EVAluation of the Equivalent Vector Boson Approximation at highest energy colliders

TL;DR

The paper rigorously tests the Equivalent Vector Boson Approximation (EVA) at multi‑TeV energies using Whizard, across a suite of SM processes to quantify its accuracy relative to full matrix elements. It develops the EVA formalism, implements multiple modes in Whizard, and demonstrates how the cross section factorizes into polarized vector boson structure functions and hard scattering amplitudes, illustrating with a 2→2 convolution example. Across di‑Higgs, neutrino, di‑photon, top‑pair, ZH, and vector boson scattering channels, the study finds no universal prescription that makes EVA universally accurate; the agreement is highly sensitive to polarization, kinematic cuts, and the chosen scales, with uncertainties up to $O(100\%)$ in many cases. The work concludes that while EVA can describe certain longitudinally dominated processes reasonably well and offers a fast, scalable tool for exploring EW splitting regimes and BSM scenarios, it is not a reliable replacement for full matrix‑element calculations in general, especially for transverse contributions, and emphasizes the need for careful, process‑dependent phase‑space selections and further development of EW resummation techniques.

Abstract

Collider processes at the highest available partonic center-of-mass energies - 10 TeV and above - exhibit a new regime of electroweak interactions where electroweak gauge bosons mostly act as quasi-massless partons in vector boson fusion processes. We scrutinize these processes using the Equivalent Vector boson Approximation (EVA) based on its implementation in the Monte Carlo generator framework Whizard. Using a variety of important physics processes, including top pairs, Higgs pairs, neutrino pairs, and vector boson pairs, we study the behavior of processes initiated by transverse and longitudinal vector bosons, both $W$ and $Z$ induced. By considering several distributions for each process, we conclude that: there is no universal, process-independent prescription which minimizes the discrepancies between EVA- and matrix-element-based predictions; even by resorting to process-by-process prescriptions, we typically observe significant observable-dependent effects; the uncertainties associated with parameter dependencies in the EVA can be as large as $\mathcal{O}$(100%), and can only possibly be reduced by careful process-dependent kinematical selections.

Figures (15)

• Figure 1: Prototype diagram in the EW deep inelastic scattering (DIS) picture as the starting point for the derivation of the EVA.
• Figure 2: Differential $m_{VV}$ distribution for the $\ell^+\ell^{\prime -} \to W^+ W^- \rightarrow HH$ process at $\sqrt{s} = 14$ TeV for pure longitudinal (blue), pure transverse (red) and mixed incoming polarizations computed Mathematica (solid line) and with Whizard (dashed line), with $p_{\perp,\text{max}}\xspace$ set to $m_{VV} / 4$. We additionally show the cases where $p_{\perp,\text{max}}\xspace$ is varied by a factor of 2 up and down as a band for the semi-analytical setup and as dotted lines for the Whizard setup.
• Figure 3: Invariant mass distributions of the di-Higgs system in the process $e^+ \mu^- \to HH + X$ at $\sqrt{s} = 10$ TeV for the full matrix element evaluation (red) and the EVA for different values of $x_\text{min}\xspace$ and $p_{\perp,\text{max}}$, respectively. The green band represents a variation of $x_{min} = 2m_V/E_\textnormal{CM}$ by a factor of two. The blue band in the left panel represents a scale variation by a factor of two around the central scale $p_{\perp,\text{max}}\xspace = \sqrt{\hat{s}}/4$. To facilitate the comparison between the two effects, the scale variation is not shown in the right plot.
• Figure 4: Invariant mass distributions of the di-Higgs system in $e^+ \mu^- \to HH + X$ for different collision energies.
• Figure 5: Transverse momentum distributions for the leading Higgs-$p_\perp$ (left) and sub-leading $p_\perp$ (right) in $e^+ \mu^- \to HH + X$ at $\sqrt{s} = 10$ TeV for the full matrix element evaluation (red) and the EWA (blue) for different values of $x_\text{min}\xspace$ and $p_{\perp,\text{max}}$. The blue band represents a scale variation by a factor of two around the central scale $p_{\perp,\text{max}}\xspace = \sqrt{\hat{s}}/4$ and the green one around $x_\text{min} = 2 m_V/E_\text{CM}$ at this central scale.