What happens when you fail a pre-employment drug test, say for very
light recent marijuana consumption. The company is a global investment
bank. I have already worked on the job for week, and was tested the
first day. What happens if I fail? How will I be notified? Are they
required to fire me, or is there some leeway? Will they offer, or be
amenable to, a retest?

They are not required to fire you, but most likely will.  They don't
want stoned employees.

The choice of whether to keep you or fire you is up to your employers.
Unless you have very valuable skills and are difficult to replace, you
may get the axe with no recourse.

Regarding the matter of how you'll be notified, that, too, is up to
your employers. A friend of mine flunked a drug test, and he learned
of this when two of the company's security guards arrived to escort
him out of the building. His belongings were later boxed up and mailed
to him.

In most companies if you fail a pre-employment drug test you normally
return to pre-employment status.

Everyone else pretty much covered it..

Keep in mind that these drug tests ONLY test for marijuana-- so that
little tidbit is not going to help you in this situation.

If you'd shot up heroin prior to the test, it wouldn't have shown up
on the test.   These tests usually only check for metabolites of
marijuana.

Contrary to the prior poster's statement, these tests often test for
drugs other than marijuana. The most common drugs to test for are
amphetamines, cocaine, opiates, and marijuana. The test you took may
test for these and other drugs. The test my company uses test for nine
different substances, and unless an employee who tests positive can
produce a doctor's note saying that they've been legally prescribed
one of the substances, they're fired immediately with no severance
pay. Other employers may work differently, but unless you have an
employment contract or union agreement requiring them to retest you,
they can fire you immediately without notice or retest.