Erratum to: Eur. Phys. J. C 34, 297–316 (2004) DOI 10.1140/epjc/s2004-01712-xThe Eq. (2.13) contains an error related to improper counting of number of transverse dimensions within the dimensional regularisation method with the dimension d=4+2ϵ=2+2(1+ϵ)\documentclass[12pt]{minimal}
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\begin{document}$$d=4+2\epsilon = 2+2(1+\epsilon )$$\end{document}. The correct Eq. (2.13) is obtained with the help of substitution:-gμν⊥2→-gμν⊥2(1+ϵ),\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \left( \frac{-g_{\mu \,\nu }^{\perp }}{2} \right) \;\;\; \rightarrow \;\;\; \left( \frac{-g_{\mu \,\nu }^\perp }{2(1+\epsilon )} \right) \;, \end{aligned}$$\end{document}
that can be understood as making an average over the number of transverse polarization states available to the gluons in d\documentclass[12pt]{minimal}
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\begin{document}$$d$$\end{document}-dimensions, see also Eq. (10) in [1]. Note that this prescription is in accordance with conventional definition of the evolution kernels needed also for the subtraction of collinear divergences. We are grateful to Kornelija Passek-Kumericki and Dieter Müller for the discussion of these issues.
This correction requires the following changes in some intermediate results:The corrected expression for Tg(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$T_g(x,\xi )$$\end{document} in the first line of Eq. (2.16) is obtained after the substitution in (2.16) ξ(x-ξ+iε)(x+ξ-iε)→ξ(x-ξ+iε)(x+ξ-iε)(1+ϵ)\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned}&\frac{\xi }{(x-\xi +i\varepsilon )(x+\xi -i\varepsilon )}\nonumber \\&\quad \rightarrow \;\;\; \frac{\xi }{(x-\xi +i\varepsilon )(x+\xi -i\varepsilon )(1+\epsilon )} \end{aligned}$$\end{document}![]()
The corrected expressions for T~g(0)(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$\tilde{T}_g^{(0)}(x,\xi )$$\end{document} and T~g(1)(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$\tilde{T}_g^{(1)}(x,\xi )$$\end{document} in Eq. (3.56) are obtained after the substitution in (3.56) ξ(x-ξ)(x+ξ)→ξ(x-ξ)(x+ξ)(1+ϵ)\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{\xi }{(x-\xi )(x+\xi )}\;\;\; \rightarrow \;\;\; \frac{\xi }{(x-\xi )(x+\xi )(1+\epsilon )} \end{aligned}$$\end{document}![]()
The corrected expressions for the gluonic counterterm Δgcoll(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$\Delta _g^\mathrm{coll}(x,\xi )$$\end{document} in Eq. (3.62) and for the quark counterterm Δqcoll(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$\Delta _q^\mathrm{coll}(x,\xi )$$\end{document} in Eq. (3.63) are obtained after the substitutions in Eqs. (3.62) and (3.63) 1ϵ^+1+lnμF2μ2→1ϵ^+lnμF2μ2\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{1}{\hat{\epsilon }} \,+\,1 \,+\,\ln \left( \frac{\mu _\mathrm{F}^2}{\mu ^2} \right) \;\;\; \rightarrow \;\;\; \frac{1}{\hat{\epsilon }} \,+\,\ln \left( \frac{\mu _\mathrm{F}^2}{\mu ^2} \right) \end{aligned}$$\end{document}![]()
The corrected expression for the renormalisation of the strong coupling constant counterterm ΔgαS(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$\Delta _g^{\alpha _\mathrm{S}}(x,\xi )$$\end{document} in Eq. (3.67) is obtained after the substitution in (3.67) 1ϵ^+1+lnμR2μ2→1ϵ^+lnμR2μ2.\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \frac{1}{\hat{\epsilon }} \,+\,1 \,+\,\ln \left( \frac{\mu _\mathrm{R}^2}{\mu ^2} \right) \;\;\; \rightarrow \;\;\; \frac{1}{\hat{\epsilon }} \,+\,\ln \left( \frac{\mu _\mathrm{R}^2}{\mu ^2} \right) \,. \end{aligned}$$\end{document}![]()
The final expressions for the gluonic hard scattering amplitude Tg(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$T_g(x,\xi )$$\end{document} of Eqs. (3.72) and (3.73) remain unchanged. Although the corrections in intermediate steps listed above affect all terms defining the finite part of Tg(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$T_g(x,\xi )$$\end{document} in the first line of Eq. (3.69), the net effect on the final result is zero.
The final expressions for the quark hard scattering amplitude Tq(x,ξ)\documentclass[12pt]{minimal}
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\begin{document}$$T_q(x,\xi )$$\end{document} of Eqs. (3.70) and (3.71) has to be changed due to the correction of the quark collinear counterterm (3.63). The corrected form of Eq. (3.71) is obtained after performing the substitutionln4m2μF2-1→ln4m2μF2\documentclass[12pt]{minimal}
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\begin{document}$$\begin{aligned} \ln \,\frac{4m^2}{\mu _\mathrm{F}^2} \, - \,1\,\;\;\; \rightarrow \;\;\; \ln \,\frac{4m^2}{\mu _\mathrm{F}^2} \end{aligned}$$\end{document}
in the second line of Eq. (3.71).
The above corrections do not change the main conclusions of the paper based on the numerical analysis performed.