Time-like Form Factors Research Articles

Branching ratios and CP asymmetries of the quasi-two-body decays Bc→K0∗(1430,1950)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow \\ K^{*}_0(1430,1950) D_{(s)} \\rightarrow K \\pi D_{(s)} $$\\end{document} in the PQCD approach

In this paper, we investigate the quasi-two-body decays Bc→K0∗(1430,1950)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1430,1950) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document} within the perturbative QCD (PQCD) framework. The S-wave two-meson distribution amplitudes (DAs) are introduced to describe the final state interactions of the Kπ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K\\pi $$\\end{document} pair, which involve the time-like form factors and the Gegenbauer polynomials. In the calculations, we adopt two kinds of parameterization schemes to describe the time-like form factors: one is the relativistic Breit–Wigner (RBW) formula, which is usually more suitable for the narrow resonances, and the other is the LASS line shape proposed by the LASS Collaboration, which includes both the resonant and nonresonant components. We find that the branching ratios and the direct CP violations for the decays Bc→K0∗(1430)D(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1430) D_{(s)}$$\\end{document} obtained from those of the quasi-two-body decays Bc→K0∗(1430)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1430) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document} under the narrow width approximation (NWA) can be consistent well with the previous PQCD results calculated in the two-body framework by assuming that K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*_0(1430)$$\\end{document} is the lowest lying q¯s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\bar{q} s$$\\end{document} state, which is the so-called scenario II (SII). We conclude that the LASS parameterization is more suitable to describe the K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_0^{*}(1430)$$\\end{document} than the RBW formula, and the nonresonant components play an important role in the branching ratios of the decays Bc→K0∗(1430)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1430) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document}. In view of the large difference between the decay width measurements for the K0∗(1950)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K_0^{*}(1950)$$\\end{document} given by BaBar and LASS collaborations, we calculate the branching ratios and the CP violations for the quasi-two-body decays Bc→K0∗(1950)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1950) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document} by using two values, ΓK0∗(1950)=0.100±0.04\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _{K^*_0(1950)}=0.100\\pm 0.04$$\\end{document} GeV and ΓK0∗(1950)=0.201±0.034\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _{K^*_0(1950)}=0.201\\pm 0.034$$\\end{document} GeV, besides the two kinds of parameterizations for the resonance K0∗(1950)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*_0(1950)$$\\end{document}. We find that the branching ratios and the direct CP violations for the decays Bc→K0∗(1950)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1950) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document} have not as large difference between the two parameterizations as the case of decays involving the K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*_0(1430)$$\\end{document}, especially for the results with ΓK0∗(1950)=0.201±0.034\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Gamma _{K^*_0(1950)}=0.201\\pm 0.034$$\\end{document} GeV. The effect of the nonresonant component in the K0∗(1950)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*_0(1950)$$\\end{document} may be not so serious as that in the K0∗(1430)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$K^*_0(1430)$$\\end{document}. The quasi-two-body decays Bc+→K0∗+(1430)D0→K0π+D0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+_c \\rightarrow K^{*+}_0(1430) D^{0} \\rightarrow K^0 \\pi ^+ D^{0}$$\\end{document} and Bc+→K0∗0(1430)D+→K+π-D+\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B^+_c \\rightarrow K^{*0}_0(1430) D^{+} \\rightarrow K^+ \\pi ^- D^{+}$$\\end{document} have large branching ratios, which can reach to the order of 10-4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$10^{-4}$$\\end{document} and are most likely to be observed in the future LHCb experiments. Furthermore, the branching ratios of the quasi-two-body decays Bc→K0∗(1950)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1950) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document} are about one order smaller than those of the corresponding decays Bc→K0∗(1430)D(s)→KπD(s)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$B_c \\rightarrow K_0^{*}(1430) D_{(s)} \\rightarrow K \\pi D_{(s)}$$\\end{document}.

Measuring the Neutron Timelike Electromagnetic Form Factor with the SND Detector

Results are presented from measuring the e+e− → n¯n cross section and effective neutron timelike form factor. Data are collected in 2020–2021 at the VEPP-2000 e+e− collider in the 1891 to 2007 MeV center-of-mass range of energies. The general purpose nonmagnetic SND detector is used to detect neutron–antineutron events. The time-of-flight approach is used to select n¯n events. The measuredcross section is 0.4–0.6 nbn. The neutron form factor in the investigated range of energies varies from 0.3 to 0.2.

