3 research outputs found
Spectrum for Heavy Quankonia and Mixture of the Relevant Wave Functions within the Framework of Bethe-Salpeter Equation
Considering the fact that some excited states of the heavy quarkonia
(charmonium and bottomonium) still missing in experimental observations and
potential applications of the relevant wave functions of the bound states, we
re-analyze the spectrum and the relevant wave functions of the heavy quarkonia
within the framework of Bethe-Salpeter (B.S.) equation with a proper
QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to
potential of non-relativistic quark model, is instantaneous, so we call the
corresponding B.S. equation as BS-In equation throughout the paper.
Particularly, a new way to solve the B.S. equation, which is different from the
traditional ones, is proposed here, and with it not only the known spectrum for
the heavy quarkonia is re-generated, but also an important issue is brought in,
i.e., the obtained solutions of the equation `automatically' include the
'fine', 'hyperfine' splittings and the wave function mixture, such as
wave mixing in states, wave mixing in
states for charmonium and bottomonium etc. It is pointed out that the best
place to test the wave mixture probably is at -factory ( collider
running at -boson pole with extremely high luminosity).Comment: 26 pages, 8 figure
The magnetic dipole transitions in the binding system
The magnetic dipole transitions between the vector mesons and their
relevant pseudoscalar mesons (, , , ,
and etc, the binding states of system) of
the family are interesting. To see the `hyperfine' splitting due to
spin-spin interaction is an important topic for understanding the spin-spin
interaction and the spectrum of the the binding system. The
knowledge about the magnetic dipole transitions is also very useful for
identifying the vector boson mesons experimentally, whose masses are
just slightly above the masses of their relevant pseudoscalar mesons
accordingly. Considering the possibility to observe the vector mesons via the
transitions at factory and the potentially usages of the theoretical
estimate on the transitions, we fucus our efforts on calculating the magnetic
dipole transitions, i.e. precisely to calculate the rates for the transitions
such as decays and , and particularly
work in the Behte-Salpeter framework. In the estimate, as a typical example, we
carefully investigate the dependance of the rate
on the mass difference as well.Comment: 10 pages, 2 figures, 1 tabl