Impact of PDF uncertainties at large x on heavy boson production

TL;DR

This paper investigates how uncertainties in parton distributions at large $x$, driven by deuteron nuclear corrections in global fits, propagate into W and Z boson production and into the production of heavy beyond-Standard-Model bosons. Using the CJ11 next-to-leading order analysis, the authors quantify how the uncertain $d/u$ ratio at large $x$ affects differential and integrated cross sections and lepton/W asymmetries in $pp$ and $par{p}$ collisions, with pronounced effects at large boson rapidities. They find substantial sensitivity for high-$|y|$ observables—up to ~15% for Z at large rapidity and dramatic, sometimes exceeding 100%, for certain heavy boson channels—driven primarily by the $d$-quark PDF. The work highlights experimental avenues (forward Z measurements, W asymmetries, and Jefferson Lab upgrades) to constrain large-$x$ PDFs and cautions that predictions for high-mass, high-rapidity heavy bosons must account for these sizable uncertainties in poorly constrained regions.

Abstract

We explore the sensitivity of W and Z boson production in hadronic collisions to uncertainties in parton distribution functions (PDFs) at large x arising from uncertainties in nuclear corrections when using deuterium data in global QCD fits. The W and Z differential cross sections show increasing influence of nuclear corrections at high boson rapidities, particularly for the d quark, which is diluted somewhat in the decay lepton rapidity distributions. The effects of PDF uncertainties on heavy W' and Z' bosons beyond the Standard Model become progressively more important for larger boson masses or rapidities, both in p-p collisions at the LHC and in p-pbar scattering at the Tevatron.

Figures (9)

• Figure 1: Ratio of $d$ to $u$ quark distributions for the CJ PDFs CJ11 at $Q^2 = 10$ GeV$^2$. The shaded band illustrates the uncertainty range between maximum (blue dashed) and minimum (red dot-dashed) nuclear corrections in the deuteron.
• Figure 2: Differential $Z$ boson cross section as a function of the $Z$ rapidity $y_Z$, computed from CJ PDFs with maximum (blue dashed) and minimum (red dot-dashed) nuclear corrections, relative to the reference cross section $\sigma_Z(\rm ref)$ calculated using the central CJ PDF set CJ11. The cross sections are computed for $pp$ collisions at the LHC with $\sqrt{s}=7$ TeV (left) and for $p\overline{p}$ collisions at the Tevatron with $\sqrt{s}=1.96$ TeV (right).
• Figure 3: Differential $W^+$(top) and $W^-$(bottom) boson cross sections as a function of the $W$ rapidity $y_W$, computed from CJ PDFs with maximum (blue dashed) and minimum (red dot-dashed) nuclear corrections, relative to the reference cross sections $\sigma_{W^\pm}{\rm (ref)}$ calculated using the central CJ PDF set CJ11. The cross sections are computed for $pp$ collisions at the LHC with $\sqrt{s}=7$ TeV (left) and for $p\overline{p}$ collisions at the Tevatron with $\sqrt{s}=1.96$ TeV (right).
• Figure 4: $W$ boson asymmetry $A_W$ as a function of the $W$ rapidity $y_W$ at LHC (left) and Tevatron (right) kinematics, computed from CJ PDFs CJ11 with minimum (upper blue solid) and maximum (lower blue solid) nuclear corrections. For comparison, the asymmetries using the ABKM Alekhin10 (red dot-dashed), CT10 CT10 (green dashed) and MSTW MSTW09 (black dotted) PDF sets are also shown.
• Figure 5: Lepton charge asymmetry $A_\eta$ as a function of lepton pseudorapidity $\eta$ at the LHC (left) and Tevatron (right), computed from CJ PDFs CJ11 with maximum (blue dotted) and minimum (red solid) nuclear corrections. The calculations are compared with CMS $W \to e\nu_e$ (red squares) and $W \to \mu\nu_\mu$ (blue triangles) data for a lepton transverse momentum cut $p_T > 25$ GeV Ae:CMS, and preliminary LHCb data (black circles) for $p_T > 20$ GeV Ae:LHCb, as well as with D0 data from the Tevatron $p_T > 25$ GeV Ae:D0.