Lasius niger on peony flower buds

This is a new behaviour for me, so perhaps others can fill me in.

We have two different peonies in our garden planted right next to each other; either different species or varieties. The flower buds on one of them is currently covered in black garden ants Lasius niger, which are clearly attending them for some reason. The other peony has no ants - not one - on the flower buds.

I spent some time yesterday watching and photographing the behaviour and still can't explain it. There are no aphids, so it can't be honeydew, and I can't see any obvious extra-floral nectaries. The ants' attentions seem to be focused on the sides of what are probably  sepals but may be developing petals (see photo).

Lasius niger on garden peony © M. J. Lush, 2013

Most of the time when I see ants on plants they are attending homoptera, so the relationship is unlikely to be very beneficial to the plants. This may be one case that is really advantageous to the plant, but I don't see what the ants are getting out of it or why they are only on one of the two plants.

Is this familiar to anyone?