How can I style a JavaFX SplitMenuButton in CSS

I try to style a SplitMenuButton in JavaFX. I‘ve got a menuButton and a SplitMenuButton in my fxml-file.

My CSS-File looks like this:

.menu-button {
    -fx-background-color: red;
    }

.split-menu-button .label {
    -fx-background-color: green;
    }

.split-menu-button .arrow {
    -fx-background-color: yellow;
    }

But I can‘t figure out how to style the area around the arrow for the SplitMenuButton. I tried several ways, but nothing worked

.split-menu-button .menu-button {
    -fx-background-color: blue;
    }

.split-menu-button .menu-button .label {
    -fx-background-color: blue;
    }

.split-menu-button .menu{
    -fx-background-color: blue;
    }

.split-menu-button .menu-item {
    -fx-background-color: blue;
    }

.split-menu-button .button {
    -fx-background-color: blue;
    }

.split-menu-button .menu-bar {
    -fx-background-color: blue;
    }