Lately, the LHCb Collaboration reported the discovery of two new states in the
B
+
→
D
+
D
-
K
+
decay, i.e.,
X
0
(
2866
)
and
X
1
(
2904
)
. In the present work, we study whether these states can be ...understood as
D
¯
∗
K
∗
molecules from the perspective of their two-body strong decays into
D
-
K
+
via triangle diagrams and three-body decays into
D
¯
∗
K
π
. The coupling of the two states to
D
¯
∗
K
∗
are determined from the Weinberg compositeness condition, while the other relevant couplings are well known. The obtained strong decay width for the
X
0
(
2866
)
state, in marginal agreement with the experimental value within the uncertainty of the model, hints at a large
D
¯
∗
K
∗
component in its wave function. On the other hand, the strong decay width for the
X
1
(
2904
)
state, much smaller than its experimental counterpart, effectively rules out its assignment as a
D
¯
∗
K
∗
molecule.
This article investigates adaptive state-feedback stabilization problem for a class of stochastic high-order nonlinear systems with unknown time-varying powers and stochastic inverse dynamics for the ...first time. The existence of stochastic inverse dynamics, unknown parameters, and time-varying powers makes stochastic high-order nonlinear systems essentially different from the related papers, which brings a series of obstacles to achieve the control objective. By virtue of the parameter separation principle, adaptive technique and some flexible algebraic methods, a novel adaptive state-feedback controller is designed to guarantee that the equilibrium of the closed-loop system is globally stable in probability. Finally, a simulation is provided to demonstrate the effectiveness of the control scheme.
Recently, the Belle collaboration measured the ratios of the branching fractions of the newly observed
Ω
(
2012
)
excited state. They did not observe significant signals for the
Ω
(
2012
)
→
K
¯
Ξ
∗
...(
1530
)
→
K
¯
π
Ξ
decay, and reported an upper limit for the ratio of the three body decay to the two body decay mode of
Ω
(
2012
)
→
K
¯
Ξ
. In this work, we revisit the newly observed
Ω
(
2012
)
from the molecular perspective where this resonance appears to be a dynamically generated state with spin-parity
3
/
2
-
from the coupled channels interactions of the
K
¯
Ξ
∗
(
1530
)
and
η
Ω
in
s
-wave and
K
¯
Ξ
in
d
-wave. With the model parameters for the
d
-wave interaction, we show that the ratio of these decay fractions reported recently by the Belle collaboration can be easily accommodated.
Summary
This paper investigates the problem of finite‐time output‐feedback stabilization of a class of high‐order nonholonomic systems under weaker conditions on system powers and nonlinearities. By ...constructing the appropriate Lyapunov function and observer, skillfully combining generalized adding a power integrator technique, sign function, and homogeneous domination method, and successfully introducing a new mathematical method, an output‐feedback controller is constructed to guarantee that all the states of the closed‐loop system converge to origin in a finite time.
We investigate the charmless decays of excited
P
-wave charmonia
χ
c
1
′
→
V
V
and
χ
c
2
′
→
V
P
via intermediate charmed meson loops, where
V
and
P
denote the light vector and pseudoscalar mesons, ...respectively. Within the model parameters, the charmed meson loop contributions are evaluated by using the effective Lagrangian approach. For
χ
c
1
′
→
V
V
, the partial widths of the
ρ
ρ
,
ω
ω
, and
K
∗
K
¯
∗
channels can reach to the order of MeV, while the partial width of the
ϕ
ϕ
channel is very small and in the order of keV. For
χ
c
2
′
→
V
P
, the partial widths of
χ
c
2
′
→
K
∗
K
¯
+
c
.
c
turns out to be sizeable, while the partial widths of
χ
c
2
′
→
ρ
+
π
-
+
c
.
c
is found to be much smaller than the
K
∗
K
¯
+
c
.
c
channel. Our calculations may be examined by the future BESIII experiments.
Spectrum of the low-lying hidden- and double-charm tetraquark states are investigated in a nonrelativistic quark potential model, where the instanton-induced interaction is taken as the residual ...spin-dependent hyperfine interaction between quarks. The model parameters are fixed by fitting the spectrum of the ground hadron states. Our numerical results show that masses of several presently studied tetraquark states are close to those of the experimentally observed candidates of exotic meson, which indicates that the corresponding compact tetraquark components may take considerable probabilities in those observed exotic states.
We calculate the valence quark distribution functions of the π meson using the non-relativistic chiral constituent quark model. The π wave function is obtained by solving the two-body Schrödinger ...equation within the framework of constituent quark model. We transform the π wave function from the rest frame to the light cone or infinite momentum frame based on the Lorentz boost. The valence quark distributions at the initial evolution scale are obtained. The QCD evolution is given with the DGLAP equations with parton-parton recombination corrections. With tuning the valence up (down) quark mass to 70 MeV, the calculated valence up quark distributions at Q2=20 GeV2 are in good agreement with the E615 experimental data. The structure functions F2π(x,Q2) of pion are also calculated which consist with the H1 experimental data. The proposed mechanisms here could be also used to study other hadrons.
A formalism is discussed that allows for a straightforward treatment of the relativistic three-body problem while keeping the correct analytic structure. In particular it is demonstrated that ...sacrificing covariance for analyticity can be justified by the hierarchy of different contributions in the spirit of an effective field theory. For definiteness the formalism is applied to the
K
K
K
¯
system allowing for the emergence of the
a
0
(
980
)
and the
f
0
(
980
)
as hadronic molecules. For simplicity all inelastic channels are switched off.
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