Dalitz Plot Research Articles

Evidence of the low-lying baryon Σ*(1/2−) in the process Λc+→ηπ+Λ

Motivated by the Belle measurements of the process Λc+→ηπ+Λ, we investigate this process by considering the contributions from the Λ(1670), a0(980), and Σ(1385). In addition, we also consider the predicted low-lying baryon Σ*(1/2−). Our results involving the Σ*(1/2−) are favored by fitting to the Belle data of the ηΛ and π+Λ invariant mass distributions. Furthermore, we predict the ηπ+ invariant mass distribution and the angular distribution dΓ/dcosθ, which are significantly different depending on whether or not the contribution from the Σ*(1/2−) is considered. Finally, we show that, with the contribution from the Σ*(1/2−), the calculated Dalitz plot agrees with the Belle measurements. Future precise measurements of the process Λc+→ηπ+Λ could shed further light on the existence of the low-lying Σ*(1/2−). Published by the American Physical Society 2024

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.

Dalitz-plot analysis of B±→K±K+K− decays

We study B±→K±K+K− decays using the QCD factorization model with final state interactions between K+ and K− mesons taken into account. The parameters of the model are fitted to the data of the and LHCb collaborations. We describe the KK¯ effective mass distributions and examine the CP-violating asymmetry effects in the full range of the Dalitz plot. Published by the American Physical Society 2024

Anomalous thresholds in B → (P, V)γ* form factors

We study the effects of anomalous thresholds on the non-local form factors describing the hadronization of the light-quark contribution to B → (P, V)γ* transitions. Starting from a comprehensive discussion of anomalous thresholds in the triangle loop function for different mass configurations, we detail how the dispersion relation for ππ intermediate states is affected by contour deformations mandated by the anomalous branch points. Phenomenological estimates of the size of the anomalous contributions to the form factors are provided with couplings determined from measured branching fractions and Dalitz plot distributions. Our key finding is that anomalous effects are suppressed on the ρ(770) resonance, while off-peak the effects can become as large as O\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\mathcal{O} $$\\end{document}(10%) of the full (light-quark-loop induced) non-local form factors. We comment on future generalizations towards higher intermediate states and the charm loop, outlining how the dispersive framework established in this work could help improve the non-local form factors needed as input for a robust interpretation of B → (P, V)ℓ+ℓ− decays.

Three-body unitary coupled-channel approach to radiative J/ψ decays and η(1405/1475)

Recent BESIII data on radiative J/ψ decays from ∼1010 J/ψ samples should significantly advance our understanding of the controversial nature of η(1405/1475). This motivates us to develop a three-body unitary coupled-channel model for radiative J/ψ decays to three-meson final states of any partial wave (JPC). Basic building blocks of the model are bare resonance states such as η(1405/1475) and f1(1420), and πK, KK¯, and πη two-body interactions that generate resonances such as K*(892), K0*(700), and a0(980). This model reasonably fits KSKSπ0 Dalitz plot pseudodata generated from the BESIII’s JPC=0−+ amplitude for J/ψ→γKSKSπ0. The experimental branching ratios of η(1405/1475)→ηππ and η(1405/1475)→γρ relative to that of η(1405/1475)→KK¯π are simultaneously fitted. Our 0−+ amplitude is analytically continued to find three poles, two of which correspond to η(1405) on different Riemann sheets of the K*K¯ channel, and the third one for η(1475). This is the first pole determination of η(1405/1475) and, furthermore, the first-ever pole determination from analyzing experimental Dalitz plot distributions with a manifestly three-body unitary coupled-channel framework. Process-dependent ηππ, γπ+π−, and πππ lineshapes of J/ψ→γ(0−+)→γ(ηππ), γ(γρ), and γ(πππ) are predicted, and are in reasonable agreement with data. A triangle singularity is shown to play a crucial role to cause the large isospin violation of J/ψ→γ(πππ). Published by the American Physical Society 2024

