The Importance of Weak Bosons Emission at LHC

TL;DR

The paper addresses the impact of real weak boson emissions on LHC observables, showing that inclusive electroweak double-log corrections can be large and depend sensitively on how emissions are treated. It presents a general SU(2) isospin overlap-matrix formalism with all-order resummation of soft W emissions, comparing Bloch-Nordsieck inclusive corrections to Sudakov exclusive ones. The approach is applied to third-generation quark production, where BN corrections can drastically alter cross sections, notably enhancing channels like bbbar and tbbar due to interference with QCD amplitudes. These findings highlight the practical importance of including inclusive weak boson emissions in LHC phenomenology and provide a framework for more precise future calculations.

Abstract

We point out that gauge bosons emissions should be carefully estimated when considering LHC observables, since real $Ws$ and $Zs$ contributions can dramatically change cross sections with respect to tree level values. Here we consider observables that are fully inclusive respect to soft gauge bosons emission and where a certain number of nonabelian isospin charges in initial and/or final states are detected. We set up a general formalism to evaluate leading, all order resummed electroweak corrections and we consider the phenomenologically relevant case of third family quark production at the LHC. In the case of $b\bar{t}$ production we find that, due to the interplay between strong and weak interactions, the production cross section can become an order of magnitude bigger than the tree level value.

Figures (5)

• Figure 1: Diagrammatic Isospin description of the overlap matrix with three isospin charged legs and one inclusive final state.
• Figure 2: Parton distributions for the sea of the proton at $Q=4000 GeV$ as a function of $x$, the fraction of momentum carried by the parton. Left: $s=\bar{s},c=\bar{c},b=\bar{b}$. Right: $\bar{u},\bar{d}$.
• Figure 3: Sudakov and BN electroweak corrections at Leading Log order for the process $PP\rightarrow t\bar{t}$ (similar results hold for $PP\rightarrow b\bar{b}$) in the massless limit. Top: effects of radiative corrections on $\frac{d^2\sigma}{d\hat{s}d\cos\theta}$ at $\theta=\frac{\pi}{2}$, $\hat{s}$ being the partonic c.m. energy (which is also the $t \bar{t}$ invariant mass) and $\theta$ the partonic reference frame scattering angle. Bottom: the same for $\frac{d\sigma}{d\hat{s}}$, integrated over $\theta$ for $\hbox{$p$}_{\perp }>400$ GeV.
• Figure 4: Top: angular dependence at fixed energy ($\sqrt{\hat{s}}=2000$ GeV in the partonic frame) of the LL BN cross section (red dashed line) and of the Sudakov one for $t\bar{b}$ production (blue continuous line). Bottom: $\sqrt{\hat{s}}$ dependence of the ratio of BN and Sudakov cross sections for $p_{\perp}\geq 400$ GeV. Dashed (red) line for $b\bar{t}$, continuous (blue) line for $t\bar{b}$.
• Figure 5: The differential cross section for $b\bar{t}$ production, $\frac{d\sigma}{d\hat{s}}$ in $\frac{pb}{GeV^2}$, integrated over $\theta$ for $\hbox{$p$}_{\perp }>400$ GeV. Dashed (red) line is for the fully inclusive LL BN case, while continuous (blue) line for the exclusive Sudakov case.