Can you get me a closeup of the flower so I can see the center part--the pistil and the stamen?  Thanks!

Thanks, Alice! Here are the close-up photos of the flower.

Sorry it's taken me so long--I had a heck of a time finding this one. It looks like it's a garden escapee--they sell it in nurseries as a desirable groundcover.

Pratia peduculata, or star creeper.   https://portlandnursery.com/groundcovers/pratia/

If you do a search on it as a weed, you'll find that it's a real garden bully, and nearly impossible to get rid of when it starts growing beyond where you want it.  Apparently pulling it out by the roots only lets it regenerate new little plants.  People have been really frustrated because the selective herbicides (that don't kill grass) like tricopyr and 2,4-d don't work. Most elected the "nuclear option" and used glyphosate (E.g., Roundup) and killed everything, including their lawn.  They decided to just re-seed the lawn. I can't recommend an  herbicide because I don't believe this plant is listed on any herbicide labels.  I will contact our state pesticide coordinator and ask her and get back to you.

Alice, thank you so much for identifying the weed! It looks like a tough species to deal with. Hope there will be a good herbicide to tackle it.

So I just heard back. "There is not an effective herbicide available at this time to recommend." I was afraid that would be the answer.  I'm sorry I can't be of more help!  It is possible that people with a pesticide applicator license might be able to help you.

Thank you, Alice!

If I cover the area with construction black plastic from October until April next year, can the rhizomes of the blue star creeper be effectively killed?

Actually, research has shown that clear plastic works better for solarization!! YIt usually takes very hot weather to produce this effect.

Here are some options. A test was done on some tough to manage perennial weeds. 4 different covers were used and held in place by cinder blocks--the edges must be sealed completely--also use soil on the edges to maintain full, continual coverage.  The problem with the results is that they kept the covers in place for a full year and covered in April. The advantage to covering in early spring is that the vegetation under the cover basically "cooks" in the heat.  That wouldn't be the case if you covered it in winter. However, it's worth giving it a try.

Thanks for the info! I'll report back in a year.

Hope so--thanks!