A new approach to the parameterization of pion form factors is presented and for illustration applied to the pion vector form factor. It has the correct analytic structure, is at low energies ...consistent with recent high accuracy analyses of ππ scattering phase shifts and, at high energies, maps smoothly onto the well-known, successful isobar model.
The last decade has witnessed great experimental progress that has led to measurements of near-threshold cross sections—polarized as well as unpolarized—of high accuracy for various inelastic ...nucleon–nucleon collision channels. These data, naturally, pose challenges to theorists to develop methods by which they can be understood and explained in commensurate detail.
In this work we review the status of the present theoretical understanding of this class of reactions with special emphasis on model-independent methods. We discuss in detail not only the many observables involved in the reactions, but also the physical questions that can be addressed by studying them in the various reaction channels. The special advantages of nucleon–nucleon-induced reactions are stressed. Foremost among these is the use of the initial and final states as a spin/isospin filter. This opens, for example, a window into the spin dependence of the hyperon–nucleon interaction and the dynamics of the light scalar mesons.
We discuss in general terms pole trajectories of resonances coupling to a continuum channel as some strength parameter is varied. It is demonstrated that, regardless of the underlying dynamics, the ...trajectories of poles that couple to the continuum in a partial wave higher than s-wave are qualitatively the same, while in case of s-waves the pole trajectory can reveal important information on the internal structure of the resonance. In addition we show that only molecular (or extraordinary) states appear near thresholds naturally, while more compact structures need a significant fine tuning in the parameters.
This study is of current relevance especially in strong interaction physics, since lattice QCD may be employed to deduce the pole trajectories for hadronic resonances as a function of the quark mass thus providing additional, new access to the structure of s-wave resonances.
We propose a practical parametrization for the line shapes of near-threshold states compatible with all requirements of unitarity and analyticity. The coupled-channel system underlying the proposed ...parametrization includes bare poles and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting formulas are general enough to be used for a simultaneous analysis of the data in all available production and decay channels of the (system of) state(s) under consideration for a quite wide class of reactions. As an example, we fit the experimental data currently available for several decay channels for the charged Z super((')) sub(b) states in the spectrum of bottomonia and find a good overall description of the data. We find the present data to be consistent with the Z sub(b)(10610) as a virtual state and with the Z sub(b)(10650) as a resonance, both residing very close to the BB* and B*B* threshold, respectively.
Numerous quarkonium(like) states lying near S-wave thresholds are observed experimentally. We propose a self-consistent approach to these near-threshold states compatible with unitarity and ...analyticity. The underlying coupled-channel system includes a bare pole and an arbitrary number of elastic and inelastic channels treated fully nonperturbatively. The resulting analytical parametrization is ideally suited for a combined analysis of the data available in various channels that is exemplified by an excellent overall description of the data for the charged Z(b)(10610) and Z(b)(10650) states.
(ProQuest: ... denotes formulae and/or non-USASCII text omitted; see image).Exploiting B-meson decays for Standard Model tests and beyond requires a precise understanding of the strong final-state ...interactions that can be provided model-independently by means of dispersion theory. This formalism allows one to deduce the universal pion-pion final-state interactions from the accurately known pi pi phase shifts and, in the scalar sector, a coupled-channel treatment with the kaon-antikaon system. In this work an analysis of the decays ... and ... is presented. We find very good agreement with the data up to 1.05 GeV in the pi pi invariant mass, with a number of parameters reduced significantly compared to a phenomenological analysis. In addition, the phases of the amplitudes are correct by construction, a crucial feature for many CP violation measurements in heavy-meson decays.
In a recent paper Phys. Rev. D 98, 074023 (2018), the most up-to-date experimental data for all measured production and decay channels of the bottomoniumlike states Zb(10610) and Zb(10650) were ...analyzed in a field-theoretical coupled-channel approach which respects analyticity and unitarity and incorporates both the pion exchange and a short-ranged potential nonperturbatively. All parameters of the interaction were fixed directly from data, and pole positions for both Zb 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 Zb states. They are conventionally referred to as WbJ's with the quantum numbers JPC = J++ (J = 0, 1, 2). It is demonstrated that the results of our most advanced pionful fit, which gives the best χ2/d.o.f. for the data in the Zb channels, are consistent with all WbJ 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 WbJ'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 B(*)B¯(*) systems can be inferred from the once available experimental data directly.
Resonances are uniquely characterized by their complex pole locations and the corresponding residues. In practice, however, resonances are typically identified experimentally as structures in ...invariant mass distributions, with branching fractions of resonances determined as ratios of count rates. To make contact between these quantities it is necessary to connect line shapes and resonance parameters. In this work we propose such a connection and illustrate the formalism with detailed studies of the
ρ
(
770
)
and
f
0
(
500
)
resonances. Based on the line shapes inferred from the resonance parameters along these lines, expressions for partial widths and branching ratios are derived and compared to other approaches in the literature.
We revisit the consequences of the heavy-quark spin symmetry for the possible spin partners of the X(3872). We confirm that, if the X(3872) were a DD¯⁎ molecular state with the quantum numbers ...JPC=1++, then in the strict heavy-quark limit there should exist three more hadronic molecules degenerate with the X(3872), with the quantum numbers 0++, 1+−, and 2++ 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 D 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 2++ 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 X(3872) a significant shift of the mass as well as a width of the order of 50 MeV.
Pion–kaon (
π
K
) pairs occur frequently as final states in heavy-particle decays. A consistent treatment of
π
K
scattering and production amplitudes over a wide energy range is therefore mandatory ...for multiple applications: in Standard Model tests; to describe crossed channels in the quest for exotic hadronic states; and for an improved spectroscopy of excited kaon resonances. In the elastic region, the phase shifts of
π
K
scattering in a given partial wave are related to the phases of the respective
π
K
form factors by Watson’s theorem. Going beyond that, we here construct a representation of the scalar
π
K
form factor that includes inelastic effects via resonance exchange, while fulfilling all constraints from
π
K
scattering and maintaining the correct analytic structure. As a first application, we consider the decay
τ
→
K
S
π
ν
τ
, in particular, we study to which extent the
S
-wave
K
0
∗
(
1430
)
and the
P
-wave
K
∗
(
1410
)
resonances can be differentiated and provide an improved estimate of the
CP
asymmetry produced by a tensor operator. Finally, we extract the pole parameters of the
K
0
∗
(
1430
)
and
K
0
∗
(
1950
)
resonances via Padé approximants,
s
K
0
∗
(
1430
)
=
1408
(
48
)
-
i
180
(
48
)
MeV
and
s
K
0
∗
(
1950
)
=
1863
(
12
)
-
i
136
(
20
)
MeV
, as well as the pole residues. A generalization of the method also allows us to formally define a branching fraction for
τ
→
K
0
∗
(
1430
)
ν
τ
in terms of the corresponding residue, leading to the upper limit
BR
(
τ
→
K
0
∗
(
1430
)
ν
τ
)
<
1.6
×
10
-
4
.
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