Polarized-boson pairs at NLO in the SMEFT

Abstract

We present a computation of diboson production in the $W^\pm Z$ channel at the Large Hadron Collider (LHC), incorporating leptonic decays of the gauge bosons and considering intermediate gauge bosons with definite polarization states. The analysis includes contributions from the Standard Model effective field theory (SMEFT) and is carried out at next-to-leading order accuracy in QCD, matched to a parton-shower simulation. Our implementation allows for the selection of specific helicity configurations, both in the Standard Model and in the presence of dimension-six operators inducing anomalous triple-gauge-boson couplings. This work provides a key ingredient for both polarization-template and quantum-tomography analyses of diboson systems at the LHC within the SMEFT framework.

Figures (8)

• Figure 1: Example tree-level resonant (left) and non-resonant (right) diagrams contributing to $W^+ Z$ production and decay in proton-proton ($pp$) collisions. Further explanations can be found in the main text.
• Figure 2: Differential NLO QCD distributions in the $Z$-boson transverse momentum ($p_{T, Z}$) in the right panel, and in the antimuon decay angle in the $Z$-boson rest frame ($\phi_{\mu^+}^\ast$) in the left panel, within the ATLAS fiducial phase space, as defined in \ref{['eq:fiducial']}. A comparison is made between the $\sqrt{s}= 13 \, {\rm TeV}$ results obtained with Recola 2 and Powheg-Box-Res (solid lines) and those using Smeft@Nlo and Mg5_aMC@Nlo (dashed lines), as presented in Ref. ElFaham:2024uop. In the left (right) panel the displayed BSM results correspond to $C_W/\Lambda^2 = 1 \, {\rm TeV}^{-2}$ ($C_{\widetilde{W}}/\Lambda^2 = 1 \, {\rm TeV}^{-2}$). The notation $\text{SMEFT}_6$ ($\text{SMEFT}_8$) refers to the sum of the SM and SMEFT contributions, including terms up to order $1/\Lambda^2$ ($1/\Lambda^4$). The lower sections of the panels show the ratios between the BSM and SM predictions.
• Figure 3: Transverse-mass distributions of the $W$ boson ($m_{T,W}$) at $\sqrt{s}= 13 \, {\rm TeV}$ are shown for both the inclusive (left panel) and fiducial (right panel) setups, as defined in \ref{['eq:inclusive', 'eq:fiducial']}, respectively. Solid lines represent the full off-shell predictions, while dashed lines correspond to the unpolarized DPA results. Each panel is divided into two sections, with the absolute SM prediction in the upper section and ratios of BSM to SM results in the lower section within the same approximation. The BSM curves employ $C_W/\Lambda^2 = 1 \, {\rm TeV}^{-2}$, with $\text{SMEFT}_6$ and $\text{SMEFT}_8$ defined as in \ref{['fig:comp']}.
• Figure 4: Contributions from the dimension-six SMEFT operator $Q_W$ to the triple-gauge-boson couplings $WWZ$ (left) and $WW\gamma$ (right) in $W^+ Z$ production with leptonic decays. The black boxes represent the operator insertions. Both diagrams are included in the full off-shell calculation, whereas only the left diagram is taken into account in the DPA.
• Figure 5: Distributions of the cosine of the polar decay angle of the positron in the $W$-boson rest frame ($\cos\theta^\ast_{\text{e}\xspace^+}$) at $\sqrt{s} = 13 \, {\rm TeV}$ are shown for the inclusive setup defined in \ref{['eq:inclusive']}. The analysis considers a $W$ boson with a fixed polarization state ($L,+,-$) and an unpolarized $Z$ boson. Solid lines represent the results of a direct simulation of singly-polarized signals in the DPA, while dashed lines are obtained by projecting the unpolarized DPA results onto Legendre polynomials of degree up to 2. The left and right figures show the linear and quadratic SMEFT contributions, respectively, corresponding to the choice $C_W/\Lambda^2 = 1 \, {\rm TeV}^{-2}$. Please note that the $W_L$ contribution in the quadratic case, shown in the right plot, has been inflated by a factor of $10$.