52 research outputs found
Baryons in O(4) and Vibron Model
The structure of the reported excitation spectra of the light unflavored
baryons is described in terms of multi-spin valued Lorentz group
representations of the so called Rarita-Schwinger (RS) type (K/2, K/2)* [(1/
2,0)+ (0,1/2)] with K=1,3, and 5. We first motivate legitimacy of such pattern
as fundamental fields as they emerge in the decomposition of triple fermion
constructs into Lorentz representations. We then study the baryon realization
of RS fields as composite systems by means of the quark version of the U(4)
symmetric diatomic rovibron model. In using the U(4)/ O(4)/ O(3)/ O(2)
reduction chain, we are able to reproduce quantum numbers and mass splittings
of the above resonance assemblies. We present the essentials of the four
dimensional angular momentum algebra and construct electromagnetic tensor
operators. The predictive power of the model is illustrated by ratios of
reduced probabilities concerning electric de-excitations of various resonances
to the nucleon.Comment: Phys. Rev. D (in press, 2001
Spin-1 gravitational waves and their natural sources
Non-vacuum exact gravitational waves invariant for a non Abelian
two-dimensional Lie algebra generated by two Killing fields whose commutator is
of light type, are described. The polarization of these waves, already known
from previous works, is related to the sources. Non vacuum exact gravitational
waves admitting only one Killing field of light type are also discussed.Comment: 10 pages, late
Rotational symmetry and degeneracy: a cotangent-perturbed rigid rotator of unperturbed level multiplicity
We predict level degeneracy of the rotational type in diatomic molecules
described by means of a cotangent-hindered rigid rotator. The problem is shown
to be exactly solvable in terms of non-classical Romanovski polynomials. The
energies of such a system are linear combinations of t(t+1) and 1/[t(t+1)+1/4]
terms with the non-negative integer principal quantum number t=n+|/bar{m}|
being the sum of the degree n of the polynomials and the absolute value,
|/bar{m}|, of the square root of the separation constant between the polar and
azimuthal motions. The latter obeys, with respect to t, the same branching
rule, |/bar{m}|=0,1,..., t, as does the magnetic quantum number with respect to
the angular momentum, l, and, in this fashion, the t quantum number presents
itself indistinguishable from l. In effect, the spectrum of the hindered
rotator has the same (2t+1)-fold level multiplicity as the unperturbed one. For
small t values, the wave functions and excitation energies of the perturbed
rotator differ from the ordinary spherical harmonics, and the l(l+1) law,
respectively, while approaching them asymptotically with increasing t. In this
fashion the breaking of the rotational symmetry at the level of the
representation functions is opaqued by the level degeneracy. The model provides
a tool for the description of rotational bands with anomalously large gaps
between the ground state and its first excitation.Comment: 10 pages, 6 figures; Molecular Physics 201
The Trigonometric Rosen-Morse Potential in the Supersymmetric Quantum Mechanics and its Exact Solutions
The analytic solutions of the one-dimensional Schroedinger equation for the
trigonometric Rosen-Morse potential reported in the literature rely upon the
Jacobi polynomials with complex indices and complex arguments. We first draw
attention to the fact that the complex Jacobi polynomials have non-trivial
orthogonality properties which make them uncomfortable for physics
applications. Instead we here solve above equation in terms of real orthogonal
polynomials. The new solutions are used in the construction of the
quantum-mechanic superpotential.Comment: 16 pages 7 figures 1 tabl
On the and f(1420) Couplings to the Nucleon
We consider neutral pseudoscalar, , and axial vector, ,
mesons in the OZI-rule-respecting flavor basis, , and suggest a scenario for their
coupling to the nucleon. Within this framework, the non--strange parts of the
and f couplings are modeled by means of triangular ,
and vertices, while the strange ones partly proceed
via Goldberger-Treiman relations, which have been concluded solely on the
grounds of current universality. The suggested model explains the observed
suppression of the coupling with respect to the constituent quark
model expectations, and predicts the coupling of to the nucleon.Comment: appears in Int. J. Mod. Phys. A (in press
Nucleon form factors in the canonically quantized Skyrme model
The explicit expressions for the electric, magnetic, axial and induced
pseudoscalar form factors of the nucleons are derived in the {\it ab initio}
quantized Skyrme model. The canonical quantization procedure ensures the
