Higher Partial Waves Research Articles

The influence of spin-spin interaction on high partial wave Feshbach resonance in ultracold 23Na -87Rb system.

In this paper, we investigate the Feshbach resonances of high partial waves and the influence of spin-spin (S-S) interaction on ultracold scattering processes. Taking the Na23- Rb87 system as an example, we plot the variations of weakly bound state energy and elastic scattering cross section with magnetic field and with collision energy. We find that the number of splittings in high partial wave Feshbach resonances does not strictly conform to the expected l + 1 (l is rotational angular momentum), and the deviation is attributed to the influence of bound states in other channels coupled by S-S interaction. For different ml (the projection of l on the external magnetic field direction), the effects of S-S interaction lead to different scattering patterns in the incident channels. These results reveal the complex features of ultracold scattering processes in high partial waves caused by S-S interaction.

Exploration of the LHCb Pc\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$P_c$$\\end{document} states and possible resonances in a unitary coupled-channel model

We extend our previous study of the interactions of D¯(∗)Λc-D¯(∗)Σc(∗)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{D}^{(*)} \\Lambda _c - \\bar{D}^{(*)}\\Sigma _c^{(*)}$$\\end{document} within an analytic, unitary, coupled-channel approach by including the J/ψp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J/\\psi p$$\\end{document} channel and performing fits to the J/ψp\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J/\\psi p$$\\end{document} invariant mass distributions in the Λb0→J/ψpK-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda _b^0 \\rightarrow J/\\psi p K^-$$\\end{document} decay by the LHCb Collaboration. We take into account the contributions of t-channel pseudoscalar and vector meson exchanges and u-channel baryon exchanges in this work, and a series of bound states and resonances with different spin-parities are dynamically generated. According to the results, four states have a significant impact on the physical observables, with two having a spin-parity of 1/2-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$1/2^-$$\\end{document} and the other two having 3/2-\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3/2^-$$\\end{document}. These states can be associated with the LHCb hidden-charm pentaquarks. We further provide the coupling strength between each pole and different channels, which provides some insights on how to search for them in future experiments. Moreover, we also search for poles in higher partial waves up to J=7/2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$J=7/2$$\\end{document} and find indications for the existence of several states with larger widths.

Velocity-Dependent Potential for nn-αn-αα Scattering

An energy momentum-dependent potential is considered to study nucleon-nucleon, nucleon-nucleus and nucleus-nucleus elastic scattering by exploiting the variable phase method to potential scattering. The velocity dependent potential, equivalent to Graz separable potential, has the ability to reproduce the correct nature and numerical values of the NN phase parameters up to 400 MeV. Also it works equally well for alpha-nucleon and alpha-alpha systems up to few higher partial waves. Our results are in close conformity with the previous theoretical and experimental data. For alpha-alpha scattering we have treated only s-wave case.

Single-particle spectroscopies of p-wave and d-wave interacting Bose gases in normal phase

Motivated by experiments with interacting quantum gases across high partial wave resonance, we investigate the thermodynamic properties and single-particle spectra of Bose gases in normal phase for different interaction strengths for both p- and d-wave interactions. The equation of state, contact density, momentum distributions and self-energies of single-particle Green’s functions are obtained in the spirit of ladder diagram approximations. The radio-frequency (RF) spectrum, as an important experimental approach for detecting Feshbach molecules or the interaction effect, is calculated at different temperatures. A reversed temperature dependence on the Bose–Einstein condensation side and Bardeen–Cooper–Schrieffer side is identified for both p- and d-wave interactions. An estimate for the signal of RF spectra under typical experimental conditions is also provided.

