28,771 research outputs found
Generalized disconnection exponents
We introduce and compute the generalized disconnection exponents
which depend on and another real
parameter , extending the Brownian disconnection exponents
(corresponding to ) computed by Lawler, Schramm and Werner 2001
(conjectured by Duplantier and Kwon 1988).
For , the generalized disconnection exponents have a
physical interpretation in terms of planar Brownian loop-soups with intensity
, which allows us to obtain the first prediction of the dimension
of multiple points on the cluster boundaries of these loop-soups. In
particular, according to our prediction, the dimension of double points on the
cluster boundaries is strictly positive for and equal to zero for
the critical intensity , leading to an interesting open question of
whether such points exist for the critical loop-soup.
Our definition of the exponents is based on a certain general version of
radial restriction measures that we construct and study. As an important tool,
we introduce a new family of radial SLEs depending on and two
additional parameters , that we call radial hypergeometric SLEs. This
is a natural but substantial extension of the family of radial
SLE.Comment: 43 pages, 9 figures. Final version, to appear in Probab. Theory
Relat. Fields. Contains a clarification about the terminology 'hypergeometric
SLE' inappropriately used in other work
Is a molecular state
Assuming the newly observed to be a molecular state of , we calculate the partial widths of and within the light front
model (LFM). is the channel by which was
observed, our calculation indicates that it is indeed one of the dominant modes
whose width can be in the range of a few MeV depending on the model parameters.
Similar to and , Voloshin suggested that there should be a
resonance at 4030 MeV which can be a molecular state of .
Then we go on calculating its decay rates to all the aforementioned final
states and as well the . It is found that if is a
molecular state of , the partial width of
is rather small, but the rate of
is even larger than . The
implications are discussed and it is indicated that with the luminosity of BES
and BELLE, the experiments may finally determine if is a molecular
state or a tetraquark.Comment: 17 pages, 6 figures, 3 table
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