Measurements of the branching fractions of the semileptonic decays
B
→
D
(
*
)
τ
ν
¯
τ
and
B
c
→
J
/
ψ
τ
ν
¯
τ
systematically exceed the Standard Model predictions, pointing to possible signals of new physics that can violate lepton flavor universality. The unknown origin of new physics realized in these channels can be probed using a general effective Hamiltonian constructed from four-fermion operators and the corresponding Wilson coefficients. Previously, constraints on these Wilson coefficients were obtained mainly from the experimental data for the branching fractions. Meanwhile, polarization observables were only theoretically studied. The situation has changed with more experimental data having become available, particularly those regarding the polarization of the tau and the
D
*
meson. In this study, we discuss the implications of the new data on the overall picture. We then include them in an updated fit of the Wilson coefficients using all hadronic form factors from our covariant constituent quark model. The use of our form factors provides an analysis independent of those in the literature. Several new-physics scenarios are studied with the corresponding theoretical predictions provided, which are useful for future experimental studies. In particular, we find that under the one-dominant-operator assumption, no operator survives at
1
σ
. Moreover, the scalar operators
O
S
L
and
O
S
R
are ruled out at
2
σ
if one uses the constraint
B
(
B
c
→
τ
ν
τ
)
≤
10
%
, while the more relaxed constraint
B
(
B
c
→
τ
ν
τ
)
≤
30
%
still allows these operators at
2
σ
, but only minimally. The inclusion of the new data for the
D
*
polarization fraction
F
L
D
*
reduces the likelihood of the right-handed vector operator
O
V
R
and significantly constrains the tensor operator
O
T
L
. Specifically, the
F
L
D
*
alone rules out
O
T
L
at
1
σ
. Finally, we show that the longitudinal polarization
P
L
τ
of the tau in the decays
B
→
D
*
τ
ν
¯
τ
and
B
c
→
J
/
ψ
τ
ν
¯
τ
is extremely sensitive to the tensor operator. Within the
2
σ
allowed region, the best-fit value
T
L
=
0.04
+
i
0.17
predicts
P
L
τ
(
D
*
)
=
−
0.33
and
P
L
τ
(
J
/
ψ
)
=
−
0.34
, which are at about 33% larger than the Standard Model (SM) prediction
P
L
τ
(
D
*
)
=
−
0.50
and
P
L
τ
(
J
/
ψ
)
=
−
0.51
.
The order analysis for the two loop corrections to lepton MDM
