Weak Boson Emission in Hadron Collider Processes

TL;DR

This paper evaluates the role of weak-boson emission in hadron collider processes where ${ m O}(\alpha)$ virtual weak corrections become large at high energies. It shows that weak-boson emission cross sections can be substantial and often partially cancel the virtual corrections, but the net effect is highly sensitive to the process and experimental selections (e.g., jet vetoes and exclusive vs inclusive observables). Across QCD-dominated processes (inclusive jet, isolated photon, Z+1 jet) and electroweak-rich channels (Drell-Yan, di-boson, top quark production), the emission contributions can either moderate or rival the one-loop corrections, particularly at the LHC, while jet vetoes frequently suppress these effects. The study underscores the need for process-specific inclusion of weak-boson emission in precision EW calculations and advocates for MC frameworks that incorporate full ${ m O}( ext{EW})$ corrections. The results highlight that a universal prescription is insufficient and that careful treatment of observables and cuts is essential for accurate predictions at the Tevatron and LHC.

Abstract

The O(alpha) virtual weak radiative corrections to many hadron collider processes are known to become large and negative at high energies, due to the appearance of Sudakov-like logarithms. At the same order in perturbation theory, weak boson emission diagrams contribute. Since the W and Z bosons are massive, the O(alpha) virtual weak radiative corrections and the contributions from weak boson emission are separately finite. Thus, unlike in QED or QCD calculations, there is no technical reason for including gauge boson emission diagrams in calculations of electroweak radiative corrections. In most calculations of the O(alpha) electroweak radiative corrections, weak boson emission diagrams are therefore not taken into account. Another reason for not including these diagrams is that they lead to final states which differ from that of the original process. However, in experiment, one usually considers partially inclusive final states. Weak boson emission diagrams thus should be included in calculations of electroweak radiative corrections. In this paper, I examine the role of weak boson emission in those processes at the Fermilab Tevatron and the CERN LHC for which the one-loop electroweak radiative corrections are known to become large at high energies (inclusive jet, isolated photon, Z+1 jet, Drell-Yan, di-boson, t-bar t, and single top production). In general, I find that the cross section for weak boson emission is substantial at high energies and that weak boson emission and the O(alpha) virtual weak radiative corrections partially cancel.

Figures (16)

• Figure 1: Ratio of the NLO QCD $Vj$ ($V=W^\pm,\, Z$; $W\to\ell\nu,\, jj$, $Z\to\ell^+\ell^-,\,\bar{\nu}\nu, \,jj$) and the ${\cal O}(\alpha_s^2)$ di-jet cross section for inclusive jet production as a function of the jet transverse momentum a) at the Tevatron, and b) at the LHC. Results are shown for two extreme cases: with no $p\hbox{/}_T$ veto imposed (solid line), and removing all events with non-zero $p\hbox{/}_T$ (dashed line). The cuts imposed are described in the text.
• Figure 2: Relative correction with respect to the LO $\gamma j$ cross section, ${\cal R}_{\gamma j}$, as a function of the photon transverse momentum, $p_T(\gamma)$, for a) the Tevatron and b) the LHC. The blue curve shows the result if only the ${\cal O}(\alpha)$ virtual weak corrections of Ref. Kuhn:2005gv are taken into account. The black dashed (solid) curve shows ${\cal R}$ if in addition $V\gamma (j)$ production is included and a (no) $p\hbox{/}_T$ veto is imposed. The definition of ${\cal R}$ and the cuts imposed are described in the text.
• Figure 3: Relative correction with respect to the LO $Z+1$ jet cross section, ${\cal R}_{Zj}$, as a function of the $Z$ boson transverse momentum, $p_T(Z)$, for a) the Tevatron and b) the LHC. The solid curve shows the result if only the ${\cal O}(\alpha)$ virtual weak corrections of Ref. Kuhn:2004em are taken into account. The dashed curve shows ${\cal R}_{Zj}(p_T(Z))$ if $ZV (j)$ production with $V\to jj$ is included as well. The definition of ${\cal R}_{Zj}(p_T(Z))$ and the cuts imposed are described in the text.
• Figure 4: The relative correction with respect to the LO $e\nu$ cross section at the Tevatron as a function a) of the $e\nu$ transverse mass and b) the electron $p_T$. The solid curve shows the result if only the ${\cal O}(\alpha)$ corrections of Ref. Baur:2004ig are taken into account. The dashed curve shows ${\cal R}_{e\nu}$ if ${\cal O}(\alpha^3)$$e\nu V$ production with $V\to jj$ and $Z\to\bar{\nu}\nu$ is included as well. The definition of ${\cal R}_{e\nu}$ and the cuts imposed are described in the text.
• Figure 5: The relative correction with respect to the LO $e\nu$ cross section at the LHC as a function a) of the $e\nu$ transverse mass and b) the electron $p_T$. The solid curve shows the result if only the ${\cal O}(\alpha)$ corrections of Ref. Baur:2004ig are taken into account. The dashed blue (red) curve shows ${\cal R}_{e\nu}$ in the $e^+\nu$ ($e^-\nu$) channel if ${\cal O}(\alpha^3)$$e\nu V$ production with $V\to jj$ and $Z\to\bar{\nu}\nu$ is included in addition. The definition of ${\cal R}_{e\nu}$ and the cuts imposed are described in the text.