314 research outputs found
Spin partners of the and revisited
We study the implications of the heavy-quark spin symmetry for the possible
spin partners of the exotic states and in the
spectrum of bottomonium. We formulate and solve numerically the coupled-channel
equations for the states that allow for a dynamical generation of these
states as hadronic molecules. The force includes short-range contact terms and
the one-pion exchange potential, both treated fully nonperturbatively. The
strength of the potential at leading order is fixed completely by the pole
positions of the states such that the mass and the most prominent
contributions to the width of the isovector heavy-quark spin partner states
with the quantum numbers () come out as predictions.
Since the accuracy of the present experimental data does not allow one to fix
the pole positions of the 's reliably enough, we also study the pole
trajectories of their spin partner states as functions of the binding
energies. It is shown that, once the heavy-quark spin symmetry is broken by
means of the physical and masses, especially the pion tensor force
has a significant impact on the location of the partner states clearly
demonstrating the need of a coupled-channel treatment of pion dynamics to
understand the spin multiplet pattern of hadronic molecules.Comment: 21 pages, 5 figures, 1 tabl
Binding energy of the at unphysical pion masses
Chiral extrapolation of the binding energy is investigated using
the modified Weinberg formulation of chiral effective field theory for the scattering. Given its explicit renormalisability, this approach is
particularly useful to explore the interplay of the long- and short-range forces in the from studying the light-quark (pion) mass
dependence of its binding energy. In particular, the parameter-free
leading-order calculation shows that the -pole disappears for unphysical
large pion masses. On the other hand, without contradicting the naive
dimensional analysis, the higher-order pion-mass-dependent contact interaction
can change the slope of the binding energy at the physical point yielding the
opposite scenario of a stronger bound at pion masses larger than its
physical value. An important role of the pion dynamics and of the 3-body
effects for chiral extrapolations of the -pole is emphasised.
The results of the present study should be of practical value for the lattice
simulations since they provide a non-trivial connection between lattice points
at unphysical pion masses and the physical world.Comment: 24 pages, 4 figure
Spin partners from the line shapes of the and
In a recent paper Phys.Rev. D98, 074023 (2018), the most up-to-date
experimental data for all measured production and decay channels of the
bottomonium-like states and were analysed in a
field-theoretical coupled-channel approach which respects analyticity and
unitarity and incorporates both the pion exchange as well as a short-ranged
potential nonperturbatively. All parameters of the interaction were fixed
directly from data, and pole positions for both states were determined.
In this work we employ the same approach to predict in a parameter-free way the
pole positions and the line shapes in the elastic and inelastic channels of the
(still to be discovered) spin partners of the states. They are
conventionally referred to as 's with the quantum numbers
(). It is demonstrated that the results of our most
advanced pionful fit, which gives the best for the data
in the channels, are consistent with all states being
above-threshold resonances which manifest themselves as well pronounced hump
structures in the line shapes. On the contrary, in the pionless approach, all
's are virtual states which can be seen as enhanced threshold cusps in
the inelastic line shapes. Since the two above scenarios provide different
imprints on the observables, the role of the one-pion exchange in the
systems can be inferred from the once available
experimental data directly.Comment: 24 pages, 12 figure
Quark mass dependence of the X(3872) binding energy
We explore the quark-mass dependence of the pole position of the X(3872)
state within the molecular picture. The calculations are performed within the
framework of a nonrelativistic Faddeev-type three-body equation for the
system in the channel. The interaction is
parametrised via a pole, and a three-body force is included to render the
equations well defined. Its strength is adjusted such that the X(3872) appears
as a bound state 0.5 MeV below the neutral threshold. We find that
the trajectory of the X(3872) depends strongly on the assumed quark-mass
dependence of the short-range interactions which can be determined in future
lattice QCD calculations. At the same time we are able to provide nontrivial
information on the chiral extrapolation in the channel.Comment: LaTeX2e, 14 pages, 5 figures, references updated and extended, to
appear in Phys.Lett.
Heavy-quark spin symmetry partners of the revisited
We revisit the consequences of the heavy-quark spin symmetry for the possible
spin partners of the . We confirm that, if the were a
molecular state with the quantum numbers , then in
the strict heavy-quark limit there should exist three more hadronic molecules
degenerate with the , with the quantum numbers , , and
in line with previous results reported in the literature. We
demonstrate that this result is robust with respect to the inclusion of the
one-pion exchange interaction between the mesons. However, this is true
only if all relevant partial waves as well as particle channels which are
coupled via the pion-exchange potential are taken into account. Otherwise, the
heavy-quark symmetry is destroyed even in the heavy-quark limit. Finally, we
solve the coupled-channel problem in the channel with nonperturbative
pions beyond the heavy-quark limit and, contrary to the findings of previous
calculations with perturbative pions, find for the spin-2 partner of the
a significant shift of the mass as well as a width of the order of 50
MeV.Comment: 17 pages, 3 figures, 1 table, version published in Phys.Lett.
Remarks on the study of the X(3872) from Effective Field Theory with Pion-Exchange Interaction
In a recent paper Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846), the
charmonium state X(3872) is studied in the framework of an effective field
theory. In that work it is claimed that (i) the one-pion exchange (OPE) alone
provides sufficient binding to produce the X as a shallow bound state at the
threshold, (ii) short-range dynamics (described by a contact
interaction) provides only moderate corrections to the OPE, and (iii) the
X-pole disappears as the pion mass is increased slightly and therefore the X
should not be seen on the lattice, away from the pion physical mass point, if
it were a molecular state. In this paper we demonstrate that the results of
Phys.Rev.Lett. 111, 042002 (2013) (arXiv:1304.0846) suffer from technical as
well as conceptual problems and therefore do not support the conclusions drawn
by the authors.Comment: LaTeX2e, 7 pages, 2 figures, to appear in Phys.Rev.
Three-body dynamics for the X(3872)
We investigate the role played by the three-body dynamics on
the near-threshold resonance X(3872) charmonium state, which is assumed to be
formed by nonperturbative dynamics. It is demonstrated that, as
compared to the naive static-pions approximation, the imaginary parts that
originate from the inclusion of dynamical pions reduce substantially the width
from the intermediate state. In particular, for a resonance
peaked at 0.5 MeV below the threshold, this contribution to
the width is reduced by about a factor of 2, and the effect of the pion
dynamics on the width grows as long as the resonance is shifted towards the
threshold. Although the physical width of the is
dominated by inelastic channels, our finding should still be of importance for
the line shapes in the channel below threshold.
For example, in the scattering length approximation, the imaginary part of the
scattering length includes effects of all the pion dynamics and does not only
stem from the width. Meanwhile, we find that another important quantity
for the phenomenology, the residue at the pole, is weakly sensitive to
dynamical pions. In particular, we find that the binding energy dependence of
this quantity from the full calculation is close to that found from a model
with pointlike interactions only, consistent with earlier claims.
Coupled-channel effects (inclusion of the charged channel) turn
out to have a moderate impact on the results.Comment: 34 pages, 6 figures, version to appear in Phys.Rev.
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