Dalitz Plot Research Articles

Evidence for an eta _c(1S) pi ^- resonance in B^0 rightarrow eta _c(1S) K^+pi ^- decays

A Dalitz plot analysis of {{B} ^0} !rightarrow eta _c(1S) {{K} ^+} {{pi } ^-} decays is performed using data samples of pp collisions collected with the text{ LHCb } detector at centre-of-mass energies of {sqrt{s}} =7,~8 and 13{,mathrm {Te}mathrm {V}} , corresponding to a total integrated luminosity of 4.7 ,text{ fb }^{-1} . A satisfactory description of the data is obtained when including a contribution representing an exotic eta _c(1S) pi ^- resonant state. The significance of this exotic resonance is more than three standard deviations, while its mass and width are 4096 pm 20~^{+18}_{-22} ,mathrm {Me}mathrm {V} and 152 pm 58~^{+60}_{-35} ,mathrm {Me}mathrm {V} , respectively. The spin-parity assignments J^P=0^+ and J^{P}=1^- are both consistent with the data. In addition, the first measurement of the {{B} ^0} !rightarrow eta _c(1S) {{K} ^+} {{pi } ^-} branching fraction is performed and gives B(B0→ηc(1S)K+π-)=(5.73±0.24±0.13±0.66)×10-4,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\begin{aligned} \\displaystyle \\mathcal {B}({{B} ^0} \\!\\rightarrow \\eta _c(1S) {{K} ^+} {{\\pi } ^-} ) = (5.73 \\pm 0.24 \\pm 0.13 \\pm 0.66) \\times 10^{-4}, \\end{aligned}$$\\end{document}where the first uncertainty is statistical, the second systematic, and the third is due to limited knowledge of external branching fractions.

Fragmentation dynamics of CS2 in collisions with 1.0 keV electrons.

The dissociation dynamics of CS2 molecules in collisions with 1.0 keV electrons is studied. We observe a series of two- and three-body fragmentation channels which are identified from the correlation map between fragment ions. For all of the channels, the kinetic energy release (KER) distributions are obtained. The Dalitz plot and Newton diagram are adopted to analyze the fragmentation dynamics of the three-body dissociation channels. For and , both the concerted and sequential fragmentation mechanisms are observed where the concerted mechanism dominates. For , only the concerted mechanism is observed. Two types of Coulomb explosion models considering the molecular vibration are adopted to simulate the experimental KER distributions of the three-body channels. While obvious deviations are observed considering each ion during the whole dissociation process with an integer charge, good agreement can be achieved within deviation less than 5% if the charge state of the ions are adopted from ab initio calculations.

Dispersive analysis of eta rightarrow 3 pi

The dispersive analysis of the decay eta rightarrow 3pi is reviewed and thoroughly updated with the aim of determining the quark mass ratio Q^2=(m_s^2-m_{ud}^2)/(m_d^2-m_u^2). With the number of subtractions we are using, the effects generated by the final state interaction are dominated by low energy pi pi scattering. Since the corresponding phase shifts are now accurately known, causality and unitarity determine the decay amplitude within small uncertainties – except for the values of the subtraction constants. Our determination of these constants relies on the Dalitz plot distribution of the charged channel, which is now measured with good accuracy. The theoretical constraints that follow from the fact that the particles involved in the transition represent Nambu–Goldstone bosons of a hidden approximate symmetry play an equally important role. The ensuing predictions for the Dalitz plot distribution of the neutral channel and for the branching ratio varGamma _{eta rightarrow 3pi ^0}/ varGamma _{eta rightarrow pi ^+pi ^-pi ^0} are in very good agreement with experiment. Relying on a known low-energy theorem that relates the meson masses to the masses of the three lightest quarks, our analysis leads to Q=22.1(7), where the error covers all of the uncertainties encountered in the course of the calculation: experimental uncertainties in decay rates and Dalitz plot distributions, noise in the input used for the phase shifts, as well as theoretical uncertainties in the constraints imposed by chiral symmetry and in the evaluation of isospin breaking effects. Our result indicates that the current algebra formulae for the meson masses only receive small corrections from higher orders of the chiral expansion, but not all of the recent lattice results are consistent with this conclusion.