Roles of the Tcs¯0(2900)0 and D0*(2300) in the process B−→Ds+K−π−

Motivated by the recent LHCb observations of Tcs¯0(2900)0 and Tcs¯0(2900)++ in the processes B0→D¯0Ds+π− and B+→D−Ds+π+, we have investigated the decay B−→Ds+K−π− by taking into account the contributions from the S-wave vector-vector interactions, and the S-wave Ds+K− interactions. Our results show that the Ds+K− invariant mass distribution has an enhancement structure near the threshold, associated with the D0*(2300), which is in good agreement with the Belle measurements. We have also predicted the Ds+π− invariant mass distribution and the Dalitz plot, which show the significant signal of the Tcs¯0(2900). With the same formalism, the Ds−Ks0 invariant mass distribution of the process B0→Ds−Ks0π+ measured by Belle could be well reproduced, and the peak of Tcs¯0(2900) is expected to be observed around 2900 MeV in the Ds−π+ invariant mass distribution. Our results could be tested by the Belle II and LHCb experiments in the future. Published by the American Physical Society 2024

Toward extracting gamma from Brightarrow DK without binning

B^pm rightarrow DK^pm transitions are known to provide theoretically clean information about the CKM angle gamma , with the most precise available methods exploiting the cascade decay of the neutral D into CP self-conjugate states. Such analyses currently require binning in the D decay Dalitz plot, while a recently proposed method replaces this binning with the truncation of a Fourier series expansion. In this paper, we present a proof of principle of a novel alternative to these two methods, in which no approximations at the level of the data representation are required. In particular, our new strategy makes no assumptions about the amplitude and strong phase variation over the Dalitz plot. This comes at the cost of a degree of ambiguity in the choice of test statistic quantifying the compatibility of the data with a given value of gamma , with improved choices of test statistic yielding higher sensitivity. While our current proof-of-principle implementation does not demonstrate optimal sensitivity to gamma , its conceptually novel approach opens the door to new strategies for gamma extraction. More studies are required to see if these can be competitive with the existing methods.

A novel unbinned model-independent method to measure the CKM angle γ in B± → DK± decays with optimised precision

We present a novel unbinned method to combine B± → DK± and charm threshold data for the amplitude-model unbiased measurement of the CKM angle γ in cases where the D meson decays to a three-body final state. The new unbinned approach avoids any kind of integration over the D Dalitz plot, to make optimal use the available information. We verify the method with simulated signal data where the D decays to KSπ+π−. Using realistic sample sizes, we find that the new method reaches the statistical precision on γ of an unbinned model-dependent fit, i.e. as good as possible and better than the widely used model-independent binned approach, without suffering from biases induced by a mis-modeled D decay amplitude.

Amplitude analysis of the {D}_s^{+} → π−π+π+ decay

A Dalitz plot analysis of the {D}_s^{+} → π−π+π+ decay is presented. The analysis is based on proton-proton collision data recorded by the LHCb experiment at a centre-of-mass energy of 8 TeV and corresponding to an integrated luminosity of 1.5 fb−1. The resonant structure of the decay is obtained using a quasi-model-independent partial-wave analysis, in which the π+π− S-wave amplitude is parameterised as a generic complex function determined by a fit to the data. The S-wave component is found to be dominant, followed by the contribution from spin-2 resonances and a small contribution from spin-1 resonances. The latter includes the first observation of the {D}_s^{+} → ω(782)π+ channel in the {D}_s^{+} → π−π+π+ decay. The resonant structures of the {D}_s^{+} → π−π+π+ and D+→ π−π+π+ decays are compared, providing information about the mechanisms for the hadron formation in these decays.

Earth mover’s distance as a measure of CP violation

We introduce a new unbinned two sample test statistic sensitive to CP violation utilizing the optimal transport plan associated with the Wasserstein (earth mover’s) distance. The efficacy of the test statistic is shown via two examples of CP asymmetric distributions with varying sample sizes: the Dalitz distributions of B0 → K+π−π0 and of D0 → π+π−π0 decays. The windowed version of the Wasserstein distance test statistic is shown to have comparable sensitivity to CP violation as the commonly used energy test statistic, but also retains information about the localized distributions of CP asymmetry over the Dalitz plot. For large statistic datasets we introduce two modified Wasserstein distance based test statistics — the binned and the sliced Wasserstein distance statistics, which show comparable sensitivity to CP violation, but improved computing time and memory scalings. Finally, general extensions and applications of the introduced statistics are discussed.

