Precise measurement of Higgs decay rate into WW* at future e^+e^- Linear Colliders

Assuming a SM or MSSM scenario, one expects a light Higgs boson which could be studied in great detail with a LC operating at \sqrt s>m_h+m_Z. In the TESLA scenario, with 500 fb^-1 accumulated at \sqrt s = 350 GeV, about 10^5 hZ events could be produced through the Higgstrahlung process. At a future LC with a \sim 1 cm beam-pipe radius and a thin Si detector there will be excellent separation between the various flavours. With the high statistics available it will thus become possible to measure the various branching ratios with a few % error. Typically one expects 8 % precision on BR(h\to\bar cc), 6 % on BR(h\to gg) and \sim 1 % on \sigma(hZ) x BR(h\to\bar bb) access to BR(h\to WW^*) and, as explained in section 3, this measurement can give access to the Higgs total decay width and therefore to all partial widths. In particular one can precisely measure \Gamma(h\to\bar bb) and \Gamma(h\to\tau^+\tau^-) which have a high sensitivity to MSSM effects\cite{gunion} and therefore allow an essential test of the Higgs sector. If m_A < 1 TeV, it becomes possible to measure a significant deviation and, within MSSM, to give an indirect estimate of m_A thus extending the effective sensitivity above the discovery domain of LHC. In the following section we describe a detailed analysis on the measurement of BR(h\to WW^*).