Double Higgs Production at the Linear Colliders and the Probing of the Higgs Self-Coupling

Abstract

We study double Higgs production in the $e^+ e^-$ and $\gamma \gamma$ modes of the linear collider. It is also shown how one can probe the scalar potential in these reactions. We discuss the effective longitudinal $W$ approximation in $\gamma \gamma$ processes and the $W_L W_L$ luminosities in the two modes of a high-energy linear collider. A generalised non-linear gauge-fixing condition, which is particularly useful for tree-level calculations of electroweak processes for the laser induced collider, is presented. Its connection with the background-field approach to gauge fixing is given.Comment: 60 pages, LateX, uses epsf, needs FEYNMAN.tex, 26 figs. (eqs. 4.1 and 4.10 changed), full paper (including figs) is also available via www at http://lapphp0.in2p3.fr/preplapp/psth/doublehiggs.ps.gz or via anonymous ftp at ftp://lapphp0.in2p3.fr/pub/preprints-theorie/doublehiggsf.u