Geometrical properties of ΩNN three-body states by realistic NN and first principles Lattice QCD ΩN potentials

The Faddeev equations in coordinate space are solved to study the ΩNN and ΩΩN three-body systems using the latest ΩNS25 and ΩΩ S01 interactions developed by the HAL QCD Collaboration. We recalculate the binding energy of the ΩNN system by examining three NN potentials, i.e., modern realistic AV18 potential, Yukawa-type Malfliet-Tjon (MT) interaction, and Gogny-Pires-Tourreil (GPT) soft and local potential. We take into account the contribution of the Coulomb potential. Our numerical calculations for Ωd(T=0) in maximum spin 5/2+ confirm ground state binding energy of 20.953, 19.368, and 20.439 MeV and a matter radius of 1.097, 1.373, and 1.309 fm using MT, GPT, and AV18 NN potentials, respectively. In the case of Ωd(0)5/2+ system, our numerical analysis shows that considering higher partial waves than s wave in NN interactions leads to an increase of about 0.2 MeV using GPT and about 0.1 MeV reduction with AV18 potentials. We study the convergence of three-body binding energies in a cluster model using the hyperspherical harmonics method and investigate the geometrical properties of Ωd(0)5/2+ ground states.

Three-particle Lellouch-Lüscher formalism in moving frames

A manifestly relativistic-invariant Lellouch-Lüscher formalism for the decays into three identical particles with no two-to-three transitions is proposed. Similarly to [1], the formalism is based on the use of the non-relativistic effective Lagrangians. Manifest Lorentz invariance is guaranteed, as in [2], by choosing the quantization axis along the total four-momentum of the three-particle system. A systematic inclusion of the higher-order derivative couplings, as well as higher partial waves is addressed.

Renormalization of one-pion exchange in higher partial waves in chiral effective field theory for antinucleon-nucleon system* *Supported by the Doctoral Fund Project of Nanfang College, Guangzhou (2020BQ03)

The renormalization of the iterated one-pion exchange (OPE) has been studied in chiral effective field theory (χEFT) for the antinucleon-nucleon () scattering in some partial waves (Phys. Rev. C 105, 054005 (2022)). In this paper, we go further for the other higher partial waves but with total angular momenta . Contact interactions are represented by a complex spherical well in the coordinate space. Changing the radius of the spherical well means changing the cutoff. We check the cutoff dependence of the phase shifts, inelasticities, and mixing angles for the partial waves and show that contact interactions are needed at leading order in channels where the singular tensor potentials of OPE are attractive. The results are compared with the energy-dependent partial-wave analysis of scattering data. Comparisons between our conclusions and applications of χEFT to the nucleon-nucleon system are also discussed.

Photodissociation spectroscopy via a rovibrational resonance in intense UV pulses

Photodissociation dynamics via a rovibrational resonance in intense UV pulses is investigated theoretically, using a showcase ${\text{CH}}^{+}$ molecule promoted to the $\text{C}\phantom{\rule{0.16em}{0ex}}^{1}\mathrm{\ensuremath{\Sigma}}^{+}$ valence excited electronic state with a potential barrier, thus giving access to study shape resonance controlled by the pulse frequency. Simulations of the kinetic energy release (KER) and angular distribution of the photofragments (ADP) spectra show dramatic differences for the cases when the pulse is tuned on and off the rovibrational resonance. It shows that as the increasing pulse intensity for the transitions to shape resonance, the KER spectra develop into new and higher energy peaks overlying on the broadened background, which is explained by the involvement of other resonances with higher partial waves through electronic Rabi flopping between the ground and excited electronic states. Those nonlinear contribution increases drastically the probability of photofragmentation along the laser polarization in the ADP spectra. The coincident KER-ADP spectra reveal clearly the correlated dynamics in the vicinity of the dissociation barrier. The present work opens possibilities for the manipulation of ultrafast photodissociation dynamics with the help of resonance states in the continuum.