Amplitude analysis of the D+→ π−π+π+ decay and measurement of the π−π+ S-wave amplitude

An amplitude analysis of the D+→ π−π+π+ decay is performed with a sample corresponding to 1.5 fb−1 of integrated luminosity of pp collisions at a centre-of-mass energy sqrt{s} = 8 TeV collected by the LHCb detector in 2012. The sample contains approximately six hundred thousand candidates with a signal purity of 95%. The resonant structure is studied through a fit to the Dalitz plot where the π−π+ S-wave amplitude is extracted as a function of π−π+ mass, and spin-1 and spin-2 resonances are included coherently through an isobar model. The S-wave component is found to be dominant, followed by the ρ(770)0π+ and f2(1270)π+ components. A small contribution from the ω(782) → π−π+ decay is seen for the first time in the D+→ π−π+π+ decay.

Three-body fragmentation dynamics of BrCNq+ (q=3–6) induced by 1-keV electron impact

The three-body fragmentation dynamics of $\mathrm{BrC}{\mathrm{N}}^{q+} (q=3--6)$ produced by 1-keV electron impact has been investigated using the ion momentum imaging technique. Up to 11 three-body Coulomb explosion channels were identified and analyzed. The corresponding kinetic energy release (KER) distributions were obtained and compared with the predictions of the Coulomb explosion model. By means of the Dalitz plot, Newton diagram, and native frame method, we have studied the concerted and sequential fragmentation mechanisms for channels leading to ${\mathrm{Br}}^{l+}+{\mathrm{C}}^{+}+{\mathrm{N}}^{+} (l=1--3)$. The KER for the intermediate dications $\mathrm{Br}{\mathrm{C}}^{2+}$ and $\mathrm{C}{\mathrm{N}}^{2+}$ from the sequential mechanism were determined and the electronic states of the intermediate molecular ion $\mathrm{C}{\mathrm{N}}^{2+}$ were discussed. For the channels leading to higher charge states of the carbon and nitrogen ions, only the concerted fragmentation mechanism was observed.

Three-body unitary coupled-channel analysis on η(1405/1475)

The recent BESIII data on $J/\psi\to\gamma(K_SK_S\pi^0)$, which is significantly more precise than earlier $\eta(1405/1475)$-related data, enables quantitative discussions on $\eta(1405/1475)$ at the previously unreachable level. We conduct a three-body unitary coupled-channel analysis of experimental Monte-Carlo outputs for radiative $J/\psi$ decays via $\eta(1405/1475)$: $K_SK_S\pi^0$ Dalitz plot distributions from the BESIII, and branching ratios of $\gamma(\eta\pi^+\pi^-)$ and $\gamma(\gamma\pi^+\pi^-)$ final states relative to that of $\gamma(K\bar{K}\pi)$. Our model systematically considers (multi-)loop diagrams and an associated triangle singularity, which is critical in making excellent predictions on $\eta(1405/1475)\to \pi\pi\pi$ lineshapes and branching ratios. The $\eta(1405/1475)$ pole locations are revealed for the first time. Two poles for $\eta(1405)$ are found on different Riemann sheets of the $K^*\bar{K}$ channel, while one pole for $\eta(1475)$. The $\eta(1405/1475)$ states are described with two bare states dressed by continuum states. The lower bare state would be an excited $\eta^\prime$, while the higher one could be an excited $\eta^{(\prime)}$, hybrid, glueball, or their mixture. This work presents the first-ever pole determination based on a manifestly three-body unitary coupled-channel framework applied to experimental three-body final state distributions (Dalitz plots).

