Baryon Semileptonic Decays
The interplay between the weak and strong interactions of
hadrons in their weak decays offers opportunities to understand the strong
interaction in the non-perturbative regime. The weak interactions also provide
access to some fundamental parameters of the standard model, namely the elements
of the Cabbibo-Kobayashi-Maskawa (CKM) quark mixing matrix. Since quarks are confined
within hadrons, accessing the CKM matrix elements requires an understanding of
the strong interaction dynamics binding the quarks into hadrons.
The semileptonic decay of a baryon is represented by the diagram on the left. In
this diagram, a quark of flavor Q changes to a quark of different flavor q, with
the emission of a virtual W boson. The virtual boson gives rise to a charged lepton and
antineutrino (or a charged antilepton and a neutrino). The new quark q forms a
baryon with the remaining two quarks from the original or parent baryon. The
final or daughter baryon may be in its ground state, but it may also be in any
of a number of excited states. In any case, the decay is described in terms of a
number of form factors, where all of the hadronic physics dwells.
In recent work with Muslema Pervin and Simon Capstick, a quark model for the
semileptonic decays of baryons was constructed, and applied to a number of
decays of heavy baryons. The wave functions for the baryons were expanded in two
bases, the harmonic oscillator basis and the sturmian basis. The form factors
were also calculated in both bases. In addition, the kinetic energy of the
quarks was treated both semirelativistically and nonrelativistically. The decays of heavy
&LambdaQ and &OmegaQ baryons were examined in the model,
and the results for the form factors compared with the predictions of the heavy
quark effective theory (HQET). Predicted decay rates were also compared with
available data, but data were only available for the decay
&Lambdac+ &rarr &Lambda e+ &nue.
Figures 1a and 1b below show the form factors for &Omegab &rarr
&Omegac transitions. Figure 1a arises in the harmonic
oscillator basis, while Figure 1b arises from the sturmian basis.
In each graph the solid curves are from the nonrelativistic version of the
model, while the dashed curves are from the semirelativistic version. Click on the
figures for full-size versions.
Fig. 1a
Fig. 1b
Figures 2a and 2b below show the rates for &Omegab &rarr
&Omegac transitions, for the ground state and a number of excited
states. Figure 2a arises in the harmonic
oscillator basis, while Figure 2b arises from the sturmian basis.
In each graph the solid curves are from the nonrelativistic version of the
model, while the dashed curves are from the semirelativistic version.
Fig. 2a
Fig. 2b
Figures 3a and 3b below show the differential decay rates for &Omegac
&rarr &Xi(*), for a number of ground state &Xi as well as a couple of
excited states. Figure 3a arises in the harmonic
oscillator basis, while Figure 3b arises from the sturmian basis.
In each graph the solid curves are from the nonrelativistic version of the
model, while the dashed curves are from the semirelativistic version.
Fig. 3a
Fig. 3b
One of the interesting results of the calculation was the 'elastic' ratio for the
semileptonic decays of the &Lambdac. Current experimental analysis assume
that decays to the ground state &Lambda saturate these decays, and this has
implications for a number of decays of the &Lambdac that are normalized to
the semileptonic decay. In the model calculations, the elastic fraction obtained is
0.88 ± 0.02. The graphs showing the differential decay rates of the
&Lambdac to three &Lambda states (&Lambda(1115), &Lambda(1405) and
&Lambda(1520)) are shown
below in Figures 4a and 4b. Each graph shows clearly that the &Lambda(1115) does not
saturate the decays of the &Lambdac.
Fig. 4a
Fig. 4b
In the future, we plan to
examine the semileptonic decays of heavy &XiQ baryons, as well as those of
light baryons. We also plan to treat the nonleptonic decays of baryons in the
same model. These are decays in which the virtual W emitted creates a quark-antiquark
pair, which then form a meson M (as shown in the figure on the right). We also plan to
examine a number of the polarization observables that can
be measured in the semileptonic and nonleptonic decays.
All
content © Winston Roberts 2006
