https://doi.org/10.1140/epja/i2018-12550-2
Regular Article - Theoretical Physics
Direct fragmentation of 
(1S) and 
(1S) considering the transverse momentum effect of constituents
1
Faculty of Physics, Yazd University, P.O. Box 89195-741, Yazd, Iran
2
School of Particles and Accelerators, Institute for Research in Fundamental Sciences (IPM), P.O.Box 19395-5531, Tehran, Iran
3
Department of Physics, Faculty of Science, University of Hormozgan, Bandar-Abbas, Iran
* e-mail: mmoosavi@yazd.ac.ir
Received:
9
March
2018
Accepted:
12
June
2018
Published online:
12
July
2018
In this work, we calculate the fragmentation function (FF) of pseudoscalar S -wave heavy quarkonia from gluon splitting. We also study, for the first time, the Fermi motion effect of constituent quarks on the fragmentation production of the 
and 
states. In all previous studies of heavy quarkonium FFs, by ignoring the Fermi motion of constituents a Dirac-delta functional form was approximated for the wave function of bound state. Here, to study the Fermi motion of quarkonium constituents we consider a typical wave function which is different from the delta form and is the nonrelativistic limit of the solution of the Bethe-Salpeter equation with the QCD kernel. We shall present our results for the fragmentation of 
and show how the Fermi motion effect changes the results.
© SIF, Springer-Verlag GmbH Germany, part of Springer Nature, 2018
