Relativistic corrections to the semi-inclusive decay of $\bm{\psi}$ and $\bm{\Upsilon}$

TL;DR

This paper calculates relativistic corrections to the decay processes of $ ext{J/} ext{ψ}$ and $ ext{Υ}$ mesons into lepton or charm pairs with jets, revealing significant modifications to leading order predictions.

Contribution

It provides the first detailed analytic expressions for relativistic corrections in these decay channels up to next-to-leading order in velocity expansion.

Findings

Relativistic corrections significantly alter decay rate predictions.

The NLO short-distance coefficient ratio ranges from -5.5 to -12.4.

Large relativistic effects depend on quarkonium and fermion masses.

Abstract

In the framework of the nonrelativistic quantum chromodynamics factorization formalism, we study the processes of $\psi(nS)$ and $\Upsilon(nS)$ decay into a lepton pair or a charm pair associated with two jets up to the next-to-leading order in velocity expansion. We present the analytic expressions for the differential decay rate to the invariant mass of the lepton pair or charm pair. We find that the ratio of the next-to-leading order short-distance coefficient to the leading order one is in the range from -5.5 to -12.4. The relativistic corrections are so large that they modify the leading order prediction significantly. Utilizing the analytic expressions, we also investigate the relativistic corrections in different kinematic regions and their dependence on the masses of the initial-state quarkonium and the final-state fermion. In addition, we study the momentum distribution of $D^{*+}$ in the process $\Upsilon(1S)\to c\bar{c}gg\to D^{*+}X$.