Power-free values of binary forms and the global determinant method

We give an improved estimate for the density of $k$-free values of integral binary forms with no fixed $k$-th power divisor. Further, we give the corresponding improvement to a theorem of Stewart and Top on the number of power-free values in an interval that may be assumed by a binary form. The approach we use involves a generalization of the global determinant method of Salberger.Comment: 45 pages; final accepted versio

Rare decay B→XsννˉB \to X_{s} \nu \bar \nu in the two-Higgs-doublet model of type-III

In this paper, we calculated the new physics contribution to theoretically very clean rare decay $B\to X_{s} \nu \bar{\nu}$ in the general two-Higgs-doublet model (model III). Within the considered parameter space, we found that (a) the new physics contribution can provide one to two orders of enhancement to the branching ratio \calb(B\to X_s \nu \bar{\nu}) and can saturate the experimental bound on \calb(B \to X_s \nu \bar{\nu}) in some regions of the parameter space; (b) besides the CLEO data of $B \to X_s \gamma$, the ALEPH upper limit on \calb (B \to X_s \nu \bar{\nu}) also lead to further constraint on the size of the Yukawa coupling $\lambda_{tt}$: $\lambda_{tt}< 6.4$ for $\lambda_{bb}=2.7$ and \mhp=200 GeV.Comment: 10 pages, 3 figures in eps and 1 in ps, Latex fil