Unintegrated parton distributions and electroweak boson production at hadron colliders

TL;DR

Problem: modeling $P_T$ distributions of electroweak bosons and the Higgs in hadron colliders without relying solely on resummation or parton showers. Method: introduce and apply DUPDFs within the $(z,k_t)$-factorisation framework, with Sudakov resummation and angular ordering, using standard collinear PDFs as inputs. Results: LO predictions with an overall K-factor and normalization reproduce Tevatron $W/Z$ data and yield Higgs $P_T$ spectra at the LHC in line with resummation results and near NNLO cross sections; the framework provides transparent physical insight into the origin of $P_T$ distributions. Significance: demonstrates a universal, analytic approach to incorporating higher-order effects via UPDFs, with potential for PDF re-fitting in the $(z,k_t)$ scheme and applications to diffractive Higgs production and other processes.

Abstract

We describe the use of doubly-unintegrated parton distributions in hadron-hadron collisions, using the (z,k_t)-factorisation prescription where the transverse momentum of the incoming parton is generated in the last evolution step. We apply this formalism to calculate the transverse momentum (P_T) distributions of produced W and Z bosons and compare the predictions to Tevatron Run 1 data. We find that the observed P_T distributions can be generated almost entirely by the leading order q_1 q_2 -> W,Z subprocesses, using known and universal doubly-unintegrated quark distributions. We also calculate the P_T distribution of the Standard Model Higgs boson at the LHC, where the dominant production mechanism is by gluon-gluon fusion.

Figures (8)

• Figure 1: (a) The transverse momentum of each parton entering the subprocess is generated by a single parton emission in the last evolution step. (b) Illustration of $(z,k_t)$-factorisation: the last evolution step is factorised into $f_{q_i}(x_i,z_i,k_{i,t}^2,\mu_i^2)$, where $i=1,2$.
• Figure 2: LO Feynman diagram contributing to the $P_T$ distribution of $W$ or $Z$ bosons in the $(z,k_t)$-factorisation approach.
• Figure 3: LO Feynman diagram contributing to the $P_T$ distribution of Higgs bosons in the $(z,k_t)$-factorisation approach. The cross represents the effective vertex in the limit $M_H\ll 2m_t$.
• Figure 4: $P_T$ distribution of $Z$ bosons compared to CDF data CDFZ.
• Figure 5: $P_T$ distribution of $Z$ bosons compared to DØ data D0Z.