Isospin violating decays of vector charmonia

We study the isospin violating decays of vector charmonia to ΛΣ¯0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Lambda \\overline{\\Sigma }^0$$\\end{document} and its charge conjugate. They are dominated by the single photon annihilation and can be evaluated reliably with timelike form factors. We utilize the quark-pair creation model, which is valid for the OZI suppressed decays, to evaluate the form factors. We obtain the branching fractions of B(J/ψ→ΛΣ¯0+c.c.)=(2.4±0.4)×10-5\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(J/\\psi \\rightarrow \\Lambda \\overline{\\Sigma }^0+c.c.)=(2.4\\pm 0.4)\ imes 10^{-5}$$\\end{document} and B(ψ(2S)→ΛΣ¯0+c.c.)=(3.0±0.5)×10-6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{B}(\\psi (2\\,S)\\rightarrow \\Lambda \\overline{\\Sigma }^0+c.c.)=(3.0\\pm 0.5)\ imes 10^{-6}$$\\end{document}, which are compatible with the measurements by the BESIII collaborations, respectively. The decay asymmetries are found to be αJ/ψ=0.314\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{J/\\psi }=0.314$$\\end{document} and αψ(2S)=0.461\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha _{\\psi (2S)}=0.461$$\\end{document}, which can be examined at BESIII in the foreseeable future.

Electromagnetic time-like form factors

We present the calculation of charged pion and kaon electromagnetic form factors in the time-like regime using Schwinger-Dyson equations and the Poincare covariant Bethe-Salpeter equations within an SU(2) isospin symmetric limit. To accurately represent the behavior of a time-like photon, we have incorporated non-valence contributions into the system of equations, enabling the decays ρ → ππ and φ → KK. The inclusion of these decay mechanisms is essential for capturing the expected behavior of the electromagnetic pion and kaon form factors. Our results for the form factors reasonably reproduce the experimental data for a time-like photon.

Study pion distribution amplitudes from the electromagnetic form factor by data-driven dispersion relation

We study the pion electromagnetic form factor in the modulus squared dispersion relation, and do the model independent extraction of the chiral mass embedded in the sub-leading twist light-cone distribution amplitude. The motivation of this work is the recent measurement of timelike form factor in the resonant regions, which makes up the piece lacking solid QCD-based calculation. With the perturbative QCD calculation up to next-to-leading-order of strong coupling and twist four level of meson distribution amplitudes, we obtain the chiral mass of pion meson as m_0^pi (1 , textrm{GeV}) = 1.31^{+0.27}_{-0.30} , textrm{GeV}. Due to the chiral enhancement contribution from the sub-leading twist distribution amplitudes in the perturbative QCD calculation, we can not extract the lowest Gegenbauer moments of pion from the study of electromagnetic form factor. This problem could be settled down with the foresee Belle-II and BESIII measurement of the transition form factor especially in the large momentum transfers regions.

Toy model to understand the oscillatory behavior in timelike nucleon form factors

To understand the oscillatory behavior exhibited in the timelike electromagnetic form factors of nucleons, we propose a toy model based on the Jost function of the $N\bar N$ pair into the timelike form factors with the help of the distorted-wave Born approximation. By constructing a simple square-well potential reflecting the final-state interaction of $N\bar N$, we naturally represent the damped oscillatory phenomenon in the timelike electromagnetic form factors of nucleons. Especially, our study reveals that the ``period" of the oscillation is approximately determined by the Yukawa interaction range $1/m_\pi$. Other possible potentials are also discussed. The threshold enhancements of the cross sections for $e^+e^-\to n\bar n$, $\Lambda\bar\Lambda$, and $\Lambda_c\bar\Lambda_c$ can also be understand within this scenario.

Quasi-two-body decays in perturbative QCD* *Supported by the National Natural Science Foundation of China (11347030), the Program of Science and Technology Innovation Talents in Universities of Henan Province, China (14HASTIT037), and the Natural Science Foundation of Henan Province, China (232300420116)

In this work, we investigate the quasi-two-body decays with using the perturbative QCD (PQCD) approach. The description of final state interactions of the pair is achieved through the two-meson distribution amplitudes (DAs), which are normalized to the time-like form factor. The PQCD predictions on the branching ratios of the quasi-two-body decays show an obvious hierarchy: and . From the invariant mass -dependence of the decay spectrum for each channel, one can find that the branching fraction is concentrated in a narrow region around the pole mass. Thus, one can obtain the branching ratios for the corresponding two-body decays under the narrow-width approximation. We find that the branching ratios of the decays are consistent with the previous PQCD calculations within errors. These predictions will be tested in future experiments.