Precision measurement of the matrix elements for η→π+π−π0 and η→π0π0π0 decays

A precision measurement of the matrix elements for $\eta\to\pi^+\pi^-\pi^0$ and $\eta\to\pi^0\pi^0\pi^0$ decays is performed using a sample of $(10087\pm44)\times10^6$ $J/\psi$ decays collected with the BESIII detector. The decay $J/\psi \to \gamma \eta$ is used to select clean samples of 631,686 $\eta\to\pi^+\pi^-\pi^0$ decays and 272,322 $\eta\to\pi^0\pi^0\pi^0$ decays. The matrix elements for both channels are in reasonable agreement with previous measurements. The non-zero $gX^2Y$ term for the decay mode $\eta\to\pi^+\pi^-\pi^0$ is confirmed, as reported by the KLOE Collaboration, while the other higher-order terms are found to be insignificant. Dalitz plot asymmetries in the $\eta\to\pi^+\pi^-\pi^0$ decay are also explored and are found to be consistent with charge conjugation invariance. In addition, a cusp effect is investigated in the $\eta\to\pi^0\pi^0\pi^0$ decay, and no obvious structure around the $\pi^+\pi^-$ mass threshold is observed.

New reaction approach to reflect exotic structure of hadronic molecular state

With the accumulation of experimental data, more and more exotic hadrons are observed. Among the interpretations of these exotic hadrons, molecular state and compact multiquark are two of the most popular pictures. However, it is still difficult to determine the structure of an exotic hadron. In this work, we propose a possible way to detect the internal structure of an exotic state. When a molecular state composed of two consistent hadrons is attacked by another particle, one of the constituents should be kicked out while another quasifree constituent stays almost unaffected. It is different from a compact multiquark which has no obvious subcluster. In this work, taking the $X(3872)$ as an example, we perform a Dalitz plot analysis of such reaction to find the effect of the different internal structures. Under the assumption of the $X(3872)$ as a molecular state or a compact tetraquark state, with the help of the effective Lagrangians, the Dalitz plot and the invariant mass spectrum are estimated with different total invariant mass of three final particles, and the effect of different binding energies is also discussed. Obvious event concentration can be observed as strips in the Dalitz plot and sharp peaks in the invariant mass spectrum for the $X(3872)$ with a small binding energy under the molecular state picture, while such concentration cannot be observed under the compact tetraquark picture. Such phenomenon can be applied to identify the internal structure of a new hadron state.

Fragmentation Dynamics of CO2q+ (q = 2, 3) in Collisions with 1 MeV Proton

The fragmentation dynamics of the CO2q+ (q = 2, 3) molecular ions formed under the impact of 1 MeV protons is studied using a recoil ion momentum spectrometer equipped with a multi-hit time- and position-sensitive detector. Both two-body and three-body fragmentation channels arising from the doubly and triply ionized molecular ions of CO2 are identified and analyzed. Kinetic energy release (KER) distributions have been obtained for various channels. With the help of Dalitz plots and Newton diagrams concerted and sequential processes have been assigned to observed fragmentation channels. In addition, angular correlations are used to determine the molecular geometry of the precursor molecular ion. It is found that the symmetric breakup into C+ + O+ + O+ involves asymmetric stretching of the molecular bonds in CO23+ prior to dissociation via concerted decay implying the fact that collisions with 1 MeV proton induces an asynchronous decay in CO2.

Fragmentation dynamics of tetrachloromethane molecule induced by highly charged Ar7+-ion impact.

The ion impact multiple ionization and subsequent dissociation of CCl4 is studied using a beam of Ar7+ ion having the energy of about 1MeV in a linear time- of-flight mass spectrometer, coupled with a position-sensitive detector. The complete, as well as incomplete Coulomb explosion pathways, for CCl4 2+ and CCl4 3+ ions are identified and studied. The kinetic energy release distributions of channels, kinetic energies, and momentum distributions of fragmented ions, as well as neutrals, are also calculated. Possible modes of fragmentation pathways, i.e., concerted and/or sequential, for all the identified channels are studied using Newton diagrams, Dalitz plots, and kinetic energy distributions. The dynamical information and fragmentation pathways were analyzed with the Dalitz plot and Newton diagram for the three-body dissociation channel. The nature of the fragmentation process is further investigated with simulated Dalitz plots and Newton diagrams using the simple classical mechanical model.

