Partial-wave Amplitudes Research Articles

CP violation of baryon decays with N π rescatterings* *Supported in part by the Natural Science Foundation of China (12335003), and the Fundamental Research Funds for the Central Universities (lzujbky-2024-oy02, lzujbky-2023-it12)

There is a long-standing puzzle that the CP violation (CPV) in the baryon systems has never been well established in experiments, while the CPV of mesons have been observed by decades. In this paper, we propose that the CPV of baryon decays can be generated with the rescatterings of a nucleon and a pion into some final states, i.e. or . Benefited by the fruitful data of scatterings, we can model-independently analyse the strong phases of -baryon decays using the partial wave amplitudes of scatterings. Avoiding the most difficult problem of non-perturbative dynamics, it makes a great advantage to predict the CPV of baryon decays with a relatively reliable understanding of the decay dynamics. We study the processes of and with or . It is found that the global CPV of the above processes in the invariant mass regions of scatterings are at the order of several percent. More importantly, the local CPV in some regions of the Dalitz plots can reach the order of 10%, or be even larger. Considering the predicted results and the experimental data samples, we strong suggest to measure the CPV of , which has a large possibility to achieve the first observation of CPV in the baryon system.

Algorithms for partial wave amplitudes in the covariant L−S scheme

With the continuous accumulation of data from hadron collision experiments, efficient partial wave analysis tools are indispensable for constructing a clear hadron spectrum. Currently, automated computations of scattering amplitudes primarily use the helicity scheme and covariant effective Lagrangian method. The automated calculations under the covariant L−S scheme, which is one of the commonly used partial wave analysis schemes, have not been fully realized. In this work, we provide a general algorithm for computing partial wave amplitudes under the covariant L−S scheme. This will lay the foundation for automated computation of partial wave amplitudes under the covariant L−S scheme. Published by the American Physical Society 2024

A discussion on the anomalous threshold enhancement of – couplings and peak* *Supported in part by the National Nature Science Foundations of China (12335002). This work is also supported by the Fundamental Research Funds for the Central Universities

The attractive interaction between and has to be strong enough if X(6900) is of the molecule type. We argue that since decays predominantly into a pair, the interactions between and may be significantly enhanced owing to the three point loop diagram. The enhancement originates from the anomalous threshold located at GeV , whose effect propagates into the s-channel partial wave amplitude in the vicinity of GeV. This effect may be helpful in the formation of the peak.

Partial Wave Amplitude Analysis in Pion-Induced Reactions at the HADES Experiment

The High Acceptance Di-Electron Spectrometer (HADES) collaboration at GSI employs a pion beam to examine the characteristics of baryonic resonances and their decay channels. This pion-beam facility enables the generation of baryonic resonances at a fixed center of mass energy (√s), i.e. in the S-channel. In anticipation of conducting a more comprehensive exploration of the resonance regions in pion-proton collisions, a new implementation of the K-matrix & D-matrix frameworks is currently under development. This updated implementation aims to offer a refined mapping of these regions. Example fits are presented showing the current status and the potential of the new framework.

A sensitivity-improved amplitude method for determining film thickness based on the partial reflection waves

A sensitivity-improved reflection coefficient amplitude method for determining wide-range lubricating oil film thickness is proposed based on partial reflection waves, which are obtained by removing the first reflection wave. Numerical analysis and experimental testing are conducted to verify the proposed method. The results show the lubricating oil film thickness ranging from the spring model region to the resonant region can be calculated based on the proposed partial-wave reflection coefficient amplitude method. In comparison to the existing reflection coefficient amplitude method, the measurement accuracy of the lubricating oil film thickness is significantly improved for the transition region which locates between the spring model region and the resonant region, for instance, the observed maximum relative error is decreased to 9% from 60%.

Covariant orbital-spin scheme for any spin based on irreducible tensor

In hadron spectrum physics, the partial wave analysis is a primary method used to extract properties of hadronic resonances. The covariant orbital-spin coupling scheme holds unique advantages over other partial wave methods due to its Lorentz covariant form and determined orbital-spin quantum numbers. This paper presents a general form of the covariant orbital-spin coupling scheme based on the irreducible tensor of the homogeneous proper Lorentz group and its little groups. A systematic procedure for constructing partial wave amplitude in a Lorentz covariant way is provided, which can be applied to both massive and massless particles. Specific examples are also included.

Constructing the general partial wave and renormalization in effective field theory

We construct the general partial wave amplitude basis for the $N\ensuremath{\rightarrow}M$ scattering, which consists of Poincar\'e Clebsch-Gordan coefficients, in a Lorentz invariant form given in terms of the spinor-helicity variables. The inner product of the Clebsch-Gordan coefficients is defined, which converts on-shell phase space integration into an algebraic problem. We also develop the technique of partial wave expansions of arbitrary amplitudes, including those with infrared divergence. These are applied to the computation of anomalous dimension matrix for general effective operators, where unitarity cuts for the loop amplitudes, with an arbitrary number of external particles, are obtained via partial wave expansion.