existence of stable soliton solutions with good quantum numbers. The form
factors are derived for representations of arbitrary dimension of the SU(2)
group. After fixing the two parameters of the model, and , by the
empirical mass and electric mean square radius of the proton, the calculated
electric and magnetic form factors are fairly close to the empirical ones,
whereas the the axial and induced pseudoscalar form factors fall off too slowly
with momentum transfer.Comment: 14pp including figure
Electromagnetic couplings of elementary vector particles
On the basis of the three fundamental principles of (i) Poincar\'{e} symmetry
of space time, (ii) electromagnetic gauge symmetry, and (iii) unitarity, we
construct an universal Lagrangian for the electromagnetic interactions of
elementary vector particles, i.e., massive spin-1 particles transforming in the
/1/2,1/2) representation space of the Homogeneous Lorentz Group (HLG). We make
the point that the first two symmetries alone do not fix the electromagnetic
couplings uniquely but solely prescribe a general Lagrangian depending on two
free parameters, here denoted by \xi and g. The first one defines the
electric-dipole and the magnetic-quadrupole moments of the vector particle,
while the second determines its magnetic-dipole and electric-quadrupole
moments. In order to fix the parameters one needs an additional physical input
suited for the implementation of the third principle. As such, one chooses
Compton scattering off a vector target and requires the cross section to
respect the unitarity bounds in the high energy limit. In result, we obtain the
universal g=2, and \xi=0 values which completely characterize the
electromagnetic couplings of the considered elementary vector field at tree
level. The nature of this vector particle, Abelian versus non-Abelian, does not
affect this structure. Merely, a partition of the g=2 value into non-Abelian,
g_{na}, and Abelian, g_{a}=2-g_{na}, contributions occurs for non-Abelian
fields with the size of g_{na} being determined by the specific non-Abelian
group appearing in the theory of interest, be it the Standard Model or any
other theory.Comment: 10 pages, 2 figures, contributed to the XI Mexican Workshop on
Particles and Fields. Accepted in Phys. Rev.
The Axial-Vector Current in Nuclear Many-Body Physics
Weak-interaction currents are studied in a recently proposed effective field
theory of the nuclear many-body problem. The Lorentz-invariant effective field
theory contains nucleons, pions, isoscalar scalar () and vector
() fields, and isovector vector () fields. The theory exhibits a
nonlinear realization of chiral symmetry and has three
desirable features: it uses the same degrees of freedom to describe the
axial-vector current and the strong-interaction dynamics, it satisfies the
symmetries of the underlying theory of quantum chromodynamics, and its
parameters can be calibrated using strong-interaction phenomena, like hadron
scattering or the empirical properties of finite nuclei. Moreover, it has
recently been verified that for normal nuclear systems, it is possible to
systematically expand the effective lagrangian in powers of the meson fields
(and their derivatives) and to reliably truncate the expansion after the first
few orders. Here it is shown that the expressions for the axial-vector current,
evaluated through the first few orders in the field expansion, satisfy both
PCAC and the Goldberger--Treiman relation, and it is verified that the
corresponding vector and axial-vector charges satisfy the familiar chiral
charge algebra. Explicit results are derived for the Lorentz-covariant,
axial-vector, two-nucleon amplitudes, from which axial-vector meson-exchange
currents can be deduced.Comment: 32 pages, REVTeX 4.0 with 12pt.rtx, aps.rtx, revsymb.sty,
revtex4.cls, plus 14 figures; two sentences added in Summary; two references
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The effects of meson mixing on dilepton spectra
The effect of scalar and vector meson mixing on the dilepton radiation from
hot and dense hadronic matter is estimated in different isospin channels. In
particular, we study the effect of - and mixing and
calculate the corresponding rates. Effects are found to be significant compared
to standard - and - annihilations. While the mixing in
the isoscalar channel mostly gives a contribution in the invariant mass range
between the two-pion threshold and the peak, the isovector channel
mixing induces an additional peak just below that of the .
Experimentally, the dilepton signals from - mixing seem to be more
tractable than those from - mixing.Comment: 10 pages, 9 figure
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