  We study the phenomenology of two leptoquarks, the Standard Model $SU(2)$
singlets $S_1$ and $U_1$, with regard to the latest experimental data from the
low-energy flavor physics measurements, LHC, and the IceCube neutrino
experiment. We consider a scenario when scalar (vector) leptoquark $S_1$
($U_1$) couples exclusively to the down quark and the neutrinos (charged
leptons) of all flavors, where the leptoquark in question couples to the SM
lepton doublets. The couplings of $S_1$ ($U_1$) to the up-type quarks and the
charged leptons (neutrinos) are in turn uniquely determined via $SU(2)$
symmetry. We find that the most important constraints on the leptoquark
parameter space originate from flavor physics measurements, followed by the LHC
search limits that take over the flavor physics ones in the large LQ mass
regime. We furthermore show that $S_1$ ($U_1$) marginally improves (spoils) the
fit of the current IceCube data with respect to the SM case within the region
of parameter space that is otherwise consistent with various low-energy flavor
physics measurements and the latest LHC input. Our study offers an up-to-date
analysis for these two leptoquarks in view of the latest experimental data.
