CHICAGO – Laws strictly curbing school sales of junk food and sweetened drinks may play a role in slowing childhood obesity, according to a study that seems to offer the first evidence such efforts could pay off.

The results come from the first large national look at the effectiveness of the state laws over time. They are not a slam-dunk, and even obesity experts who praised the study acknowledge the measures are a political hot potato, smacking of a “nanny state” and opposed by industry and cash-strapped schools relying on food processors’ money.

But if the laws have even a tiny effect, “what are the downsides of improving the food environment for children today?” asked Dr. David Ludwig, an obesity specialist at Harvard Medical School and Boston Children’s Hospital. “You can’t get much worse than it already is.”