Charm rescattering contribution in rare [formula omitted] decay

Following the experimental results from LHCb on the rare decay Bc+→K−K+π+, we investigate the possibility where this process is dominated by a double charm rescattering. The Bc decay to double charm channels have a weak topology that is favored in comparison with the direct production of K−K+π+ in the final state, suppressed by quark annihilation. The decay amplitude for Bc+→K−K+π+ with Bc decaying first to double charm channels is described by charm hadronic triangle loops, which reach the final state of interest after DD¯→KK¯ or D+Ds−→π+K− transitions. We show that these processes give rise to non-resonant amplitudes with a clear signature in the Dalitz plot. In a near future, the new data from LHCb run II will be able to confirme if the main hypotheses of this work is correct and the dominant mechanism to produce K+K+π− from the decay of Bc+ is through charm rescattering.

Eta ^{prime }rightarrow eta pi pi decays in unitarized resonance chiral theory

We study the hadronic eta ^{prime }rightarrow eta pi pi decays within the framework of U(3)_{L}otimes U(3)_{R} Chiral Perturbation Theory including resonance states and the complete one-loop corrections. The amplitude is projected in partial waves and unitarized by means of the N / D method resumming both the important S- and D-wave pi pi and the subleading S-wave pi eta final-state interactions. The participating scalar multiplet mass and coupling strengths are determined from fits to the Dalitz plot experimental data recently released by the A2 collaboration. As a byproduct of our analysis, the associated Dalitz-plot slope parameters are found to be a=-,0.072(7)_{mathrm{stat}}(8)_{mathrm{syst}},,b=-,0.052(1)_{mathrm{stat}}(2)_{mathrm{syst}}, d=-,0.051(8)_{mathrm{stat}}(6)_{mathrm{syst}}, which lie in the ballpark of the current experimental and theoretical determinations.

Recent results on CP violation at B factories

We review recent results of the Beauty Factories BaBar and Belle on CP violation in the quark sector and constraints on the CKM unitarity triangle. We first present the recent measurement, using BaBar and Belle data, of cos(2β) = cos(2ϕ1) in B0 → D(∗)h0 with $D \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{-}$ decays, using a combined time-dependent Dalitz plot analysis. The BaBar Dalitz plot analysis of the $B^{+} \rightarrow {K^{0}_{S}} \pi ^{+} \pi ^{0}$ decay is also presented, and shows an evidence for direct CP violation in B+ → K∗(892)π0. A recently published BaBar measurement of the |V ub| CKM matrix element allows to contrain one side of the unitarity triangle. These analyses use the data sets of the BaBar and Belle experiments containing 471 × 106 and 772 × 106 $B\overline {B}$ pairs collected at the Υ(4S) resonance at the asymmetric-energy B factories PEP-II at SLAC and KEKB at KEK, respectively.

Measurement of the CKM angle \u03b3 using B\xb1 \u2192 DK\xb1 with D\u2009\u2192\u2009KS0\u03c0+\u03c0\u2212,\u2002KS0K+K\u2212 decays

A binned Dalitz plot analysis of B± → DK± decays, with D → KS0π+π− and D → KS0K+K−, is used to perform a measurement of the CP-violating observables x± and y±, which are sensitive to the Cabibbo-Kobayashi-Maskawa angle γ. The analysis is performed without assuming any D decay model, through the use of information on the strong-phase variation over the Dalitz plot from the CLEO collaboration. Using a sample of proton-proton collision data collected with the LHCb experiment in 2015 and 2016, and corresponding to an integrated luminosity of 2.0 fb−1, the values of the CP violation parameters are found to be x− = (9.0 ± 1.7 ± 0.7 ± 0.4) × 10−2, y− = (2.1 ± 2.2 ± 0.5 ± 1.1) × 10−2, x+ = (−7.7 ± 1.9 ± 0.7 ± 0.4) × 10−2, and y+ = (−1.0 ± 1.9 ± 0.4 ± 0.9) × 10−2. The first uncertainty is statistical, the second is systematic, and the third is due to the uncertainty (on the strong-phase measurements. These values are used to obtain γ = (87− 12+ 11)∘, rB = 0.086− 0.014+ 0.013, and δB = (101±11)°, where rB is the ratio between the suppressed and favoured B-decay amplitudes and δB is the corresponding strong-interaction phase difference. This measurement is combined with the result obtained using 2011 and 2012 data collected with the LHCb experiment, to give γ = (80− 9+ 10)∘, rB = 0.080 ± 0.011, and δB = (110 ± 10)°.

