Would this be a: Periwinkle Vinca minor? It was growing thickly in an area that had other ground cover on it in Russellville, AR USA. Blooms were about one half inch. This area has been mowed a couple of times.
Michael is correct - Vinca minor usually has a round stem - this one looks to be oval with a groove - and the leaf tip is generally not quite as pointed and tapers at a less acute angle then this one. Vinca minor flowers are similar in color to this and have 5-6 petals that are joined at the base of each petal, but do not have a groove up the center of the petal, and generally have a blunted tip. This one has a groove and a round tip.
Close enough! Triodanis perfoliata from Campanulaceae fits better: http://plants.usda.gov/java/largeImage?imageID=sppe5_007_avp.tif
Thanks to the contributors for this ID post. I viewed several photos on various sites for Triodanis perfoliata and Legousia. Triodanis perfoliata appears to be the plant.
I am just checking everything with the distribution maps at USDA site. Out of all Legousia (Triodanis perfoliata has an alternative name Legousia perfoliata), only T. perfoliata is described for Arkansas.