Near-threshold Resonances Research Articles

Structure of near-threshold resonances with new interpretation scheme of complex compositeness

The nature of near-threshold resonances is quantitatively studied with a new interpretation scheme using the complex compositeness. A difficulty was known in the understanding of the internal structure of unstable resonances because their complex compositeness is not an interpretable measure. To overcome this problem, we develop a new interpretation scheme respecting the ambiguous aspects of the identification of the internal structure of resonances. We then apply the interpretation scheme to the near-threshold resonances slightly above the threshold, described by the effective range expansion. With the new interpretation scheme, we show that near-threshold resonances are dominated by the non-molecular component. Namely, even in the near-threshold region, the nature of resonances is sharply contrasted with bound states whose internal structure is usually molecular dominant.

Physics of near-threshold resonances

In this paper, we present our approach to the treatment of final-state interaction of hadrons. It is based on the assumption that quark–antiquark pairs are produced at small distances, while the interaction of hadrons takes place at larger distances. As a result, the effects of final-state interaction are determined by the wave function of produced hadronic system. The account for final-state interaction within this approach allows us to successfully describe the energy dependence of cross-sections of many processes, as well as electromagnetic form factors of hadrons.

Search for the γ decay of the narrow near-threshold proton resonance in 11B

The γ decay of the elusive narrow, near-threshold proton resonance in 11B was investigated at Laboratori Nazionali di Legnaro (INFN) in a particle-γ coincidence experiment, using the 6Li(6Li,pγ) fusion-evaporation reaction and the GALILEO-GALTRACE setup. No clear signature was found for a possible E1 decay to the 1/21−, first-excited state of 11B, predicted by the Shell Model Embedded in the Continuum (SMEC) with a branching of 0.98−69+167×10−3 with respect to the dominant particle-decaying modes. The statistical analysis of the γ-ray spectrum provided an average upper limit of 2.37×10−3 for this γ-ray branching, with a global significance of 5σ. On the other hand, by imposing a global confidence level of 3σ, a significant excess of counts was observed for E=γ9300(20) keV, corresponding to a resonance energy of 11429(20) keV (namely 200(20) keV above the proton separation energy of 11B) and a γ-ray branching of 1.12(35)×10−3. This result is compatible with the SMEC calculations, potentially supporting the existence of a near-threshold proton resonance in 11B.

Production of D(*)D¯(*) near the thresholds in e+e− annihilation

It is shown that the nontrivial energy dependencies of DD¯, DD¯*, and D*D¯* pair production cross sections in e+e− annihilation are well described within the approach based on an account of the final-state interaction of produced particles. This statement is valid for the production of charged and neutral particles. Interaction of D(*) and D¯(*) is taken into account using the effective potential method. Its applicability is based on the fact that for near-threshold resonance the characteristic width of peak in the wave function is much larger than the interaction radius. The transition amplitudes between all three channels play an important role in the description of cross sections. These transitions are possible since all channels have the same quantum numbers JPC=1−−. Published by the American Physical Society 2024

Study of a near-threshold scalar resonance in the $$\omega \phi $$ system in pion-Be interaction at momentum of 29 GeV

Study of a near-threshold scalar resonance in the $$\omega \phi $$ system in pion-Be interaction at momentum of 29 GeV

Solving the left-hand cut problem in lattice QCD: Tcc(3875)+ from finite volume energy levels

We discuss a novel effective-field-theory-based approach for extracting two-body scattering information from finite volume energies, serving as an alternative to Lüscher’s method. By explicitly incorporating one-pion exchange, we overcome the challenging left-hand cut problem in Lüscher’s method and can handle finite volume energy levels both below and above the left-hand cut. Applied to the lattice data for DD* scattering at a pion mass of 280 MeV, as an illustrative example, our results reveal the significant impact of the one-pion exchange on P-wave and S-wave phase shifts. The pole position of the Tcc(3875)+ state, extracted from the finite-volume energy levels at this pion mass while taking into account left-hand cut effects, range corrections and partial-wave mixing, is consistent with a near-threshold resonance. This study demonstrates, for the first time, that two-body scattering information can be reliably extracted from lattice spectra including the left-hand cut. Published by the American Physical Society 2024