Study of X(6900) with unitarized coupled channel scattering amplitudes

In this paper, we study the resonant state X(6900). The scattering amplitudes of coupled channels, J/psi J/psi -J/psi psi (2S)-J/psi psi (3770), are constructed with the interaction of four vector mesons described by effective Lagrangians. The amplitudes are calculated up to one loop, decomposed by partial wave projection, and unitarized by Padacute{e} approximation. These amplitudes are fitted to the latest experimental data sets of di-J/psi and J/psi psi (2S) invariant mass spectra of LHCb, CMS, and ATLAS. High-quality solutions are obtained. With these partial wave amplitudes, we extract the pole parameters of the X(6900). Its quantum number is likely to be 0^{++}. According to the pole counting rule as well as analysis of the phase shifts of the partial waves, it supports our previous conclusion that the X(6900) prefers to be a compact tetra-quark.

Seeking for resonances in unitarized one-loop graviton-graviton scattering

Some effective field theories exhibit dynamical resonances that, when properly included, mitigate their bad behavior at high energies. Unitarization of the partial wave amplitudes is the preferred method to unveil such resonances. Interpreting the Einstein-Hilbert theory in the spirit of effective Lagrangians, we implement the inverse amplitude method and unitarize the one-loop level graviton-graviton scattering in pure gravity. Due to the presence of infrared divergences, the analysis requires a careful treatment of the infrared region and the introduction of infrared regulators, carefully selected in order to fulfill perturbative unitarity.

Perturbative unitarity of strongly interacting massive particle models

Dark pion is a promising candidate for the strongly interacting massive particle dark matter. A large pion self-coupling mπ/fπ tends to be required for correct relic abundance, and hence the partial-wave amplitudes can violate the perturbative unitarity even for the coupling within naïve perturbative regime. We improve the partial-wave amplitudes in order to satisfy the optical theorem. We demonstrate that the improvement is relevant only for semi-relativistic pions, and thus this does not affect the self-scattering cross section at the cosmic structures. We also discuss the impact of the improvement of the πππ → ππ scattering process, and we find that there is an upper bound on mπ at which the correct relic abundance is never achieved even at large mπ/fπ due to the optical theorem.

Unitarizing non-relativistic Coulomb scattering

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.

Соотношение унитарности и унитарные ограничения для теории скалярных полей с разными скоростями звука

Motivated by scalar-tensor gravities, we consider a theory which contains massless scalar fields with different sound speeds. We derive unitarity relations for partial wave amplitudes of $2 \to 2$ scattering, with explicit formulas for contributions of two-particle intermediate states. Making use of these relations, we obtain unitarity bounds both in the most general case and in the case considered in literature for unit sound speed. These bounds can be used for estimating the strong coupling scale of a pertinent EFT. We illustrate our unitarity relations by explicit calculation to the first non-trivial order in couplings in a simple model of two scalar fields with different sound speeds.

Signature of a Doubly Charm Tetraquark Pole in DD^{*} Scattering on the Lattice.

The doubly charm tetraquark with flavor ccu[over ¯]d[over ¯] and isospin I=0 is investigated by calculating the DD^{*} scattering amplitude with lattice QCD. The simulation is done on CLS ensembles with dynamical u/d, s quarks and m_{π}≃280 MeV for two charm quark masses, one slightly larger and one slightly lower than the physical value. The scattering amplitudes for partial waves l=0, 1 are extracted near threshold via the Lüscher method by considering systems with total momenta PL/(2π)=0,1,sqrt[2],2 on two spatial volumes. A virtual bound state pole in the DD^{*} scattering amplitude with l=0 is found 9.9_{-7.1}^{+3.6} MeV below the DD^{*} threshold for the charm quark mass closer to the physical value. This pole is likely related to the doubly charm tetraquark discovered by LHCb less than 1MeV below the D^{0}D^{*+} threshold. Future lattice simulations closer to the continuum limit and physical quark masses would be valuable to establish this connection systematically.

Kaon electromagnetic form factors in dispersion theory

The electromagnetic form factors of charged and neutral kaons are strongly constrained by their low-energy singularities, in the isovector part from two-pion intermediate states and in the isoscalar contribution in terms of omega and phi residues. The former can be predicted using the respective pi pi rightarrow {{bar{K}}} K partial-wave amplitude and the pion electromagnetic form factor, while the latter parameters need to be determined from electromagnetic reactions involving kaons. We present a global analysis of time- and spacelike data that implements all of these constraints. The results enable manifold applications: kaon charge radii, elastic contributions to the kaon electromagnetic self energies and corrections to Dashen’s theorem, kaon boxes in hadronic light-by-light (HLbL) scattering, and the phi region in hadronic vacuum polarization (HVP). Our main results are: langle r^2rangle _text {c}=0.359(3),text {fm}^2, langle r^2rangle _text {n}=-0.060(4),text {fm}^2 for the charged and neutral radii, epsilon =0.63(40) for the elastic contribution to the violation of Dashen’s theorem, a_mu ^{Ktext {-box}}=-0.48(1)times 10^{-11} for the charged kaon box in HLbL scattering, and a_mu ^text {HVP}[K^+K^-, le 1.05,text {GeV}]=184.5(2.0)times 10^{-11}, a_mu ^text {HVP}[K_SK_L, le 1.05,text {GeV}]=118.3(1.5)times 10^{-11} for the HVP integrals around the phi resonance. The global fit to {{bar{K}}} K gives {{bar{M}}}_phi =1019.479(5),text {MeV}, {bar{ varGamma }}_phi =4.207(8),text {MeV} for the phi resonance parameters including vacuum-polarization effects.

