**59**: 647-658

https://doi.org/10.1140/epjc/s10052-008-0813-1

Regular Article - Theoretical Physics

## On the perturbative stability of the QCD predictions for the ratio *R*=*F*
_{
L
}/*F*
_{
T
} in heavy-quark leptoproduction

^{1}
Yerevan Physics Institute, Alikhanian Br. 2, 375036, Yerevan, Armenia

^{2}
II. Institut für Theoretische Physik, Universität Hamburg, Luruper Chaussee 149, 22761, Hamburg, Germany

^{*} e-mail: nikiv@mail.yerphi.am

Received:
1
September
2008

Revised:
20
October
2008

Published online:
2
December
2008

We analyze the perturbative and parametric stability of the QCD predictions for the Callan–Gross ratio, *R*(*x*,*Q*
^{2})=*F*
_{
L
}/*F*
_{
T
}, in heavy-quark leptoproduction. We consider the radiative corrections to the dominant photon–gluon fusion mechanism. In various kinematic regions, the following contributions are investigated: exact NLO results at low and moderate *Q*
^{2}≲*m*
^{2}, asymptotic NLO predictions at high *Q*
^{2}≫*m*
^{2}, and both NLO and NNLO soft-gluon (or threshold) corrections at large Bjorken variable *x*. Our analysis shows that large radiative corrections to the structure functions *F*
_{
T
}(*x*,*Q*
^{2}) and *F*
_{
L
}(*x*,*Q*
^{2}) cancel each other in their ratio *R*(*x*,*Q*
^{2}) with good accuracy. As a result, the NLO contributions to the Callan–Gross ratio are less than 10% in a wide region of the variables *x* and *Q*
^{2}. We provide compact LO predictions for *R*(*x*,*Q*
^{2}) in the case of low *x*
*≪*1. A simple formula connecting the high-energy behavior of the Callan–Gross ratio and low-*x* asymptotics of the gluon density is derived. It is shown that the obtained hadron-level predictions for *R*(*x*→0,*Q*
^{2}) are stable under the DGLAP evolution of the gluon distribution function. Our analytic results simplify the extraction of the structure functions *F*
_{2}
^{
c
}
(*x*,*Q*
^{2}) and *F*
_{2}
^{
b
}
(*x*,*Q*
^{2}) from measurements of the corresponding reduced cross sections, in particular at DESY HERA.

PACS: 12.38.Bx – / 13.60.Hb – / 13.88.+e –

*© Springer-Verlag , 2009*