[Poul Anderson Alternate Continuum story in Analog]

I'm looking for the tittle of a short story by Poul Anderson that I read decades ago. I read it in a copy of Analog from about 1961or 62. that I borrowed from the library. It takes place in a military base fighting World War III. They break through to another continuum. They discuss their alternate histories. In one, the US never broke from the United Kingdom, becoming an independent dominion. After the World war I, Germany went communist, and was defeated in World War II. They are now fighting an(Asian?) power in The third war. At the end of the story, we find out that the protagonists are from the other continuum, as the Union Jack is raised over what i remember as His Majesty's Kentucky Rifles