Fragmentation dynamics of electron-impact double ionization of helium

We study the double ionization dynamics of a helium atom impacted by electrons with full-dimensional classical trajectory Monte Carlo simulation. The excess energy is chosen to cover a wide range of values from 5 eV to 1 keV for comparative study. At the lowest excess energy, i.e., close to the double-ionization threshold, it is found that the projectile momentum is totally transferred to the recoil-ion while the residual energy is randomly partitioned among the three outgoing electrons, which are then most probably emitted with an equilateral triangle configuration. Our results agree well with experiments as compared with early quantum-mechanical calculation as well as classical simulation based on a two-dimensional Bohr’s model. Furthermore, by mapping the final momentum vectors event by event into a Dalitz plot, we unambiguously demonstrate that the ergodicity has been reached and thus confirm a long-term scenario conceived by Wannier. The time scale for such few-body thermalization, from the initial nonequilibrium state to the final microcanonical distribution, is only about 100 attoseconds. Finally, we predict that, with the increase of the excess energy, the dominant emission configuration undergoes a transition from equilateral triangle to T-shape and finally to a co-linear mode. The associated signatures of such configuration transition in the electron-ion joint momentum spectrum and triple-electron angular distribution are also demonstrated.

Measurement of the mass and width of the Λc(2625)+ charmed baryon and the branching ratios of Λc(2625)+→Σc0π+ and Λc(2625)+→Σc++π−

Using the entire data sample of 980 fb−1 collected at or near the ϒ(4S) resonance with the Belle detector operating at the KEKB asymmetric-energy e+e− collider, we report the measurement of the mass, width, and the branching ratios of the Λc(2625)+ charmed baryon. The mass difference between Λc(2625)+ and Λc+ is measured to be M(Λc(2625)+)−M(Λc+)=341.518±0.006±0.049 MeV/c2. The upper limit on the width is measured to be Γ(Λc(2625)+)<0.52 MeV/c2 at 90% confidence level. Based on a full Dalitz plot fit, branching ratios with respect to the mode Λc(2625)+→Λc+π+π− are measured to be B(Λc(2625)+→Σc0π+)B(Λc(2625)+→Λc+π+π−)=(5.19±0.23±0.40)% and B(Λc(2625)+→Σc++π−)B(Λc(2625)+→Λc+π+π−)=(5.13±0.26±0.32)%, where the first and second uncertainties are statistical and systematic, respectively. These measurements can be used to further constrain the parameters of the underlying theoretical models.Received 13 December 2022Accepted 20 January 2023DOI:https://doi.org/10.1103/PhysRevD.107.032008Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.Published by the American Physical SocietyPhysics Subject Headings (PhySH)Physical SystemsCharmed baryonsPropertiesParticle propertiesTechniquesParticle decaysParticles & Fields

Fragmentation of SO2 q+ (q = 2-4) induced by 1keV electron collision.

We report an investigation on the fragmentation dynamics of SO2 q+ (q = 2-4) induced by 1keV electron collision utilizing an ion momentum imaging spectrometer. Six complete Coulomb explosion channels were observed using the time-of-flight correlation map. The kinetic energy release distributions for these channels were obtained and compared with those available in the literature. The fragmentation mechanisms of the three-body dissociation channels were analyzed by the Dalitz plots and Newton diagrams. Both concerted breakup and sequential fragmentation pathways were identified in the channel SO2 3+ → O+ + O+ + S+, whereas only the concerted breakup mechanism was confirmed for the channels SO2 4+ → O+ + O+ + S2+ and SO2 4+ → O2+ + O+ + S+. Using the Coulomb explosion model, we determined the molecular geometry from the concerted fragmentation channels, and the obtained bond lengths and angles from the higher kinetic energy release peaks are close to that of the neutral SO2 obtained by high-level quantum chemical calculation. The present results indicate that the electron impact experiment is a potential tool for the Coulomb explosion imaging of small molecules.