Determination of the $WW$ polarization fractions in $pp\to W^{\pm }{W}^{\pm }jj$ using a deep machine learning technique

The unitarization of the longitudinal vector boson scattering (VBS) cross section by the Higgs boson is a fundamental prediction of the Standard Model which has not been experimentally verified. One of the most promising ways to measure VBS uses events containing two leptonically decaying same-electric-charge $W$ bosons produced in association with two jets. However, the angular distributions of the leptons in the $W$ boson rest frame, which are commonly used to fit polarization fractions, are not readily available in this process due to the presence of two neutrinos in the final state. In this paper we present a method to alleviate this problem by using a deep machine learning technique to recover these angular distributions from measurable event kinematics and demonstrate how the longitudinal-longitudinal scattering fraction could be studied. We show that this method doubles the expected sensitivity when compared to previous proposals.

Figure 1

A comparison of the truth level $\cos {\theta }^{*}$ and the NN output $\cos {\theta }^{NN}$ distributions for $--$, $++$, and $LL$ events (a), $R_{pT}$ templates for the corresponding polarization states with log scaling (b), and a comparison of the $\cos {\theta }^{NN}$ for the signal and dominant $WZjj$ background (c) are shown with arbitrary units (arb. units). (a), (c) are projections of the 2D distributions onto one of the two leptons, which are identical to the projections onto the other lepton due to arbitrary sorting.

Figure 2

The two-dimensional distribution of ${\cos }_1^{NN}$ versus $\cos {\theta }_2^{NN}$ for the two leptons in each event is shown for each of the three polarization states: $TT$, $TL$, and $LL$, respectively.

Figure 3

One example fit where the pseudo data are compared to the sum of contributions from the $TT$, $TL$, and $LL$ components. There are five groups with five bins inside each group. These five groups represent $\cos {\theta }_2^{NN}$ from $-1$ to 1 with a step size of 0.4, while five bins inside each group represent $\cos {\theta }_1^{NN}$ from $-1$ to 1 with a step size of 0.4.

Figure 4

68% (yellow) and 95% (green) expected confidence intervals for the measured $LL$ fraction $f_{LL}$ (top panels), the $TL$ fraction $f_{TL}$ (middle panels), and the $TT$ fraction $f_{TT}$ (bottom panels) as a function of the integrated luminosity for, from left to right, scenarios (a), (b), and (c) discussed in the text.