Ratios of partial wave amplitudes in the decays of J = 1 and J = 2 mesons

We study the two-body decay of mesons using the covariant helicity formalism. We find that to explain the ratio of partials wave amplitudes (PWAs) of the decay, the Lagrangian must include derivative interactions in addition to contact interactions. We estimate the ratios of the coupling constants for the vector decays of the axial-vector, pseudovector and pseudotensor meson, and the tensor decays of the pseudotensor mesons by fitting the ratios of the PWAs to the available data and predict the ratios to some new decays.

Composite nature of Z_b states from data analysis

We use a near-threshold parameterization with explicit inclusion of the Castillejo–Dalitz–Dyson poles, which is more general than the effective range expansion, to study the bottomonium-like states Z_b(10610) and Z_b(10650). In terms of the partial-wave amplitude, we fit the event number distribution of B^{(*)}{bar{B}}^* system to the experimental data for these resonances from Belle Collaboration. The data could be described very well in our method, which supports the molecular interpretation. Then the relevant physical quantities are obtained, including the B^{(*)}bar{B}^* scattering length (a), effective range (r), and residue squared (gamma _s^2) of the pole in the complex plane. In particular, we find the compositeness can range from about 0.4 up to 1 for the B{bar{B}}^* (B^*{bar{B}}^*) component in the resonance Z_b(10610) (Z_b(10650)).

Scalar resonance in graviton-graviton scattering at high-energies: The graviball

We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply S-matrix techniques, based on unitarity and analyticity, we introduce an S-matrix associated to this resummation that is free of infrared divergences. This is achieved by removing the diverging phase factor calculated by Weinberg that multiplies the S matrix, and that stems from the virtual infrared gravitons. A scalar graviton-graviton resonance with vacuum quantum numbers (JPC=0++) is obtained as a pole in the nonperturbative S-wave amplitude, which we call the graviball. Its resonant effects along the physical real-s axis may peak at values substantially lower than the UV cutoff squared of the theory. For some scenarios, this phenomenon could have phenomenological consequences at relatively low-energy scales, similarly to the σ resonance in QCD.

Unitarizing infinite-range forces: Graviton-graviton scattering, the graviball, and Coulomb scattering

We study graviton-graviton scattering in partial-wave amplitudes after unitarizing their Born terms. In order to apply S -matrix techniques, based on unitarity and analyticity, we introduce an S -matrix associated to this resummation that is free of infrared divergences. This is achieved by removing the diverging phase factor calculated by Weinberg that multiplies the S matrix, and that stems from the virtual infrared gravitons. A scalar graviton-graviton resonance with vacuum quantum numbers is obtained as a pole in the nonperturbative S -wave amplitude, which is called the graviball. Its resonant effects along the physical real s-axis may peak at values substantially lower than the UV cutoff squared of the theory, similarly to the σ resonance in QCD. These techniques are also applied to study nonrelativistic Coulomb scattering up to next-to-leading order in the unitarization program. A comparison with the exact known solution is very illuminating.

Ladder resummation of spin 1/2 fermion many-body systems with arbitrary partial-wave content

We resum the ladder diagrams for the calculation of the energy density E of a spin 1/2 fermion many-body system in terms of arbitrary vacuum two-body scattering amplitudes. The partial-wave decomposition of the in-medium two-body scattering amplitudes is developed, and the expression for calculating E in a partial-wave amplitude expansion is also given. The case of contact interactions is completely solved for any content in partial waves and it is shown to provide renormalized results, expressed directly in terms of scattering data parameters, within cutoff regularization in a wide class of schemes. The S- and P-wave interactions are considered up to including the first three-terms in the effective-range expansion, paying special attention to the parametric region around the unitary limit.

An N/D study of the S 11 channel πN scattering amplitude * *Support in part by National Nature Science Foundations of China (11975028, 10925522), the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) (196253076 -TRR 110)

Extensive dynamical calculations are conducted in the study of channel low energy scatterings, based on various phenomenological model inputs of left cuts at the tree level. The subtleties of the singular behavior of the partial wave amplitude, at the origin of the complex plane, are analysed in detail. Furthermore, it is found that the dispersion representation for the phase shift, , must be modified in the case of scatterings. An additional contribution from the dispersion integral exists, which approximately cancels the contribution of the two virtual poles located near the end points of the segment cut, induced by channel nucleon exchanges. With limited reliance on the details of the dynamical inputs, the subthreshold resonance survives.