We investigate the geometric interpretation of the standard model based on
noncommutative geometry. It is pointed out that real spectral triples, i.e.
, triples satisfying the reality structure J, can nevertheless contain spec
ific and well-defined couplings of lepton doublets to right-handed up antiq
uarks, via scalar leptoquarks. We explore in detail the consequences of the
possible existence of such leptoquarks, both for the Connes-Lott and the s
pectral action, and compare with physical bounds. For either case the resul
ts are in contradiction with experimental information. [S0556-2821(99)08101
-1].