203 research outputs found
The quantum N-body problem with a minimal length
The quantum -body problem is studied in the context of nonrelativistic
quantum mechanics with a one-dimensional deformed Heisenberg algebra of the
form , leading to the existence of a
minimal observable length . For a generic pairwise interaction
potential, analytical formulas are obtained that allow to estimate the
ground-state energy of the -body system by finding the ground-state energy
of a corresponding two-body problem. It is first shown that, in the harmonic
oscillator case, the -dependent term grows faster with than the
-independent one. Then, it is argued that such a behavior should be
observed also with generic potentials and for -dimensional systems. In
consequence, quantum -body bound states might be interesting places to look
at nontrivial manifestations of a minimal length since, the more particles are
present, the more the system deviates from standard quantum mechanical
predictions.Comment: To appear in PR
Mass formula for strange baryons in large QCD versus quark model
A previous work establishing a connection between a quark model, with
relativistic kinematics and a -confinement plus one gluon exchange, and the
expansion mass formula is extended to strange baryons. Both methods
predict values for the SU(3)-breaking mass terms which are in good agreement
with each other. Strange and nonstrange baryons are shown to exhibit Regge
trajectories with an equal slope, but with an intercept depending on the
strangeness. Both approaches agree on the value of the slope and of the
intercept and on the existence of a single good quantum number labeling the
baryons within a given Regge trajectory.Comment: 2 figure
- Glueball Spectrum within a Constituent Picture
The quantum numbers and mass hierarchy of the glueballs observed in
-dimensional lattice QCD with gauge group SU() are shown to be in
agreement with a constituent picture. The agreement is maintained when going
from glueballs to gluelumps, and when the gauge group SO() is taken
instead of SU()
String deformations induced by retardation effects
The rotating string model is an effective model of mesons, in which the quark
and the antiquark are linked by a straight string. We previously developed a
new framework to include the retardation effects in the rotating string model,
but the string was still kept straight. We now go a step further and show that
the retardation effects cause a small deviation of the string from the straight
line. We first give general arguments constraining the string shape. Then, we
find analytical and numerical solutions for the string deformation induced by
retardation effects. We finally discuss the influence of the curved string on
the energy spectrum of the model.Comment: 3 figure
Effective potential between two transverse gluons from lattice QCD
Modeling glueballs as bound states of transverse constituent gluons allows to
understand the main features of the lattice QCD glueball spectrum. In
particular it has been shown in previous works that the lightest C-even
glueballs can be seen as bound states of two transverse constituent gluons
interacting via a funnel potential. In the present study we show that such an
effective potential emerges from the available lattice QCD data. Starting from
the scalar glueball mass and wave function computed in lattice QCD, we indeed
compute the equivalent local potential between two transverse constituent
gluons in the scalar channel and show that it is compatible with a funnel
shape, where standard values of the parameters are used and where a negative
constant has to be added to reproduce the absolute height of the potential.
Such a constant could be related to instanton-induced effects in glueballs.Comment: 1 figure, to appear in Phys. Rev.
Towers of hybrid mesons
A hybrid meson is a quark-antiquark pair in which, contrary to ordinary
mesons, the gluon field is in an excited state. In the framework of constituent
models, the interaction potential is assumed to be the energy of an excited
string. An approximate, but accurate, analytical solution of the
Schr\"{o}dinger equation with such a potential is presented. When applied to
hybrid charmonia and bottomonia, towers of states are predicted in which the
masses are a linear function of a harmonic oscillator band number for the
quark-antiquark pair. Such a formula could be a reliable guide for the
experimental detection of heavy hybrid mesons.Comment: 3 figure
Gluelump model with transverse constituent gluons
We show that C-odd gluelumps can be successfully described as bound states of
a single transverse constituent gluon evolving in the flux-tube-like potential
generated by a static color-octet source. The use of a helicity degree of
freedom rather than a spin one for the constituent gluon forbids the states
that are not observed in lattice QCD. Our model leads to a gluelump mass
spectrum in remarkable agreement with the available lattice data provided that
an additional parity-splitting mass term is introduced. We argue that such a
term is due to instanton-induced interactions in gluelumps.Comment: 4 page
- …