Nuclear-matter modification of decay widths in the $phi to e^{+}e^{-}$ and $phi to K^{+}K^{-}$ channels

The invariant mass spectra of $phi to K^{+}K^{-}$ are measured in 12 GeV $p+A$ reactions in order to search for the in-medium modification of $phi$ mesons. The observed $K^{+}K^{-}$ spectra are well reproduced by the relativistic Breit-Wigner function with a combinatorial background shape in three $betagamma$ regions between 1.0 and 3.5. The nuclear mass-number dependence of the yields of the $K^{+}K^{-}$ decay channel is compared to the simultaneously measured $e^{+}e^{-}$ decay channel for carbon and copper targets. We parameterize the production yields as $sigma (A) = sigma_0 times A^alpha$ and obtain $alpha_{phito K^+K^-} - alpha_{phito e^+e^-}$ to be 0.14 $pm$ 0.12. Limits are obtained for the partial decay widths of $phi$ mesons in nuclear matter.