Analytic approximations to the strengths of near-threshold optical Feshbach resonances

Optical Feshbach resonances allow one to control cold atomic scattering, produce ultracold molecules, and study atomic interactions via photoassociation spectroscopy. In the limit of ultracold $s$-wave collisions, the strength of an optical Feshbach resonance can be expressed via an energy-independent parameter called the optical length. Here we give fully analytic approximate expressions for its magnitude applicable to near-threshold bound states of an excited molecular state dominated by a single resonant-dipole or van der Waals interaction. We express these magnitudes in terms of intuitive quantities, such as the laser intensity, the excited-state binding energy, the $s$-wave scattering length, and the Condon point. Additionally, we extend the utility of the optical length to associative stimulated Raman adiabatic passage in three-dimensional optical lattices by showing that the free-bound Rabi frequency induced by a laser coupling a pair of atoms in an optical lattice site can be approximately related to the trap frequency and the optical length.

Ab Initio Study of Near-Threshold Neutron Resonances of the $${}^{{10}}$$Be Nucleus

Ab Initio Study of Near-Threshold Neutron Resonances of the $${}^{{10}}$$Be Nucleus

Fate of multiparticle resonances: From Q -balls to He3 droplets

We consider a system of $N$ nonrelativistic particles which form a near-threshold resonance. Assuming no subset of these particles can form a bound state, the resonance can only decay through an "explosion" into $N$ particles. We show that the decay width of the resonance scales as $E^{\Delta-5/2}$ in the limit when the energy $E$ of the resonance goes to zero, where $\Delta$ is the ground state energy of a system of $N$ particles in a spherical harmonic trap with unit frequency. The formula remains valid when some pairs of final particles have zero-energy $s$-wave resonance, but the Efimov effect is not present. In the limit of large $N$, we show that the final particles follow a Maxwell-Boltzmann distribution if they are bosons, and a semicircle-like law if they are fermions. We argue that metastable $^3$He droplets exist with the lifetime varying over many orders of magnitudes ranging from a fraction of a nanosecond to values greatly exceeding the age of the Universe.

Single-particle properties of the near-threshold proton-emitting resonance in B11

The excitation function of proton elastic scattering from $^{10}\mathrm{Be}$ at keV energy is calculated using the method of self-consistent Skyrme Hartree-Fock in the continuum. The calculation successfully reproduces the narrow near-threshold proton-emitting resonance (${E}_{x}=11.4$ MeV, $\mathrm{\ensuremath{\Gamma}}=6$ keV, and quantum number ${J}^{\ensuremath{\pi}}=1/{2}^{+}$) in $^{11}\mathrm{B}$ relevant to the $\ensuremath{\beta}$-delayed proton emission of $^{11}\mathrm{Be}$. This supports the recent experimental result of Ayyad et al. at the ReA3 reaccelerator facility of the National Superconducting Cyclotron Laboratory (NSCL) at Michigan State University. The resonance is interpreted as the ${s}_{1/2}$ single-proton resonance state in the Skyrme Hartree-Fock mean-field theory.

Pseudoscalar charmonium pair interactions via the Pomeron exchange mechanism

Following the observation of the fully-heavy tetraquark candidates $X(6900)$ and possible $X(6300)$ in the di-$J/\psi$ spectrum by the LHCb Collaboration, we investigate the near-threshold dynamics of the pseudoscalar quarkonium pairs in a coupled-channel approach in the di-$\eta_c$ channel. We show that the Pomeron exchange mechanism should be a general dynamics in the near-threshold heavy quarkonium pair interactions. In the di-$\eta_c$ channel, a coupled-channel system involving the di-$\eta_c$, $\eta_c$-$\eta_c(2S)$ and di-$\eta_c(2S)$ interactions can be established. Their $S$-wave interactions near threshold via the Pomeron exchange potential can produce near-threshold resonance poles similar to the di-$J/\psi$, $J/\psi$-$\psi(2S)$ and di-$\psi(2S)$ coupled channels. Interestingly, we find here that the pole positions are more shifted to the corresponding thresholds and turn out to be different from those seen in the di-$J/\psi$ spectrum. Taking into account the suppression of the heavy quark spin flips in the transitions between two vector and two pseudoscalar heavy quarkonium systems, the enhancements in the di-$\eta_c$ spectrum should be different from those seen in the di-$J/\psi$ channel. Experimental study of the di-$\eta_c$ channel should be useful for disentangling the nature of the fully-heavy tetraquark systems.

