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We clarify the confusion in a recent paper by Aurenche, Zakharov and Zaraket(AZZ) \cite{azz} over the procedure and region of validity of the collinearapproximation in the twist expansion approach to induced gluon emission indeeply inelastic scattering (DIS) off a nucleus target. We point out that, inthis approach to the semi-inclusive spectrum, the transverse momentum$\vec\ell_\perp$ of the induced gluon must be fixed in the collinear expansionin the transverse momentum $\vec k_\perp$ of the initial partons, therefore theresult is valid for $<k_\perp^2> \ll \ell_\perp^2 \ll Q^2$. In the twist-fourcontribution, one can single out the double-hard term corresponding tocollinear quark-gluon Compton scattering which can be calculated independentlyof the collinear expansion approach. We will discuss the connection between thecollinear approximation in the twist expansion approach and the small $k_T$approximation of the results in the Light-Cone Path Integral (LCPI) andGyulassy-Levai-Vitev (GLV) opacity expansion approach. We point out themisconstrued variable change by AZZ before the $k_T$ expansion in LCPI andopacity expansion approach, without which one obtains the same result for theinduced gluon spectrum under collinear approximation as in the twist expansionapproach. We also show that corrections beyond the collinear approximation tothe transverse momentum integrated gluon spectrum within the static potentialmodel in the GLV approach give rise to a logarithmic factor difference from theresult of collinear approximation.

Success of collinear expansion in the calculation of induced gluon emission