Triply polarized $WWW$ at the LHC: first glimpse at LO

Abstract

We present first results for triply polarized $WWW$ events at the LHC. The calculation is performed at leading order for fully leptonic decays using the Standard Model. Employing an inclusive kinematic cut setup, we found that the triply-transverse polarization fraction is about $51\%$, while the triply-longitudinal (LLL) fraction is smallest with $1.4\%$ for the $W^-W^+W^+$ process. The interference between different polarization amplitudes amounts to $+1.8\%$. Results for the $W^+W^-W^-$ case are similar. Based on known higher-order results for the diboson processes, radiative corrections are not expected to increase the LLL fraction to the level of tens of percent. This means that measuring the LLL cross section at the LHC will be very challenging. A new on-shell mapping for triboson processes, being a crucial element of polarized cross-section calculation, is also presented.

Figures (9)

• Figure 1: Representative Feynman diagrams at Born level for the full off-shell process, classified into the triply-resonant diagrams (a, b, c, d, k), doubly-resonant diagrams (e, f), singly-resonant diagrams (g, h), and $WH$ diagram (k).
• Figure 2: Cross sections as functions of the factorization scale parameter $\xi = \mu/\mu_0$ for fixed (left) and dynamical (right) scales. The vertical bars on the interference curve represent the statistical errors.
• Figure 3: Distributions in $\cos \theta_e^{WWW}$ (left) and in azimuthal-angle difference between the muon and the tauon (right) are shown. The polar angle $\theta_e^{WWW}$ is defined in the $WWW$ c.m.f. (see the text for details). The top panels show the values of the LO differential cross sections. The middle panels show the normalized distributions (areas are equal to unity), while the bottom panels display the interference contribution and the off-shell effect (difference between the unpolarized TPA and the full off-shell).
• Figure 4: Same as Fig. but for the rapidity difference between the muon and the electron-tauon system (left) and cosine of the angle between the tauon and the electron-muon system (right).
• Figure 5: Same as Fig. but for the invariant mass of the six-lepton system (left) and the transverse momentum of the electron-muon-tauon system (right).