Resonances in heavy meson–heavy baryon coupled-channel interactions

The interactions of {bar{D}}^{(*)} Lambda _c - {bar{D}}^{(*)}Sigma _c^{(*)} are studied within the framework of a dynamical coupled-channel approach. A series of bound states and resonances with different spin and parity are dynamically generated in the hidden charm sector. Four S-wave bound states are found in the mass range of 4.3–4.5 GeV, close to the pentaquark states observed by LHCb. Two of the states have a spin parity of J^P= 1/2^- and the other two have J^P=3/2^-. In addition, several resonances with different spin and parity in higher partial waves are predicted.

Towards high partial waves in lattice QCD with an extended two-hadron operator

An extended two-hadron operator is developed to extract the spectra of irreducible representations (irreps) in the finite volume. The irreps of the group for the finite volume system are projected using a coordinate-space operator. The correlation function of this operator is computationally efficient to extract lattice spectra of the specific irrep. In particular, this new formulation only requires propagators to be computed from two distinct source locations, at fixed spatial separation. We perform a proof-of-principle study on a ${24}^{3}\ifmmode\times\else\texttimes\fi{}48$ lattice volume with ${m}_{\ensuremath{\pi}}\ensuremath{\approx}900\text{ }\text{ }\mathrm{MeV}$ by isolating various spectra of the $\ensuremath{\pi}\ensuremath{\pi}$ system with isospin-2 including a range of total momenta and irreps. By applying the L\"uscher formalism, the phase shifts of $S$- and $D$-wave $\ensuremath{\pi}\ensuremath{\pi}$ scattering with isospin-2 are extracted from the spectra, with a tentative look at the role and influence of the $G$-wave.

Relativistic-invariant formulation of the NREFT three-particle quantization condition

A three-particle quantization condition on the lattice is written down in a manifestly relativistic-invariant form by using a generalization of the non-relativistic effective field theory (NREFT) approach. Inclusion of the higher partial waves is explicitly addressed. A partial diagonalization of the quantization condition into the various irreducible representations of the (little groups of the) octahedral group has been carried out both in the center-of-mass frame and in moving frames. Furthermore, producing synthetic data in a toy model, the relativistic invariance is explicitly demonstrated for the three-body bound state spectrum.

Interactions of two and three mesons including higher partial waves from lattice QCD

We study two- and three-meson systems composed either of pions or kaons at maximal isospin using Monte Carlo simulations of lattice QCD. Utilizing the stochastic LapH method, we are able to determine hundreds of two- and three-particle energy levels, in nine different momentum frames, with high precision. We fit these levels using the relativistic finite-volume formalism based on a generic effective field theory in order to determine the parameters of the two- and three-particle K-matrices. We find that the statistical precision of our spectra is sufficient to probe not only the dominant s-wave interactions, but also those in d waves. In particular, we determine for the first time a term in the three-particle K-matrix that contains two-particle d waves. We use three Nf = 2 + 1 CLS ensembles with pion masses of 200, 280, and 340 MeV. This allows us to study the chiral dependence of the scattering observables, and compare to the expectations of chiral perturbation theory.

Scattering amplitudes for monopoles: pairwise little group and pairwise helicity

On-shell methods are particularly suited for exploring the scattering of electrically and magnetically charged objects, for which there is no local and Lorentz invariant Lagrangian description. In this paper we show how to construct a Lorentz-invariant S-matrix for the scattering of electrically and magnetically charged particles, without ever having to refer to a Dirac string. A key ingredient is a revision of our fundamental understanding of multi-particle representations of the Poincaré group. Surprisingly, the asymptotic states for electric-magnetic scattering transform with an additional little group phase, associated with pairs of electrically and magnetically charged particles. The corresponding “pairwise helicity” is identified with the quantized “cross product” of charges, e1g2− e2g1, for every charge-monopole pair, and represents the extra angular momentum stored in the asymptotic electromagnetic field. We define a new kind of pairwise spinor-helicity variable, which serves as an additional building block for electric-magnetic scattering amplitudes. We then construct the most general 3-point S-matrix elements, as well as the full partial wave decomposition for the 2 → 2 fermion-monopole S-matrix. In particular, we derive the famous helicity flip in the lowest partial wave as a simple consequence of a generalized spin-helicity selection rule, as well as the full angular dependence for the higher partial waves. Our construction provides a significant new achievement for the on-shell program, succeeding where the Lagrangian description has so far failed.

