Distinguishing a minimal supersymmetric standard model Higgs boson from the SM Higgs boson at a linear collider

The decoupling properties of the Higgs sector in the minimal supersymmetric standard model (MSSM) imply that a light CP-even Higgs boson discovered at the Fermilab Tevatron or CERN LHC may closely resemble the standard model (SM) Higgs boson. In this paper, we investigate how precision measurements of Higgs properties at a linear collider (LC) can distinguish between a CP-even Higgs boson of the MSSM and the SM Higgs boson. We review the expected theoretical behavior of the partial widths and branching ratios for decays of the neutral MSSM Higgs bosons with significant couplings to the W and Z bosons, including the leading radiative corrections to the mixing angle α and $\tan \beta$-enhanced vertex corrections. The general expectation is that the Higgs couplings to $W^{+}{W}^{-},$ ZZ, $c\overline{c},$ and $t\overline{t}$ should quickly approach their SM values for increasing CP-odd Higgs boson mass $m_A,$ while the couplings to $b\overline{b}$ and ${\tau }^{+}{\tau }^{-}$ do so more slowly. Using the expected experimental and theoretical accuracy in determining SM branching ratios and partial widths, we demonstrate the sensitivity of measurements at the LC to variations in the MSSM parameters, with particular attention to the decoupling limit. For a wide range of MSSM parameters, the LC is sensitive to $m_A\sim 600\mathrm{GeV}$ almost independently of $\tan \beta .$ For large values of $\tan \beta$ and some specific choices of MSSM parameters [e.g., $A_t\mu <0\mathrm{}$ and $|A_t|\simeq |\mu |\simeq \mathcal{O}{(M}_S)$], one of the CP-even Higgs bosons can be SM-like independent of the value of $m_A.$ In the case of large deviations from the SM, we present a procedure using Higgs coupling measurements to extract the supersymmetric correction to the relation between the b quark mass and Yukawa coupling.