Experimental study of the e^+e^-rightarrow n{bar{n}} process at the VEPP-2000 e^+e^- collider with the SND detector

The process e^+e^-rightarrow n{bar{n}} is studied in the experiment at the VEPP-2000 e^+e^- collider with the SND detector. The technique of the time measurements in the multichannel NaI(Tl) electromagnetic calorimeter is used to select n{bar{n}} events. The value of the measured cross section in the center-of-mass energy range from 1.894 to 2 GeV varies from 0.5 to 0.35 nb. The effective neutron timelike form factor is derived from the measured cross section and compared with the proton form factor. The ratio of the neutron electric and magnetic form factors is obtained from the analysis of the antineutron polar angle distribution and found to be consistent with unity.

Quasi-two-body decays in the perturbative QCD approach* *Supported in part by the National Natural Science Foundation of China under (11347030), the Program of Science and Technology Innovation Talents in Universities of Henan Province (14HASTIT037)

In this study, we investigate quasi-two-body decays in the perturbative QCD approach. Two-meson distribution amplitudes are introduced to describe the final state interactions of the pair, which involve time-like form factors and Gegenbauer polynomials. We calculate the CP averaged branching ratios of the decays. Our results are in agreement with newly updated data measured by Belle II. This suggests that it is more appropriate to analyze these quasi-two-body B decays in the three-body framework than the two-body framework. We also predict direct CP asymmetries for the considered decay modes and find that is small and less than % in magnitude, whereas is larger and can reach a few percent. Our predictions can be tested in future B meson experiments.

Recent results on hyperon pair production and nucleon time-like form factors at BESIII

The BESIII experiment, based on the BEPCII collider at IHEP in Beijing, China, is capable of measuring nucleon form factors with unprecedented precision. We report recent results achieved by the BESIII collaboration concerning the nucleon time-like form factors and the hyperon pair production. Specifically, we outline the results obtained by the study of the process e^+e^- \to p \overline pe+e−→pp¯, using both the scan-energy and initial-state radiation techniques, those of the process e^+e^- \to n \overline ne+e−→nn¯, and the study of the \SigmaΣ polarization regarding the process e^+e^- \to J/\psi \to \Sigma^+\overline \Sigma{}^-e+e−→J/ψ→Σ+Σ¯−.

Comparative analysis of time-like hyperon form factors

Data on hyperon form factors recently obtained from annihilation reactions are compared each other, and to proton and neutron form factors, in terms of two kinematical variables: the transferred momentum square, $q^2$, and the modulus $P$ of the relative momentum between the outgoing baryons. They are critically discussed in terms of possible correlated structures. The present status of the time-like form factor data for baryons is described and suggestions are given on the reactions and the kinematical range where data are desirable in order to clarify the arisen questions.

Timelike transition form factor for CP-odd Higgs boson production

We investigate the production of CP-odd Higgs boson A^0A0 associated with a real \gammaγ in e^+e^-e+e− collisions. Because of the properties of A^0A0 coupling to the other fields, the main contribution comes from the top-quark triangle loop diagrams. We obtain the “timelike” transition form factor which describes the production amplitude of A^0A0 in the e^+e^-e+e− collisions. This timelike transition form factor is related to the spacelike transition form factor relevant for the A^0A0 production in e^-\gammae−γ collisions. It turns out that the possible extra contributions from chargino-sneutrino and neutralino-selectron box diagrams do not give sizable effects.

Contributions of S-, P-, and D-wave resonances to the quasi-two-body decays B^{0}_{s} rightarrow psi (3686,3770)K pi in the perturbative QCD approach

Based on the perturbative quantum chromodynamics (pQCD) approach and the quasi-two-body approximation, we have studied the three-body decays B^{0}_{s}rightarrow psi (3686,3770)K pi , which include the contributions of the intermediate resonances overline{K }^{*}_{0}(1430)^{0}, overline{K }^{*}(892)^{0}, overline{K }^{*}(1410)^{0}, overline{K }^{*}(1680)^{0}, and overline{K }^{*}_{2}(1430)^{0}. The time-like form factors corresponding to the distribution amplitudes of the S-, P-, and D-wave of the kaon–pion pair were adopted in parameterized form, and describe the interactions between K and pi in the resonance region. First, the decays B^{0}_{s}rightarrow psi (2S,1D)K ^{-}pi ^{+} were calculated, followed by the calculation of the branching ratios of the decays B^{0}_{s}rightarrow psi (3686,3770)K ^{-}pi ^{+} using the 2S–1D mixing scheme. In addition, the pQCD predictions for the decays B^{0}_{s}rightarrow psi (2S,1D)K pi and B^{0}_{s}rightarrow psi (3686,3770)K pi were obtained using the narrow-width approximation relation given by the Clebsch–Gordan coefficients. Our work shows that the overline{K }^{*}(892)^{0} resonance is the main contributor to the total decay, and the branching ratio and the longitudinal polarization fraction of the psi (2S)overline{K }^{*}(892)^{0} decay mode agree well with the currently available data within errors. Furthermore, the theoretical predictions of the psi (2S) and psi (3686) decay modes are very close, indicating that they can be regarded as the same meson state. Finally, the pQCD predictions for branching ratios of decays B^{0}_{s}rightarrow psi (3686,3770)K pi are of the order of 10^{-5} and 10^{-6}, respectively, which can be verified using the ongoing LHCb and Belle II experiments.

