On the Resummation of Subleading Logarithms in the Transverse Momentum Distribution of Vector Bosons Produced at Hadron Colliders

Abstract

The perturbation series for electroweak vector boson production at small transverse momentum is dominated by large double logarithms at each order in perturbation theory. An accurate theoretical prediction therefore requires a resummation of these logarithms. This can be performed either directly in transverse momentum space or in impact parameter (Fourier transform) space. While both approaches resum the same leading double logarithms, the subleading logarithms are, in general, treated differently. We comment on two recent approaches to this problem, emphasising the particular subleading logarithms resummed in each case and the numerical differences in the cross sections which result.

Figures (5)

• Figure 1: Schematic representation of contributions to (\ref{['FNR_sum']}) and to (\ref{['qt_sum2']}). Circles correspond to the former expression, triangles to the latter one. An empty marker of a certain shape means that there exist other contributions in the perturbation series with the same power of $\alpha_S$ and $\ln(Q^2/q_T^2)$ which are not included in an expression coded with that shape. The points along the line labelled '$M=2N$' represent terms coming from the Sudakov factor.
• Figure 2: Schematic representation of contributions to (\ref{['FNR_sum']}) with the Sudakov factor expanded and (\ref{['qt_sum1']}). Circles correspond to the former expression, triangles to the latter one. An empty marker of a certain shape means that there exist other contributions in perturbation theory of the same power of $\alpha_S$ and $\ln(Q^2/q_T^2)$ which are not included in an approach coded with that shape.
• Figure 3: The $b-$space result compared to the expression (\ref{['qt_sum2']}), calculated for various values of $N_{\rm max}$. Here $N_{\rm max}=1$ corresponds to the DLLA approximation.
• Figure 4: The $b-$space result compared to the expression (\ref{['FNR2']})and (\ref{['FNR_sum']}), calculated for various values of $N_{\rm max}$. With the choice $\alpha_s=0.2$, (\ref{['FNR2']}) is only applicable for $\eta {\ \hbox{$\buildrel>\over\sim$}\ } 8. \times 10^{-6}$.
• Figure 5: The ratio of the numerically calculated (\ref{['FNR2']}) (m=0 curve) and (\ref{['m01']}) (m=0,1 curve) to the $b-$space result.