Direct observation of ultracold atom-ion excitation exchange

Atom-ion interactions occur through the electric dipole which is induced by the ion on the neutral atom. In a Langevin collision, in which the atom and ion overcome the centrifugal barrier and reach a short internuclear distance, their internal electronic states deform due to their interaction and can eventually alter. Here we explore the outcome products and the energy released from a single Langevin collision between a single cold $^{88}$Sr$^{+}$ ion initialized in the metastable $4d^2D_{5/2,3/2}$ states, and a cold $^{87}$Rb atom in the $5s^2S_{1/2}$ ground state. We found that the long-lived $D_{5/2}$ and $D_{3/2}$ states quench after roughly three Langevin collisions, transforming the excitation energy into kinetic energy. We identify two types of collisional quenching. One is an Electronic Excitation-Exchange process, during which the ion relaxes to the $S$ state and the atom is excited to the $P$ state, followed by energy release of $\sim$ 3000 K$\cdot$k$_B$. The second is Spin-Orbit Change where the ion relaxes from the higher fine-structure $D_{5/2}$ level to the lower $D_{3/2}$ level releasing $\sim$ 400 K$\cdot$k$_B$ into kinetic motion. These processes are theoretically understood to occur through Landau-Zener avoided crossings between the different molecular potential curves. We also found that these relaxation rates are insensitive to the mutual spin orientation of the ion and atoms. This is explained by the strong inertial Coriolis coupling present in ultracold atom-ion collisions due to the high partial wave involved, which strongly mixes different angular momentum states. This inertial coupling explains the loss of the total electronic angular-momentum which is transferred to the external rotation of nuclei. Our results provide deeper understanding of ultracold atom-ion inelastic collisions and offer additional quantum control tools for the cold chemistry field.

Efficient emulators for scattering using eigenvector continuation

Eigenvector continuation (EC) has been shown to accurately and efficiently reproduce ground states for targeted sets of Hamiltonian parameters. It uses as variational basis vectors the corresponding ground-state eigensolutions from selected other sets of parameters. Here we extend the EC approach to scattering using the Kohn variational principle. We first test it using a model for S-wave nucleon-nucleon scattering and then demonstrate that it also works to give accurate predictions for non-local potentials, charged-particle scattering, complex optical potentials, and higher partial waves. These proofs-of-principle validate EC as an accurate emulator for applying Bayesian inference to parameter estimation constrained by scattering observables. The efficiency of such emulators is because the accuracy is achieved with a small number of variational basis elements and the central computations are just linear algebra calculations in the space spanned by this basis.

Toward a quantitative analysis of the temperature dependence of electron attachment to SF6.

New flowing afterglow/Langmuir probe investigations of electronic attachment to SF6 are described. Thermal attachment rate constants are found to increase from 1.5 × 10-7 cm3 s-1 at 200 K to 2.3 × 10-7 cm3 s-1 at 300 K. Attachment rate constants over the range of 200-700 K (from the present work and the literature), together with earlier measurements of attachment cross sections, are analyzed with respect to electronic and nuclear contributions. The latter suggest that only a small nuclear barrier (of the order of 20 meV) on the way from SF6 to SF6 - has to be overcome. The analysis shows that not only s-waves but also higher partial waves have to be taken into account. Likewise, finite-size effects of the neutral target contribute in a non-negligible manner.

