Directly Measuring the Tensor Structure of the Scalar Coupling to Gauge Bosons

TL;DR

The paper addresses whether the 125 GeV resonance couples to Z bosons through the Standard Model Higgs-like tensor structure or via higher-dimensional operators. It analyzes full kinematic distributions in the four-lepton decay channel, comparing a renormalizable a_h coupling with a_s and a_{Zγ} operators using an unbinned likelihood approach and pseudo-experiments. The results show that, with tens of signal events, the tensor structure can be discriminated at high significance, enabling direct tests of whether the resonance provides mass to the Z. These findings provide a practical path for early LHC data to constrain the particle's role in electroweak symmetry breaking and guide follow-up analyses in related channels.

Abstract

Kinematic distributions in the decays of the newly discovered resonance to four leptons can provide a direct measurement of the tensor structure of the particle's couplings to gauge bosons. Even if the particle is shown to be a parity even scalar, measuring this tensor structure is a necessary step in determining if this particle is responsible for giving mass to the Z. We consider a Standard Model like coupling as well as coupling via a dimension five operator to either ZZ or Zγ. We show that using full kinematic information from each event allows discrimination between renormalizable and higher dimensional coupling to ZZ at the 95% confidence level with O(50) signal events, and coupling to Zγcan be distinguished with as few as 20 signal events. This shows that these measurements can be useful even with this year's LHC data.

Figures (5)

• Figure 1: Normalized distributions for $\Phi$ (top), $\cos\theta_i$ (middle), and $M_2$ (bottom) for $m_\phi = 125$ GeV. Each plot shows curves from our three different scenarios with $a_h$ blue (solid), $a_s$ red (dashed), and $a_{Z\gamma}$ green (dot-dashed).
• Figure 2: Normalized distribution for $\cos\theta$ in the $a_h$ scenario. The blue (solid) curve is the same as the theory curve from Fig. \ref{['fig:distributions']}, the red (dashed) histogram is the distribution for $\cos\theta_1$ for 1000 Monte Carlo events, while the green (dot-dashed) histogram is $\cos\theta_2$ for the same events.
• Figure 3: Normalized $M_2$ distributions. The blue (solid) curve is the theory prediction in the $a_h$ scenario, while the light blue (dot-dashed) histogram is 1000 Monte Carlo events also in the $a_h$ scenario. The red (dashed) histogram is 1000 events in the $a_s$ scenario.
• Figure 4: Normalized distribution of our test statistic $\Lambda$ when $a_h$ is true on the right (blue), and when $a_s$ is true on the left (pink). Each histogram is the result of 5000 pseudo-experiments with 50 events each. The vertical (green) line is $\hat{\Lambda}$ defined in Eq. (\ref{['eq:lambdahat']}) such that the area to the right of $\hat{\Lambda}$ under the $a_s$ histogram is equal to the area to the left of $\hat{\Lambda}$ under the $a_h$ histogram. We also draw a Gaussian over each histogram with the same median and standard deviation.
• Figure 5: Expected significance as a function of number of events in the case of $a_h$ vs $a_s$ on top, and $a_h$ vs $a_{Z\gamma}$ on bottom. We use a different horizontal scale for the top and bottom plots because far fewer events are needed to discriminate $a_h$ from $a_{Z\gamma}$ than from $a_s$. We also fit with a function proportional to $\sqrt{N}$, which is the expected scaling. We mark the $\sigma$ value of 95% and 99% confidence level exclusion.