Effective range expansion for narrow near-threshold resonances

We discuss some general features of the effective range expansion, the content of its parameters with respect to the nature of the pertinent near-threshold states and the necessary modifications in the presence of coupled channels, isospin violations and unstable constituents. As illustrative examples, we analyse the properties of the χc1(3872) and Tcc+ states supporting the claim that these exotic states have a predominantly molecular nature.

Evidence of a Near-Threshold Resonance in ^{11}B Relevant to the β-Delayed Proton Emission of ^{11}Be.

A narrow near-threshold proton-emitting resonance (E_{x}=11.4 MeV, J^{π}=1/2^{+}, and Γ_{p}=4.4 keV) was directly observed in ^{11}B via proton resonance scattering. This resonance was previously inferred in the β-delayed proton emission of the neutron halo nucleus ^{11}Be. The good agreement between both experimental results serves as a ground to confirm the existence of such exotic decay and the particular behavior of weakly bound nuclei coupled to the continuum. R-matrix analysis shows a sizable partial decay width for both, proton and α (Γ_{α}=11 keV) emission channels.

Observation of a Near-Threshold Proton Resonance in ^{11}B.

A near-threshold proton resonance in ^{11}B at E_{ex}=11.44±0.04 MeV is observed via the reaction ^{10}Be(d,n)^{11}Be→^{10}Be+p in inverse kinematics, measured with a beam of the radioactive isotope ^{10}Be. The resonance energy at E_{res}=211(40) keV is consistent with a proton signal observed by Ayyad etal. in the β-delayed proton decay of ^{11}Be. By comparison to a distorted wave Born approximation calculation, a 0.27(6) spectroscopic factor is extracted and a tentative (ℓ=0) character is assigned for this resonance. The significant cross section in the proton-transfer (d,n) reaction, as well as the observation of its proton-decay signal, point to the threshold-resonance character of this state. The position of this state, its structure, and strong coupling to the s-wave continuum represent an ideal case to study quantum near-threshold many-body dynamics of unstable states. The presence of this state is an important step toward understanding the excessively large beta-delayed proton-decay branch of ^{11}Be.

Deep learning exotic hadrons

We perform the first model independent analysis of experimental data using Deep Neural Networks to determine the nature of an exotic hadron. Specifically, we study the line shape of the $P_c(4312)$ signal reported by the LHCb collaboration and we find that its most likely interpretation is that of a virtual state. This method can be applied to other near-threshold resonance candidates.

Analysis on the composite nature of the light scalar mesons f0(980) and a0(980)

We study the weight or compositeness of the $\pi\pi$-$K\bar{K}$ and $\pi\eta$-$K\bar{K}$ in the composition of the $f_0(980)$ and $a_0(980)$ resonances, respectively. Either we use the saturation of the total width and compositeness, or we use a Flatt\'e parameterization taking also into account the spectral function of a near-threshold resonance. We make connections and compare between these two methods. We take input values for the pole mass and width from several determinations in the literature. In addition, we take as third input either the total compositeness or the decay-width branching ratio to the lighter channel for each resonance. It turns out that for the poles considered the meson-meson components are dominant for the $f_0(980)$, while for the $a_0(980)$ resonance they are subdominant. We also provide partial decay widths and partial compositeness coefficients, so that the $K\bar{K}$ component is the most important one for the $f_0(980)$. Additionally, this study stresses the need to distinguish between the bare and dressed couplings and widths in a Flatt\'e parameterization. We elaborate on the connection between the partial-decay widths calculated in terms of the dressed couplings and the actual measured ones. Due to the coupled-channel dynamics when the pole lies near the heavier threshold in the second Riemann sheet some changes are needed with respect to standard relations.

