Transverse momentum resummation at small x for the Tevatron and LHC

TL;DR

The paper investigates how small-$x$ broadening, observed in semi-inclusive DIS, can modify transverse momentum resummation for electroweak boson production at hadron colliders within the Collins-Soper-Sterman framework.By introducing a phenomenological Gaussian broadening factor at small $x$ into the resummed form factor and connecting SIDIS constraints to Drell-Yan, the authors generate concrete predictions for $W$, $Z$, and Higgs $q_T$ distributions in forward regions at the Tevatron and at the LHC.The work leverages the $b$-space formalism with the BLNY nonperturbative Sudakov factor and a $b_*$ prescription, plus a universal relation between spacelike and timelike parton densities, to interpolate $x$-dependent effects across kinematic regimes.The results indicate observable forward-region broadening at Tevatron Run-2 and stronger effects at the LHC, with notable implications for precision $W$-mass measurements and Higgs-search strategies, motivating experimental tests of the predicted rapidity dependence of $q_T$ spectra.

Abstract

Analysis of semi-inclusive DIS hadroproduction suggests broadening of transverse momentum distributions at $x$ below a few $10^{-3}$, which can be modeled in the Collins-Soper-Sterman formalism by a modification of impact-parameter-dependent parton densities. We discuss the consequences of such a modification for the production of electroweak bosons at hadron-hadron colliders. If substantial small-$x$ broadening is observed in forward Z boson production in the Tevatron Run-2, it will strongly affect predicted transverse momentum distributions for W, Z, and Higgs boson production at the Large Hadron Collider.

Figures (10)

• Figure 1: Parton momentum fractions $x_{A}$ and $x_{B}$ accessible in $W,$$Z,$ and Higgs boson production (for $M_{H}=120$ GeV) in the Tevatron Run-2 ($\sqrt{S}=1.96$ TeV) and at the LHC ($\sqrt{S}=14$ TeV). The accessible ranges of $x_{A}$ and $x_{B}$ are shown by the solid lines. The contours of the constant rapidity $y$ are shown by the inclined dotted lines.
• Figure 2: Rapidity distributions $d\sigma/dy$ for (a) $W^{\pm}$ boson production at the Tevatron and LHC; (b) $Z^{0}$ boson production at the Tevatron and LHC; and (c) Higgs boson production at the LHC.
• Figure 3: Transverse momentum distributions of $Z$ bosons in the Tevatron Run-2: (a) integrated over the full range of $Z$ boson rapidity $y$; (b) for events with a large $Z$ boson rapidity, $|\, y\,|>2$; (c) for events with both decay electrons registered in the forward ($y_{e^{+}}>2$, $y_{e^{-}}>2$, and $p_{Te^{\pm}}>20$ GeV) or backward ($y_{e^{+}}<-2$, $y_{e^{-}}<-2$, and $p_{Te^{\pm}}>20$ GeV) detector regions. The solid curve is the standard CSS cross section, calculated using the BLNY parametrization Landry:2002ix of the nonperturbative Sudakov factor. The dashed curve includes additional terms responsible for the $q_{T}$ broadening in the small-$x$ region, as in Eq. (\ref{['eq:full']}).
• Figure 4: Same as Fig. \ref{['fig:zTeV']}(c), for the BLNY parametrization (solid), and various choices of the parameter $x_{0}$ in Eq. (\ref{['eq:ax']}): $x_{0}=0.002$ (dashed), $0.005$ (dot-dashed), and $0.008$ (dotted).
• Figure 5: Transverse momentum distributions for a combined sample of $W^{+}$ and $W^{-}$ bosons in the Tevatron Run-2; (a) integrated over the full range of $W$ boson rapidities; (b) integrated over the forward boson rapidities $|\, y\,|>2$; (c) integrated with the selection cuts $|\, y_{e}\,|>2,\,$$p_{Te}>20$ GeV, $\, E_{T}\space/\space>20\,$GeV. The solid curve is the standard CSS cross section, calculated using the BLNY parametrization Landry:2002ix of the nonperturbative Sudakov factor. The dashed curve includes additional terms responsible for the $q_{T}$ broadening in the small-$x$ region, as in Eq. (\ref{['eq:full']}).