The recently discovered fully charmed tetraquark candidate X(6900) is analyzed within the frameworks of effective-range expansion, compositeness relation and width saturation, and a coupled ...multichannel dynamical study. By taking into account constraints from heavy-quark spin symmetry, the coupled-channel amplitude including the J/ψJ/ψ, χc0χc0, and χc1χc1 is constructed to fit the experimental di-J/ψ event distributions around the energy region near 6.9 GeV. Another dynamical two-coupled-channel amplitude with the J/ψJ/ψ and ψ(3770)J/ψ is also considered to describe the same datasets. The three different theoretical approaches lead to similar conclusions that the two-meson components do not play dominant roles in the X(6900). Our determinations of the resonance poles in the complex energy plane from the refined coupled-channel study are found to be consistent with the experimental analyses. The coupled-channel amplitudes also have another pole corresponding to a narrow resonance X(6825) that we predict sitting below the χc0χc0 threshold and of molecular origin. We give predictions to the line shapes of the χc0χc0 and χc1χc1 channels, which could provide a useful guide for future experimental measurements.
Bound, antibound and resonance states are associated to poles in the on-shell partial wave amplitudes. We show here that from the residues of the pole a rank 1 projection operator associated with any ...of these states can be extracted, in terms of which a sum rule related to the composition of the state can be derived. Although typically it involves complex coefficients for the compositeness and elementariness, except for the bound state case, we demonstrate that one can formulate a meaningful compositeness relation with only positive coefficients for resonances whose associated Laurent series in the variable s converges in a region of the physical axis around Re s sub(P) with s sub(P)the pole position of the resonance. It is also shown that this result can be considered as an analytical extrapolation in s sub(P)of the clear narrow resonance case. We exemplify this formalism to study the two-body components of several resonances of interest.
We introduce a near-threshold parameterization that is more general than the effective-range expansion up to and including the effective range because it can also handle a near-threshold zero in the
...D
0
D
¯
∗
0
S
-wave. In terms of it we analyze the CDF data on inclusive
p
p
¯
scattering to
J
/
ψ
π
+
π
-
, and the Belle and BaBar data on
B
decays to
K
J
/
ψ
π
+
π
-
and
K
D
D
¯
∗
0
around the
D
0
D
¯
∗
0
threshold. It is shown that data can be reproduced with similar quality for
X
(3872) being a bound and/or a virtual state. We also find that
X
(3872) might be a higher-order virtual-state pole (double or triplet pole), in the limit in which the small
D
∗
0
width vanishes. Once the latter is restored the corrections to the pole position are non-analytic and much bigger than the
D
∗
0
width itself. The
X
(3872) compositeness coefficient in
D
0
D
¯
∗
0
ranges from nearly 0 up to 1 in the different scenarios.
Nowadays there is a continuously increasing worldwide concern for development of alternative water reuse technologies, mainly focused on agriculture and industry. In this context, Advanced Oxidation ...Processes (AOPs) are considered a highly competitive water treatment technology for the removal of those organic pollutants not treatable by conventional techniques due to their high chemical stability and/or low biodegradability. Although chemical oxidation for complete mineralization is usually expensive, its combination with a biological treatment is widely reported to reduce operating costs. This paper reviews recent research combining AOPs (as a pre-treatment or post-treatment stage) and bioremediation technologies for the decontamination of a wide range of synthetic and real industrial wastewater. Special emphasis is also placed on recent studies and large-scale combination schemes developed in Mediterranean countries for non-biodegradable wastewater treatment and reuse. The main conclusions arrived at from the overall assessment of the literature are that more work needs to be done on degradation kinetics and reactor modeling of the combined process, and also dynamics of the initial attack on primary contaminants and intermediate species generation. Furthermore, better economic models must be developed to estimate how the cost of this combined process varies with specific industrial wastewater characteristics, the overall decontamination efficiency and the relative cost of the AOP versus biological treatment.
