Self-styled experts on child-rearing and diet have long scoffed at apple juice as mere “sugar water” with less food value than other juices. But Moms know what kids like, and they remember what their own mothers gave them. And they instinctively believe that apple juice is good for you.

They’re right.

It turns out that apple juice — especially the unfiltered kind — is loaded with phytochemicals that fight everything from cancer to Alzheimer’s to heart attacks. (Phytochemicals are usually related to plant pigments, and the brightest colors — like bright red apples — usually contain the most phytochemicals and nutrients.)

All of the research strongly suggests that plain-Jane apples and apple juice provide many of the same benefits as more currently “fashionable” exotic fruits such as pomegranates and noni fruit.

Cornell University researchers, for instance, recently discovered that the combination of beneficial chemicals in apples, which are mainly in the colorful peel, help slow tumor growth in cell cultures and animals.

Lead researcher Rui Hai Liu said the chemicals work together synergistically, and believes that the entire apple “package” is important.

Scientists at the University of Massachusetts at Lowell found, in a five-year study, that natural chemicals in apple juice helped cognitive function in mice. Now they’re studying the juice’s effect on Alzheimer’s patients.

Even before the new research came out, scientists knew about the powerful antioxidant action of apples and apple juice. (Antioxidants mop up so-called “free radicals” released by inflammatory processes in the body by donating an electron to the free radical and converting it to a harmless molecule.)

One particular antioxidant called quercetin could be the major reason behind the old “apple a day” saying, because it may help reduce cancer risk, prevent heart attacks, control asthma, and provide many other benefits as well.

While nutritionists recommend eating apples instead of just drinking the juice, they say juice can provide many of the same benefits. But which kind of apple juice — cloudy or clear?

Cloudy juice is made by shredding apples and straining the juice. Clear juice goes through an additional filtering process that removes more solids, and also goes through an enzyme treatment that removes the pectin and starch.

Consumers currently favor clear over cloudy, believing perhaps it is more pure, although both kinds are pasteurized. But is one better than the other?

A recent Polish study says cloudy is better. Researchers found that phytochemicals called polyphenols are four times higher in cloudy juice than clear. In laboratory tests, the cloudy soaked up 93 percent of free radicals while the clear juice only soaked up 24 percent.

How much should we drink?

While it’s always good to follow Mom’s advice, it’s sometimes even better to follow the advice of the Greeks: “All things in moderation.”