Electromagnetic Structure of the Neutron from Annihilation Reactions

The investigation of the fundamental properties of the nucleon is one of the most important topics in the modern hadron physics. Its internal structure and dynamics can be studied through the measurement of electromagnetic form factors which represent the simplest structure observables and serve as a test ground for our understanding of the strong interaction. Since the first attempt to measure the time-like form factors of the neutron, only four experiments published results on its structure from annihilation reactions. Due to the lack of statistics and experimental challenges, no individual determination of the form factors of the neutron has been possible so far. Modern developments of electron-positron colliders and the associated detectors allow to measure the effective FF of the neutron with the process e+e−→nn¯ with unprecedented precision at the BESIII experiment, which is based at the BEPCII collider in Beijing, China. In this report, we review the published results of the form factors on the neutron in the time-like regime, describe the experimental setup, and discuss their impact on our understanding of the strong interaction. Future works at BESIII will help to improve the precision of the neutron FFs and, combined with theoretical progress in this field, help to illuminate the properties of the neutron structure.

Time-like Proton Form Factors with Initial State Radiation Technique

Electromagnetic form factors are fundamental quantities describing the internal structure of hadrons. They can be measured with scattering processes in the space-like region and annihilation processes in the time-like region. The two regions are connected by crossing symmetry. The measurements of the proton electromagnetic form factors in the time-like region using the initial state radiation technique are reviewed. Recent experimental studies have shown that initial state radiation processes at high luminosity electron-positron colliders can be effectively used to probe the electromagnetic structure of hadrons. The BABAR experiment at the B-factory PEP-II in Stanford and the BESIII experiment at BEPCII (an electron positron collider in the τ-charm mass region) in Beijing have measured the time-like form factors of the proton using the initial state radiation process e+e−→pp¯γ. The two kinematical regions where the photon is emitted from the initial state at small and large polar angles have been investigated. In the first case, the photon is in the region not covered by the detector acceptance and is not detected. The Born cross section and the proton effective form factor have been measured over a wide and continuous range of the the momentum transfer squared q2 from the threshold up to 42 (GeV/c)2. The ratio of electric and magnetic form factors of the proton has been also determined. In this report, the theoretical aspect and the experimental studies of the initial state radiation process e+e−→pp¯γ are described. The measurements of the Born cross section and the proton form factors obtained in these analyses near the threshold region and in the relatively large q2 region are examined. The experimental results are compared to the predictions from theory and models. Their impact on our understanding of the nucleon structure is discussed.

The electromagnetic form factors of $$\Lambda _c$$ hyperon in the vector meson dominance model

We apply a modified vector meson dominance (VMD) model to analyze the electromagnetic form factors of the $\Lambda_c$ hyperon in the time-like reaction $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$. In the model, we include the contributions from the vector charmed mesons and their excitations $\psi(1S)$, $\psi(2S)$, $\psi(3770)$, $\psi(4040)$, $\psi(4160)$ and $\psi(4415)$. We perform a combined fit to the available data on the Born cross section in reaction $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$ and the ratio of the electromagnetic form factors $|G_E/G_M|$ to obtain the values of the model parameters. Our results show that the VMD model can simultaneously describe the data of electromagnetic form factors from the Belle and BESIII Collaborations, and the behavior of $|G_E/G_M|$ for the BESIII data can be qualitatively reproduced by the VMD model prediction at the threshold region. Moreover, we predict the single and double polarization observables in $e^+e^-\rightarrow \Lambda_c^+ \bar{\Lambda}_c^-$ reactions, which are experimentally accessible in the polarized process. We also obtain the form factors of the $\Lambda_c$ hyperon in the space-like region via analytic continuing the time-like form factors.