Quark degrees of freedom and nuclear matter saturation

It has been found in previous works [M. Baldo and K. Fukukawa, Phys. Rev. Lett. 113, 241501 (2014); K. Fukukawa, M. Baldo, G. F. Burgio, L. Lo Monaco and H.-J. Schulze, Phys. Rev. 92, 065802 (2015)] that the nucleon–nucleon potential of [Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki Phys. Rev. C 64, 054001 (2001); Y. Fujiwara et al., Phys. Rev. C 65, 014002 (2001)] gives an accurate saturation point in symmetric nuclear matter once the three hole-line contributions are included in the Brueckner–Bethe–Goldstone expansion without the addition of three-body forces in the nuclear Hamiltonian. The potential is based on a quark model of nucleons and on the quark–quark interaction together with quark exchange processes. These features introduce an intrinsic nonlocality of the nucleon–nucleon interaction. In order to clarify the role of the quark degrees of freedom and of the nonlocality in the saturation, we perform a comparative study of this potential and the traditional meson exchange models, exemplified in the CD-Bonn potential. We find that at the Brueckner–Hartree–Fock approximation, which corresponds to the two hole-line level of approximation, the dominant modification of the nucleon–nucleon interaction with respect to CD-Bonn is incorporated in the s-wave channels, where the quark degrees of freedom should be more relevant, in particular for the short range quark exchange processes. However, when the three hole-line contribution is included, we find that the higher partial waves play a relevant role, mainly in the term that describes the effect of the medium on the off-shell propagation of the nucleon.

Extremal and near-extremal black holes and near-CFT1

We study the behaviour of extremal and near-extremal black holes at low energies and low temperatures and find that it can be understood from the near-horizon AdS2 region. Our analysis includes charged matter and also goes beyond the S-wave approximation. We find that the leading behaviour at low energies arises from a mode linked to time reparametrisations and from phase modes arising from gauge fields. At somewhat higher energies, additional modes arising from higher partial waves can also be cumulatively significant. These results can be applied quite generally to cases where an AdS2 × Sd near-horizon geometry arises, including black holes in asymptotically AdS and flat space-times.

Implementing the three-particle quantization condition including higher partial waves

We present an implementation of the relativistic three-particle quantization condition including both s- and d-wave two-particle channels. For this, we develop a systematic expansion of the three-particle K matrix, mathcal{K} df,3, about threshold, which is the generalization of the effective range expansion of the two-particle K matrix, mathcal{K} 2. Relativistic invariance plays an important role in this expansion. We find that d-wave two-particle channels enter first at quadratic order. We explain how to implement the resulting multichannel quantization condition, and present several examples of its application. We derive the leading dependence of the threshold three-particle state on the two-particle d-wave scattering amplitude, and use this to test our implementation. We show how strong two-particle d-wave interactions can lead to significant effects on the finite-volume three-particle spectrum, including the possibility of a generalized three-particle Efimov-like bound state. We also explore the application to the 3π+ system, which is accessible to lattice QCD simulations, where we study the sensitivity of the spectrum to the components of mathcal{K} df,3. Finally, we investigate the circumstances under which the quantization condition has unphysical solutions.

High-rank separable atom-atom interaction potential used for solving two-body Lippmann-Schwinger and three-body Faddeev equations.

We derive a high-rank separable potential formula of the atom-atom interaction by using the two-body wave function in the coordinate space as inputs. This high-rank separable potential can be utilized to numerically solve the two-body Lippmann-Schwinger equation and three-body Faddeev equation. By analyzing the convenience and stability of numerical calculations for different kinds of the matrix forms of the Lippmann-Schwinger and Faddeev equations, we can find the optimal forms of the kernal matrices in the two- and three-body scattering equations. We calculate the dimer bound energy, two-body scattering phase shift and off-shell t-matrix, the trimer bound energy, atom-dimer scattering length, and three-body recombination rate using the high-rank separable potentials, taking the identical 4He atoms as an application example. All the calculations converge quickly for the rank number . The high-rank separable potential is valid for two-body scattering calculation of 4He atoms, but not accurate enough for reproducing the three-body scattering results by using only two-body s-wave interaction and describing the contributions of two-body high partial-waves to the three-body scattering for the 4He3 system.