  By estimating the Turaev genus or the dealternation number, which leads to an
estimate of knot floer thickness, in terms of the genus and the braid index, we
show that a knot $K$ in $S^{3}$ does not admit purely cosmetic surgery whenever
$g(K)\geq \frac{3}{2}b(K)$, where $g(K)$ and $b(K)$ denotes the genus and the
braid index, respectively. In particular, this establishes a finiteness of
purely cosmetic surgeries; for fixed $b$, all but finitely many knots with
braid index $b$ satisfies the cosmetic surgery conjecture.