Benchmark PhotoIonization Cross-Sections of Neutral Scandium from the Ground and Excited States

The B-spline R-matrix method has been used to investigate cross-sections for photoionization of neutral scandium from the ground and excited states in the energy region from the 3d and 4s valence electron ionization thresholds to 25 eV. The initial bound states of Sc and the final residual Sc+ ionic states have been accurately calculated by combining the multiconfiguration Hartree-Fock method with the frozen-core close-coupling approach. The lowest 20 bound states of Sc I belonging to the ground 3d4s2 and excited 3d24s, 3d24p, 3d4s4p, 4s24p, and 3d3 configurations have been considered as initial states. The 81 LS final ionic states of Sc+ belonging to the terms of 3p63d2, 3p63d4l (l = 0–3), 3p63d5l (l = 0–3), 3p63d6s, 3p64s2, 3p64s4l (l = 0–3), 3p64s5l (l = 0–1), and 3p64p2 configurations have been included in the final-state close-coupling expansion. The cross-sections are dominated by complicated resonance structures in the low energy region converging to several Sc+ ionic thresholds. The inclusion of all these final ionic states has been noted to significantly impact the near-threshold resonance structures and background cross-sections. The important scattering channels for leaving the residual ion in various final states have been identified, and the 3d electron ionization channels have been noted to dominate the cross-sections at higher photon energies.

Probing open- and closed-channel p -wave resonances

We study the near-threshold molecular and collisional physics of a strong $^{40}$K p-wave Feshbach resonance through a combination of measurements, numerical calculations, and modeling. Dimer spectroscopy employs both radio-frequency spin-flip association in the MHz band and resonant association in the kHz band. Systematic uncertainty in the measured binding energy is reduced by a model that includes both the Franck-Condon overlap amplitude and inhomogeneous broadening. Coupled-channels calculations based on mass-scaled $^{39}$K potentials compare well to the observed binding energies and also reveal a low-energy p-wave shape resonance in the open channel. Contrary to conventional expectation, we observe a nonlinear variation of the binding energy with magnetic field, and explain how this arises from the interplay of the closed-channel ramping state with the near-threshold shape resonance in the open channel. We develop an analytic two-channel model that includes both resonances as well as the dipole-dipole interactions which, we show, become important at low energy. Using this parameterization of the energy dependence of the scattering phase, we can classify the studied $^{40}$K resonance as broad. Throughout the paper, we compare to the well understood s-wave case, and discuss the significant role played by van der Waals physics. The resulting understanding of the dimer physics of p-wave resonances provides a solid foundation for future exploration of few- and many-body orbital physics.

Positron impact excitation of lowest autoionizing state of potassium atom using distorted wave method with absorption and polarization potentials

Differential and integral cross-sections, as well as the alignment and lambda parameters for positron impact excitation of the lowest autoionizing state of potassium atom, have been calculated using a non-relativistic distorted wave method in the energy range of 18.9–1500 eV. The distortion potential in the initial and final channel state comprises a linear combination of static potential plus polarization and absorption potentials. The approximate Roothan-Hartree–Fock (RHF) wavefunctions Multi zeta wave functions given by Clementi and Roetti have been used. The inclusion of polarization and absorption potentials has improved integral cross-section and alignment parameter results. The integral cross sections have shown the near-threshold resonance structure revealed in electron impact excitation experimental results. Differential cross-section and lambda parameter results have been calculated and presented for future comparison since there are no other results available in the literature for positron impact excitation.

Collectivity of the electromagnetic transitions in near-threshold resonances

Mixing of the shell model (SM) eigenstates due to the coupling via the common decay channel influences leads in many cases to the formation of a collective eigenstate which carries many features of the nearby decay channel. This generic mechanism in open quantum systems explains the phenomenological Ikeda diagram and generalizes it for various clusters/correlations in the vicinity of the respective cluster decay thresholds. The near-threshold collectivization of the SM states may also influence their electromagnetic decays. We discuss this phenomenon on the example of B(Eλ) decays of near-threshold 2+ states in 14C.