Amplitude Analysis of the Decay B[over ¯]^{0}→K_{S}^{0}π^{+}π^{-} and First Observation of the CP Asymmetry in B[over ¯]^{0}→K^{*}(892)^{-}π^{+}.

The time-integrated untagged Dalitz plot of the three-body hadronic charmless decay B[over ¯]^{0}→K_{S}^{0}π^{+}π^{-} is studied using a pp collision data sample recorded with the LHCb detector, corresponding to an integrated luminosity of 3.0 fb^{-1}. The decay amplitude is described with an isobar model. Relative contributions of the isobar amplitudes to the B[over ¯]^{0}→K_{S}^{0}π^{+}π^{-} decay branching fraction and CP asymmetries of the flavor-specific amplitudes are measured. The CP asymmetry between the conjugate B[over ¯]^{0}→K^{*}(892)^{-}π^{+} and B^{0}→K^{*}(892)^{+}π^{-} decay rates is determined to be -0.308±0.062.

Dynamics of C2H23+→H++H++C2+ investigated by 50-keV/u Ne8+ impact

Breakup dynamics of ${\mathrm{C}}_{2}\mathrm{H}{{}_{2}}^{3+}$ $\ensuremath{\rightarrow}$ ${\mathrm{H}}^{+}+{\mathrm{H}}^{+}+\mathrm{C}{{}_{2}}^{+}$ induced by 50-keV/u ${\mathrm{Ne}}^{8+}$ ion impact is investigated employing a reaction microscope. All three ionic fragments in the final state are detected in coincidence, and their momentum vectors as well as the kinetic energies are determined. The kinetic-energy correlation spectrum of the two protons displays very rich structures. Utilizing the Newton diagrams and the Dalitz plots, different dissociation mechanisms corresponding to these structures are identified. It was found that, besides the concerted and sequential breakup, fragmentation mechanisms associated with different vibration modes including molecular bending and asymmetric stretching also make significant contributions. We analyzed the correlation between different fragmentation mechanisms and the kinetic-energy release (KER) and found that the sequential process occurs with higher KER while, in contrast, the concerted process mainly contributes to the lower KER. This behavior is entirely opposite to the breakup of the ${\mathrm{CO}}_{2}$ molecule.

Radiative corrections to the η(′) Dalitz decays

We provide the complete set of radiative corrections to the Dalitz decays $\eta^{(\prime)}\to \ell^+\ell^-\gamma$ beyond the soft-photon approximation, i.e. over the whole range of the Dalitz plot and with no restrictions on the energy of a radiative photon. The corrections inevitably depend on the $\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ transition form factors. For the singly virtual transition form factor appearing e.g. in the bremsstrahlung correction, recent dispersive calculations are used. For the one-photon-irreducible contribution at the one-loop level (for the doubly virtual form factor), we use a vector-meson-dominance-inspired model while taking into account the $\eta$-$\eta^\prime$ mixing.

Laura[formula omitted]: A Dalitz plot fitter

The Dalitz plot analysis technique has become an increasingly important method in heavy flavour physics. The Laura++ fitter has been developed as a flexible tool that can be used for Dalitz plot analyses in different experimental environments. Explicitly designed for three-body decays of heavy-flavoured mesons to spinless final state particles, it is optimised in order to describe all possible resonant or nonresonant contributions, and to accommodate possible CP violation effects. Program summaryProgram title: Laura++Program Files doi:http://dx.doi.org/10.17632/jn266r57nk.1Licensing provisions: Apache License, Version 2.0Programming language:C++Nature of problem: Dalitz-plot analysis of particle decays is an important and increasingly utilised technique in particle physics, in particular in heavy flavour physics. While various software tools have been used for Dalitz plot analyses, these are usually not well optimised and are neither scalable for use with larger samples nor flexible enough to be easily adapted for other analyses.Solution method:Laura++ is a dedicated package for performing Dalitz-plot analysis that is flexible enough both to be used in a range of experimental environments and to describe many possible different decays and types of analyses. It allows analysts to create amplitude models to describe the decay of interest and to use those models either to generate pseudoexperiments or to fit them to data.