Making use of a recently proposed formalism, we analyze the composite nature of the Pc(4450) resonance observed by LHCb. We show that the present data suggest that this state is almost entirely made ...of a χc1 and a proton, due to the close proximity to this threshold. This also suppresses the decay modes into other, lighter channels, in our study represented by J/Ψp. We further argue that this is very similar to the case of the scalar meson f0(980) which is located closely to the KK¯ threshold and has a suppressed decay into the lighter ππ channel.
We revisit the classical relation between the strangeness content of the nucleon, the pion–nucleon sigma term and the SU(3)F breaking of the baryon masses in the context of Lorentz covariant chiral ...perturbation theory with explicit decuplet-baryon resonance fields. We find that a value of the pion–nucleon sigma term of ∼60 MeV is not necessarily at odds with a small strangeness content of the nucleon, in line with the fulfillment of the OZI rule. Moreover, this value is indeed favored by our next-to-leading order calculation. We compare our results with earlier ones and discuss the convergence of the chiral series as well as the uncertainties of chiral approaches to the determination of the sigma terms.
We study the scattering of the light-flavor pseudoscalar mesons (
π
,
K
,
η
) off the ground-state charmed mesons (
D
,
D
s
) within chiral effective field theory. The recent lattice simulation ...results on various scattering lengths and the finite-volume spectra both in the moving and center-of-mass frames, most of which are obtained at unphysical meson masses, are used to constrain the free parameters in our theory. Explicit formulas to include the
S
- and
P
-wave mixing to determine the finite-volume energy levels are provided. After a successful reproduction of the lattice data, we perform a chiral extrapolation to predict the quantities with physical meson masses, including phase shifts, inelasticities, resonance pole positions and the corresponding residues from the scattering of the light pseudoscalar and charmed mesons.
Coupled-channel dynamics for scattering and production processes in partial-wave amplitudes is discussed from a perspective that emphasizes unitarity and analyticity. We elaborate on several methods ...that have driven to important results in hadron physics, either by themselves or in conjunction with effective field theory. We also develop the use of the Lippmann–Schwinger equation in near-threshold scattering and compare it with other methods. The final(initial)-state interactions are discussed in detail for the elastic and coupled-channel case. Emphasis has been put in the derivation and discussion of the methods presented, with some applications examined as important examples of their usage.
A novel theoretical approach to the problem of the compositeness (X) of a resonance or bound state is developed on the basis of the expectation values of the number operators of the free particles in ...the continuum. This formalism is specially suitable for effective field theories in which the bare elementary states are integrated out but that give rise to resonance and bound states when implemented in nonperturbative calculations. We demonstrate that X=1 for finite-range energy-independent potentials, either regular or singular. A non-trivial example for an energy-dependent potential is discussed where it is shown that X is independent of any type of cutoff regulator employed. The generalization of these techniques to relativistic states is developed. We also explain how to obtain a meaningful compositeness with respect to the open channels for resonances, even if it is complex in a first turn, by making use of suitable phase-factor transformations. Defining elementariness as X=0, we derive a new universal criterion for the elementariness of a bound state. Along the same lines, a necessary condition for a resonance to be qualified as elementary is given. The application of the formalism here developed might be of considerable practical interest.
We compare the exactly solvable nonrelativistic Coulomb scattering with two recent unitarization methods for infinite-range forces. These methods require to calculate perturbatively the corresponding ...partial-wave amplitudes, which are then unitarized. We calculate the Coulomb partial-wave amplitudes up to the one-loop order. On the one hand, the unitarization method developed by Refs. 1,2 reproduces properly the exact solution, with an accuracy improving as the order in the perturbative calculation of the input perturbative partial-wave amplitudes increases. This is also shown to be the case for the pole position of the ground state. On the other hand, the method developed by the more recent Ref. 3 gives rise to partial-wave amplitudes that do not reproduce the known solvable solution, and gives rise to a pole position with zero binding energy.
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