) corrections within the framework of nonrelativistic QCD factorization theory. We then obtain improved pQCD series of those cross sections by using the Principle of Maximum Conformality (PMC). We show that the PMC can be applied for any pQCD calculable observable at the total and differential levels via a self-consistent way in perturbation theory. We observe that a more precise prompt total cross section at the NLO level can be achieved after applying the PMC, e.g. $\sigma|_{\rm prompt}^{\rm PMC}= 0.565^{+0.144}_{-0.125}~\text{pb}$. Here the uncertainty is the squared average of those from the $\alpha_s$ fixed-point uncertainty $\Delta\alpha_s(M_Z)$, the uncertainty of charm quark mass $\Delta m_c$, and an estimated contribution of the uncalculated NNLO-terms as predicted by the Pad\'{e} approximation approach. The differential cross sections $d\sigma/dP_{J/\psi}$, $d\sigma/d|\cos \theta|$, and $d\sigma/dz$ for $e^+e^- \to J/\psi+c+\bar{c}$ are further examined. Those results show that by further considering the feed-down contributions, the PMC predictions show better agreement with the Belle measurements.