Sudakov Logarithm Resummation in Transverse Momentum Space for Electroweak Boson Production at Hadron Colliders

TL;DR

The paper tackles the challenge of predicting the W/Z transverse momentum distribution at hadron colliders in the small-$q_T$ regime, where Sudakov logarithms undermine fixed-order perturbation theory. It develops and evaluates a momentum-space ($q_T$) resummation framework, extending prior work to include sub-leading and kinematic logarithms and comparing with traditional $b$-space resummation. The study demonstrates that the $q_T$-space approach can reproduce $b$-space results in the relevant region and offers a natural path to merge with fixed-order calculations, with the inclusion of up to NNNL towers producing only modest changes (about 3%) to the cross section. The authors note the continued importance of non-perturbative effects such as $k_T$ smearing for full phenomenology and discuss connections to related approaches, suggesting further comparative studies.

Abstract

A complete description of W and Z boson production at high-energy hadron colliders requires the resummation of large Sudakov double logarithms which dominate the transverse momentum (q_T) distribution at small q_T. We compare different prescriptions for performing this resummation, in particular implicit impact parameter space resummation versus explicit transverse momentum space resummation. We argue that the latter method can be formulated so as to retain the advantages of the former, while at the same time allowing a smooth transition to finite order dominance at high q_T.

Figures (17)

• Figure 1: DLLA (\ref{['DLLA']}) and $b$-space (\ref{['b_space']}) results for the transverse momentum distribution ${1 \over \sigma_0} {d \sigma \over d \eta}$.
• Figure 2: Extension of the $b$-space cross section presented in Fig. \ref{['bspace_v_DLLA']} to large values of $\eta$.
• Figure 3: The behaviour of ${|\bar{b}_m({\infty})| \over m! }$.
• Figure 4: Contributions (\ref{['contrib_sum1']}) to the cross section (\ref{['qt_sum1']}). Only positive contributions plotted here.
• Figure 5: Resummation of (\ref{['contrib_sum1']}). Each point corresponds to a contribution (\ref{['contrib_sum1']}) summed in (\ref{['qt_sum1']}) when (a): 'all' $m_{max} \geq 2N_{\rm max}-1$ coefficients $\bar{b}_m({\infty})$ are known and (b): only $m_{max}<2N_{\rm max}-1$ are known. In particular here $N_{\rm max}=4$ and $m_{\rm max}=7,1$ for the case (a),(b), respectively. Here $N$ equals power of the coupling $\alpha_S$.