Measuring the Higgs Boson Self-coupling at High Energy e^+e^- Colliders

Standard Model Higgs pair production at e^+e^- colliders has the capability to determine the Higgs boson self-coupling \lambda. I present a detailed analysis of the e^+e^- -> ZHH and e^+e^- -> \nu\bar\nu HH signal channels, and the relevant background processes, for future e^+e^- linear colliders with center of mass energies of \sqrt{s}=0.5 TeV, 1 TeV, and 3 TeV. Special attention is given to the role non-resonant Feynman diagrams play, and the theoretical uncertainties of signal and background cross sections. I also derive quantitative sensitivity limits for \lambda. I find that an e^+e^- collider with \sqrt{s}=0.5 TeV can place meaningful bounds on \lambda only if the Higgs boson mass is relatively close to its current lower limit. At an e^+e^- collider with \sqrt{s}=1 TeV (3 TeV), \lambda can be determined with a precision of 20-80% (10-20%) for integrated luminosities in the few ab^{-1} range and Higgs boson masses in the range m_H=120-180 GeV.