Logarithmic electroweak corrections to hadronic Z+1 jet production at large transverse momentum

TL;DR

This paper analyzes Z+1 jet production in hadronic collisions at high transverse momentum, focusing on electroweak logarithmic corrections. It derives analytic one- and two-loop EW LL and NLL contributions in the high-energy limit for the main partonic channels and provides explicit expressions for the corrections. Numerical results show large one-loop EW effects at the LHC (tens of percent) with partial cancellation at two loops, yielding several-percent net corrections that are nevertheless essential for precision. The Tevatron receives negligible EW corrections, while the findings emphasize the necessity of including LL and NLL two-loop terms to achieve percent-level accuracy in high-$p_T$ Z+jet predictions at the LHC.

Abstract

We consider hadronic production of a Z boson in association with a jet and study one- and two-loop electroweak logarithmic corrections in the region of high Z-boson transverse momentum, p_T >> M_Z, including leading and next-to-leading logarithms. Numerical results for the LHC and Tevatron colliders are presented. At the LHC these corrections amount to tens of per cent and will be important for interpretation of the measurements.

Figures (4)

• Figure 1: (a) Transverse momentum distribution for $p p \to Z j$ at $\sqrt{s}=14\,\mathrm{TeV}$: LO (dotted), NLO (dashed) and NNLO (solid) result for unpolarised $Z$ and LO contribution from longitudinally polarised $Z$ (dash-dotted). (b) Relative electroweak correction to the lowest order unpolarised $p_{\mathrm{T}}$ distribution for $p p \to Z j$ at $\sqrt{s}=14\,\mathrm{TeV}$: 1-loop LLs+NLLs (dashed), 2-loop LLs (dash-dotted) and 2-loop LLs+NLLs (solid).
• Figure 2: Relative electroweak correction and statistical error for the unpolarised integrated cross section for $pp \to Z j$ at $\sqrt{s}=14\,\mathrm{TeV}$ as a function of $p_{\mathrm{T}}^{\mathrm{cut}}$: (1+2)-loop LL+NLL (solid), 2-loop LL (dash-dotted) and 2-loop LL+NLL (dashed) correction and statistical error (shaded region) with respect to the lowest order cross section.
• Figure 3: (a) Transverse momentum distribution for $p \bar{p} \to Z j$ at $\sqrt{s}=2\,\mathrm{TeV}$: LO (dotted), NLO (dashed) and NNLO (solid) result for unpolarised $Z$ and LO contribution from longitudinally polarised $Z$ (dash-dotted). (b) Relative electroweak correction to the unpolarised lowest order $p_{\mathrm{T}}$ distribution for $p\bar{p} \to Z j$ at $\sqrt{s}=2\,\mathrm{TeV}$: 1-loop LLs+NLLs (dashed), 2-loop LLs (dash-dotted) and 2-loop LLs+NLLs (solid).
• Figure 4: Relative electroweak correction and statistical error for the unpolarised cross section for $p\bar{p} \to Z j$ at $\sqrt{s}=2\,\mathrm{TeV}$ as a function of $p_{\mathrm{T}}^{\mathrm{cut}}$: (1+2)-loop LL+NLL (solid), 2-loop LL (dash-dotted) and 2-loop LL+NLL (dashed) correction and statistical error (shaded region) with respect to the lowest order cross section.