Exploration of the Tensor Structure of the Higgs Boson Coupling to Weak Bosons in $e^+e^-$ Collisions

Probing signatures of anomalous interactions of the Higgs boson with pairs of weak vector bosons is an important goal of an $e^+e^-$ collider commissioned as a Higgs factory. We perform a detailed analysis of such potential of a collider operating at $250 - 300$ GeV. Mostly using higher dimensional operators in a gauge-invariant framework, we show that substantial information on anomalous couplings can be extracted from the total rates of $s$-and $t$-channel Higgs production. The most obvious kinematic distributions, based on angular dependence of matrix elements, are relatively less sensitive with moderate coefficients of anomalous couplings, unless one goes to higher centre-of-mass energies. Some important quantities to use here, apart from the total event rates, are the ratios of event rates at different energies, ratios of $s$ and $t$-channel rates at fixed energies, and under some fortunate circumstances, the correlated changes in the rates for $W$-boson pair-production. A general scheme of calculating rates with as many as four gauge-invariant operators is also outlined. At the end, we perform a likelihood analysis using phenomenological parametrization of anomalous $HWW$ interaction, and indicate their distinguishability for illustrative values of the strength of such interactions.