57 research outputs found
Electromagnetic Meson Form Factors in the Salpeter Model
We present a covariant scheme to calculate mesonic transitions in the
framework of the Salpeter equation for -states. The full Bethe
Salpeter amplitudes are reconstructed from equal time amplitudes which were
obtained in a previous paper\cite{Mue} by solving the Salpeter equation for a
confining plus an instanton induced interaction. This method is applied to
calculate electromagnetic form factors and decay widths of low lying
pseudoscalar and vector mesons including predictions for CEBAF experiments. We
also describe the momentum transfer dependence for the processes
.Comment: 22 pages including 10 figure
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 stability of the spectator, Dirac, and Salpeter equations for mesons
Mesons are made of quark-antiquark pairs held together by the strong force.
The one channel spectator, Dirac, and Salpeter equations can each be used to
model this pairing. We look at cases where the relativistic kernel of these
equations corresponds to a time-like vector exchange, a scalar exchange, or a
linear combination of the two. Since the model used in this paper describes
mesons which cannot decay physically, the equations must describe stable
states. We find that this requirement is not always satisfied, and give a
complete discussion of the conditions under which the various equations give
unphysical, unstable solutions
Instantaneous Bethe-Salpeter equation: utmost analytic approach
The Bethe-Salpeter formalism in the instantaneous approximation for the
interaction kernel entering into the Bethe-Salpeter equation represents a
reasonable framework for the description of bound states within relativistic
quantum field theory. In contrast to its further simplifications (like, for
instance, the so-called reduced Salpeter equation), it allows also the
consideration of bound states composed of "light" constituents. Every
eigenvalue equation with solutions in some linear space may be (approximately)
solved by conversion into an equivalent matrix eigenvalue problem. We
demonstrate that the matrices arising in these representations of the
instantaneous Bethe-Salpeter equation may be found, at least for a wide class
of interactions, in an entirely algebraic manner. The advantages of having the
involved matrices explicitly, i.e., not "contaminated" by errors induced by
numerical computations, at one's disposal are obvious: problems like, for
instance, questions of the stability of eigenvalues may be analyzed more
rigorously; furthermore, for small matrix sizes the eigenvalues may even be
calculated analytically.Comment: LaTeX, 23 pages, 2 figures, version to appear in Phys. Rev.
Pseuduscalar Heavy Quarkonium Decays With Both Relativistic and QCD Radiative Corrections
We estimate the decay rates of ,
, and ,
, by taking into account both relativistic and
QCD radiative corrections. The decay amplitudes are derived in the
Bethe-Salpeter formalism. The Bethe-Salpeter equation with a QCD-inspired
interquark potential are used to calculate the wave functions and decay widths
for these states. We find that the relativistic correction to the
ratio is negative and tends to compensate the positive contribution from
the QCD radiative correction. Our estimate gives and ,
which are smaller than their nonrelativistic values. The hadronic widths
and are then indicated accordingly to the first order
QCD radiative correction, if . The decay widths for
states are also estimated. We show that when making the assmption
that the quarks are on their mass shells our expressions for the decay widths
will become identical with that in the NRQCD theory to the next to leading
order of and .Comment: 14 pages LaTex (2 figures included
Charmed quark component of the photon wave function
We determine the c-anti-c component of the photon wave function on the basis
of (i) the data on the transitions e+ e- -> J/psi(3096), psi(3686), psi(4040),
psi(4415), (ii) partial widths of the two-photon decays eta_{c0}(2979),
chi_{c0}(3415), chi_{c2}(3556) -> gamma-gamma, and (iii) wave functions of the
charmonium states obtained by solving the Bethe-Salpeter equation for the
c-anti-c system. Using the obtained c-anti-c component of the photon wave
function we calculate the gamma-gamma decay partial widths for radial
excitation 2S state, eta_{c0}(3594) -> gamma-gamma, and 2P states
chi_{c0}(3849), chi_{c2}(3950) -> gamma-gamma.Comment: 20 pages, 8 figure
Quark--antiquark states and their radiative transitions in terms of the spectral integral equation. {\Huge II.} Charmonia
In the precedent paper of the authors (hep-ph/0510410), the states
were treated in the framework of the spectral integral equation, together with
simultaneous calculations of radiative decays of the considered bottomonia. In
the present paper, such a study is carried out for the charmonium
states. We reconstruct the interaction in the -sector on the basis of
data for the charmonium levels with , , ,
, , and radiative transitions
, , ,
and , ,
. The levels and their wave functions
are calculated for the radial excitations with . Also, we determine the
component of the photon wave function using the annihilation
data: , , , , , and perform the calculations of the partial widths of
the two-photon decays for the states: , ,
, and states:
, , . We discuss the status of the recently observed states
X(3872) and Y(3941): according to our results, the X(3872) can be either
or , while Y(3941) is .Comment: 24 pages, 9 figure
On the instantaneous Bethe-Salpeter equation
We present a systematic algebraic and numerical investigation of the
instantaneous Bethe-Salpeter equation. Emphasis is placed on confining
interaction kernels of the Lorentz scalar, time component vector, and full
vector types. We explore stability of the solutions and Regge behavior for each
of these interactions, and conclude that only time component vector confinement
leads to normal Regge structure and stable solutions.Comment: Latex (uses epsf macro), 26 pages of text, 12 postscript figures
included
On the Particle Data Group evaluation of Psi' and chi_c Branching Ratios
I propose a new evaluation of and branching ratios
which avoids the correlations affecting the current Particle Data Group
evaluation.
These correlations explain the apparent technique-dependent discrepancies
between the available determinations of the
and under the hypotesis that the current
values of the branching ratios are
overestimated.
In the process I also noticed that Particle Data Group has not restated many
of the older measurements, when necessary, for the new value of , which significantly affects the evaluation of some
relevant and exclusive branching ratios.Comment: 13 pages. Revised version. Submitted to Phys. Rev.
Effective Lagrangian Approach to Weak Radiative Decays of Heavy Hadrons
Motivated by the observation of the decay by
CLEO, we have systematically analyzed the two-body weak radiative decays of
bottom and charmed hadrons. There exist two types of weak radiative decays: One
proceeds through the short-distance transition and the other
occurs through -exchange accompanied by a photon emission. Effective
Lagrangians are derived for the -exchange bremsstrahlung processes at the
quark level and then applied to various weak electromagnetic decays of heavy
hadrons. Predictions for the branching ratios of and
\Xi_b^0\to\xip_c^0\gamma are given. In particular, we found . Order of magnitude
estimates for the weak radiative decays of charmed hadrons: and
are also presented. Within this approach, the decay asymmetry for antitriplet
to antitriplet heavy baryon weak radiative transitions is uniquely predicted by
heavy quark symmetry. The electromagnetic penguin contribution to
is estimated by two different methods and its
branching ratio is found to be of order . We conclude that
weak radiative decays of bottom hadrons are dominated by the short-distance
mechanism.Comment: 28 pages + 3 figures (not included), CLNS 94/1278, IP-ASTP-04-94.
[Main changes in this revised version: (i) Sect 2 and subsection 4.1 are
revised, (ii) A MIT bag method for calculating the decay rate of is presented, (iii) All predictions are updated using the
newly available 1994 Particle Data Group, and (iv) Appendix and subsections
3.3 and 4.4 are deleted.
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