New fit of timelike proton electromagnetic formfactors from e+e− colliders

The data on the proton form factors in the time-like region from the BaBar, BESIII and CMD-3 Collaborations are examined to have coherent pieces of information on the proton structure. Oscillations in the annihilation cross section, previously observed, are determined with better precision. The moduli of the individual form factors, determined for the first time, their ratio and the angular asymmetry of the annihilation reaction $e^+e^-\to\bar p p$ are discussed. Fiits of the available data on the cross section, the effective form factor, and the form factor ratio, allow to propose a description of the electric and magnetic time-like form factors from the threshold up to the highest momenta.

Feasibility studies for the measurement of time-like proton electromagnetic form factors from bar{p}p rightarrow mu ^+mu ^- at overline{text {P}}text {ANDA} at FAIR

This paper reports on Monte Carlo simulation results for future measurements of the moduli of time-like proton electromagnetic form factors, |G_{E}| and |G_{M}|, using the bar{p} p rightarrow mu ^{+} mu ^{-} reaction at overline{text {P}}text {ANDA} (FAIR). The electromagnetic form factors are fundamental quantities parameterizing the electric and magnetic structure of hadrons. This work estimates the statistical and total accuracy with which the form factors can be measured at overline{text {P}}text {ANDA}, using an analysis of simulated data within the PandaRoot software framework. The most crucial background channel is bar{p} p rightarrow pi ^{+} pi ^{-}, due to the very similar behavior of muons and pions in the detector. The suppression factors are evaluated for this and all other relevant background channels at different values of antiproton beam momentum. The signal/background separation is based on a multivariate analysis, using the Boosted Decision Trees method. An expected background subtraction is included in this study, based on realistic angular distributions of the background contribution. Systematic uncertainties are considered and the relative total uncertainties of the form factor measurements are presented.

Pion light-cone distribution amplitude from the pion electromagnetic form factor

We suggest to probe the pion light-cone distribution amplitude, applying a dispersion relation for the pion electromagnetic form factor. Instead of the standard dispersion relation, we use the equation between the spacelike form factor $F_\pi(Q^2)$ and the integrated modulus of the timelike form factor. For $F_\pi(Q^2)$, the QCD light-cone sum rule with a dominant twist-2 term is used. Adopting for the pion twist-2 distribution amplitude a certain combination of the first few Gegenbauer polynomials, it is possible to fit their coefficients $a_{2,4,6,...}$ (Gegenbauer moments) from this equation, employing the measured pion timelike form factor. For the exploratory fit we use the data of the BaBar collaboration. The results definitely exclude the asymptotic twist-2 distribution amplitude. Also the model with a single $a_2\neq 0$ is disfavoured by the fit. Considering the models with $a_{n>2}\neq 0$, we find that the fitted values of the second and fourth Gegenbauer moments cover the intervals $a_2 (1 \mbox{GeV}) = (0.22 - 0.33) $, $a_4 (1 \mbox{GeV}) = (0.12 - 0.25) $. The higher moments starting from $a_{8}$ are consistent with zero, albeit with large uncertainties. The spacelike pion form factor obtained in two different ways, from the dispersion relation and from the light-cone sum rule, agrees, within uncertainties, with the measurement by the Jefferson Lab $F_\pi$ collaboration.

P-wave contributions to B(s)→ψKπ decays in perturbative QCD approach * * Supported by the National Natural Science Foundation of China (11947013, 11605060, 11775117, 11547020); Ya Li is also Supported by the Natural Science Foundation of Jiangsu Province (BK20190508) and the Research Start-up Funding of Nanjing Agricultural University; Zhou Rui is Supported in part by the Natural Science Foundation of Hebei

We study the quasi-two-body decays by employing the perturbative QCD (PQCD) factorization approach, where the charmonia represents and . The corresponding decay channels are studied by constructing the kaon-pion distribution amplitude (DA) , which comprises important final state interactions between the kaon and pion in the resonant region. Relativistic Breit-Wigner formulas are adopted to parameterize the time-like form factor appearing in the kaon-pion DAs. The SU(3) flavor symmetry breaking effect resulting from the mass difference between the kaon and pion is taken into account, which makes significant contributions to the longitudinal polarizations. The observed branching ratios and the polarization fractions of are accommodated by tuning hadronic parameters for the kaon-pion DAs. The PQCD predictions for modes from the same set of parameters can be tested by precise data obtained in the future from LHCb and Belle II experiments.