Consistent Dalitz plot analysis of Cabibbo-favored [formula omitted] decays

We resume the study of the Cabibbo-favored charmed-meson decays D+→K¯ππ+ in a dispersive framework that satisfies unitarity, analyticity, and crossing symmetry by construction. The formalism explicitly describes the strong final-state interactions between all three decay products and relies on pion–pion and pion–kaon phase shift input. For the first time, we show that the D+→KSπ0π+ Dalitz plot obtained by the BESIII collaboration as well as the D+→K−π+π+ Dalitz plot data by CLEO and FOCUS can be described consistently, exploiting the isospin relation between the two coupled decay channels that provides better constraints on the subtraction constants.

Measurement of e+e−→π0π0ψ(3686) at s from 4.009 to 4.600 GeV and observation of a neutral charmoniumlike structure

Using $e^{+}e^{-}$ collision data collected with the BESIII detector at the BEPCII collider corresponding to an integrated luminosity of 5.2 $fb^{-1}$ at center-of-mass energies ($\sqrt{s}$) from 4.009 to 4.600 GeV, the process $e^{+}e^{-} \to \pi^{0} \pi^{0}\psi(3686)$ is studied for the first time. The corresponding Born cross sections are measured and found to be half of those of the reaction $e^{+}e^{-} \to \pi^{+}\pi^{-}\psi(3686)$. This is consistent with the expectation from isospin symmetry. Furthermore, the Dalitz plots for $\pi^{0}\pi^{0}\psi(3686)$ are accordant with those of $\pi^{+}\pi^{-}\psi(3686)$ at all energy points, and a neutral analogue to the structure in $\pi^\pm \psi(3686)$ around 4040 MeV/$c^{2}$ first observed at $\sqrt{s}$=4.416 GeV is observed in the isospin neutral mode at the same energy.

Optimizing sensitivity to γ with B0→DK+π− , D→KS0π+π− double Dalitz plot analysis

Two of the most powerful methods currently used to determine the angle $\gamma$ of the CKM Unitarity Triangle exploit $B^+ \to DK^+$, $D \to K_{\rm S}^0\pi^+\pi^-$ decays and $B^0 \to DK^+\pi^-$, $D \to K^+K^-$, $\pi^+\pi^-$ decays. It is possible to combine the strengths of both approaches in a "double Dalitz plot" analysis of $B^0 \to DK^+\pi^-$, $D \to K_{\rm S}^0\pi^+\pi^-$ decays. The potential sensitivity of such an analysis is investigated in the light of recently published experimental information on the $B^0 \to DK^+\pi^-$ decay. The formalism is also expanded, compared to previous discussions in the literature, to allow $B^0 \to DK^+\pi^-$ with any subsequent $D$ decay to be included.

Closing in on the radiative weak chiral couplings

We point out that, given the current experimental status of radiative kaon decays, a subclass of the mathcal{O} (p^4) counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay K^pm rightarrow pi ^pm pi ^0 l^+ l^-, currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the mathcal{{O}}(p^4) weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of K_Srightarrow pi ^+pi ^-gamma ^*, which will be measured by LHCb and will help reduce (together with the related K_L decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the mathcal{{O}}(p^4) weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.

Three-body fragmentation of methane dications produced by slow Ar8+ -ion impact

The three-body fragmentation dynamics of ${{\mathrm{CH}}_{4}}^{2+}$ dications induced by single-electron capture of slow (3-keV/u) $\mathrm{A}{\mathrm{r}}^{8+}$ ions is investigated. The experiment is performed on a newly built, highly charged ion collision platform which consists of an electron cyclotron resonance ion source and a cold target recoil ion momentum spectroscopy (COLTRIMS) setup. Using the COLTRIMS methodology, the complete kinematical information is determined for two three-body breakup channels, ${{\mathrm{CH}}_{4}}^{2+}\ensuremath{\rightarrow}{\mathrm{H}}^{+}+{{\mathrm{CH}}_{2}}^{+}+\mathrm{H}$ and ${{\mathrm{CH}}_{4}}^{2+}\ensuremath{\rightarrow}{{\mathrm{H}}_{2}}^{+}+\mathrm{C}{\mathrm{H}}^{+}+\mathrm{H}$. Then analyzing the complete kinematics with the Dalitz plot, very different fragmentation mechanisms (e.g., sequential and/or concerted pathway) are clearly identified for the two channels. To confirm the existence of some possible fragmentation pathways, we also simulate corresponding Dalitz plots employing a simple classical mechanical model. For the ${\mathrm{H}}^{+}+{{\mathrm{CH}}_{2}}^{+}+\mathrm{H}$ channel, the dependence of the fragmentation pathway on its kinetic energy release is studied, which reflects the different nature of the corresponding states of ${{\mathrm{CH}}_{4}}^{2+}$ dications. Furthermore, the kinetic energy ratio of two ionic fragments is analyzed to infer the three-body fragmentation mechanism of ${{\mathrm{CH}}_{4}}^{2+}$ dications.

