Why the healthy school lunch program is in trouble.

In the war to get America’s children to eat healthier, things are not going well.

Before/after photos of what students ate.

Student E114 is a case in point. E114 — the identification code she was assigned by researchers studying eating habits at her public elementary school somewhere in the Northeast — left the lunch line one day carrying a tray full of what looked like a balanced meal: chicken nuggets, some sort of mushy starch, green beans and milk.

Exactly 13 minutes later she was done. The chicken nuggets and the starch were gone. But the green beans? Still there in a neat pile and headed straight for the trash.

In a study published Tuesday in Public Health Reports, researcher Sarah Amin reports that such waste has become heartbreakingly common since the Agriculture Department rolled out new requirements in the 2012 school year that mandated that children who were taking part in the federal lunch program choose either a fruit or vegetable with their meals.

The USDA mandate — championed by first lady Michelle Obama — has been highly controversial. Some school officials had warned that picky eaters would just throw the additional food away, but proponents said they should give kids more credit and that they would make the right choice with some nudging.

“The basic question we wanted to explore was: does requiring a child to select a fruit or vegetable actually correspond with consumption. The answer was clearly no,” Amin, the lead author of the study, said in a statement.

There has been some research over the years to estimate the amount of consumption of produce and the amount of new waste created, but Amin’s study is perhaps the first to try to detail exactly what is happening on the ground.

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