Based on the measurements of (Ds+​,D+)→f0​(1370)π+ we determine, in
a model independent way, the allowed ssˉ content in the scalar meson
f0​(1370). We find that, on the one hand, if this isoscalar resonance is a
pure nnˉ state [ nnˉ≡(uuˉ+ddˉ)/2​], a very
large W-annihilation term will be needed to accommodate Ds+​→f0​(1370)π+. On the other hand, the ssˉ component of f0​(1370)
should be small enough to avoid excessive Ds+​→f0​(1370)π+ induced
from the external W-emission. Measurement of f0​(1370) production in the
decay Ds+​→K+K−π+ will be useful to test the above picture. For the
decay D0→f0​(1370)Kˉ0 which is kinematically barely or even not
allowed, depending on the mass of f0​(1370), we find that the finite width
effect of f0​(1370) plays a crucial role on the resonant three-body decay
D0→f0​(1370)Kˉ0→π+π−Kˉ0.Comment: 12 pages, 2 figure
Charmed meson decays into a pseudoscalar meson P and a tensor meson T are
studied. The charm to tensor meson transition form factors are evaluated in the
Isgur-Scora-Grinstein-Wise (ISGW) quark model. It is shown that the
Cabibbo-allowed decay Ds+​→f2​(1270)π+ is dominated by the
W-annihilation contribution and has the largest branching ratio in D→TP
decays. We argue that the Cabibbo-suppressed mode D+→f2​(1270)π+
should be suppressed by one order of magnitude relative to Ds+​→f2​(1270)π+. When the finite width effect of the tensor resonances is taken
into account, the decay rate of D→TP is generally enhanced by a factor of
2∼3. Except for Ds+​→f2​(1270)π+, the predicted branching ratios
of D→TP decays are in general too small by one to two orders of magnitude
compared to experiment. However, it is very unlikely that the D→T
transition form factors can be enhanced by a factor of 3∼5 within the
ISGW quark model to account for the discrepancy between theory and experiment.
As many of the current data are still preliminary and lack sufficient statistic
significance, more accurate measurements are needed to pin down the issue.Comment: 11 page