Measurement of the matrix elements for the decays η′→ηπ+π− and η′→ηπ0π0

Based on a sample of $1.31\times10^9$ $J/\psi$ events collected with the BESIII detector, the matrix elements for the decays $\eta^{\prime}\to\eta\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ are determined using 351,016 $\eta^{\prime}\to(\eta\to\gamma\gamma)\pi^+\pi^-$ and 56,249 $\eta^{\prime}\to(\eta\to\gamma\gamma)\pi^0\pi^0$ events with background levels less than 1\%. Two commonly used representations are used to describe the Dalitz plot density. We find that an assumption of a linear amplitude does not describe the data well. A small deviation of the obtained matrix elements between $\eta^{\prime}\to\eta\pi^{+}\pi^{-}$ and $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ is probably caused by the mass difference between charged and neutral pions or radiative corrections. No cusp structure in $\eta^{\prime}\to\eta \pi^{0}\pi^{0}$ is observed.

Charm Meson Physics at BESIII

Based on 2.93 fb[Formula: see text] data taken at the center-of-mass energy of [Formula: see text] GeV with the BESIII detector at the BEPCII collider, we report the precise measurements of the decay constant [Formula: see text], the form factors of [Formula: see text] semileptonic decays [Formula: see text] and [Formula: see text], the Dalitz plot analysis of [Formula: see text], the strong phase measurement in [Formula: see text] and the [Formula: see text] mixing parameter [Formula: see text].

Three-body fragmentation dynamics of OCS3+ induced by intermediate energy Ne4+ ion impact

The fragmentation experiment of OCS3+ induced by 56 keV/u Ne4+ ions is performed using reaction microscope, and the corresponding dissociation dynamics is investigated. By detecting the three fragment ions in coincidence, the three-dimensional (3D) momenta of all ions and the corresponding kinetic energy release (KER) distributions are reconstructed. It is found that a peak maximum of the KER distribution is locates at about 25 eV, and a shoulder structure appears around 18 eV. This result is consistent with previous heavy ion experimental results with different perturbation strengths. Taking into account that the KER distribution is related to the initial state population of the OCS3+ parent ions, it can be concluded that the perturbation strength is not a decisive parameter leading to the initial state population of OCS3+ ions. We also reconstruct the Newton diagram and Dalitz plot for the three-body fragmentation of OCS3+ ion, from which the sequential dissociation is distinguished from nonsequential dissociation clearly. By analyzing the kinetic energy of ions from each fragmentation process, we find that the KER peak at 25 eV corresponds to nonsequential dissociation process, but the shoulder at 18 eV arises from both sequential and nonsequential dissociation processes. This phenomenon suggests that the parent OCS3+ ions in ground state and low excitation states tend to fragment through sequential dissociation, while those in high excitation states tend to fragment through nosequential dissociation. Furthermore, we reconstruct the KER distributions in the second fragmentation step of sequential dissociation, whose peak maximum is at 6.2 eV, corresponding to X3, 1+ and 1 metastable states of CO2+ ion. A similar KER distribution is obtained for the second fragmentation step of the OCS4+ ion. By comparing our experimental results with previous ones, we conclude that the origin of sequential dissociation process is the existence of metastable state, and the reconstructed KER in the second step reflects the initial state information about the metastable state.

Light meson decays at BESIII

A sample of 1.3 × 109J/ψ events collected with BESIII detector at the BEPCII provide us a sample of η and η′ for decay studies, this paper reviews the latest η and η′ related results from BESIII, including dalitz plot analysis of η→π+π−π0 and η/η′→π0π0π0, amplitude analysis of η′→3π, double radiative decay of η′→γγπ0 and the weak decay η′→Kπ.