Cross Section Line Shape Research Articles

Measurement of the e+e− → KS0KL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}_S^0{K}_L^0 $$\\end{document}π0 cross sections from s\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\sqrt{s} $$\\end{document} = 2.000 to 3.080 GeV

Based on e+e− collision data collected at center-of-mass energies from 2.000 to 3.080 GeV by the BESIII detector at the BEPCII collider, a partial wave analysis is performed for the process e+e− → KS0KL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}_S^0{K}_L^0 $$\\end{document}π0. The results allow the Born cross sections of the process e+e− → KS0KL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}_S^0{K}_L^0 $$\\end{document}π0, as well as its subprocesses e+e− → K∗(892)0K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{K} $$\\end{document}0 and K2∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}_2^{\\ast } $$\\end{document}(1430)0K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{K} $$\\end{document}0 to be measured. The Born cross sections for e+e− → KS0KL0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {K}_S^0{K}_L^0 $$\\end{document}π0 are consistent with previous measurements by BaBar, but with substantially improved precision. The Born cross section lineshape of the process e+e−K∗(892)0K¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{K} $$\\end{document}0 is consistent with a vector meson state around 2.2 GeV with a significance of 3.2σ. A Breit-Wigner fit determines its mass as MY = (2164.7 ± 9.1 ± 3.1) MeV/c2 and its width as ΓY = (32.4 ± 21.0 ± 1.8) MeV.

Measurement of e+e−→ΛΛ¯η from 3.5106 to 4.6988 GeV and study of ΛΛ¯ mass threshold enhancement

Using data samples with a total integrated luminosity of approximately 18 fb$^{-1}$ collected by the BESIII detector operating at the BEPCII, the process $e^+e^-\rightarrow\Lambda\bar{\Lambda} \eta$ is studied at center-of-mass energies between 3.5106 and 4.6988 GeV. The Born cross section for the process $e^+e^-\rightarrow\Lambda\bar{\Lambda}\eta$ is measured. No significant structure is observed in the Born cross section line shape. An enhancement near the $\Lambda\bar{\Lambda}$ mass threshold is observed for the first time in the process. The structure can be described by an $S$-wave Breit-Wigner function. Neglecting contribution of excited $\Lambda$ states and potential interferences, the mass and width are determined to be ($2356\pm 7\pm17$) MeV/$c^2$ and ($304\pm28\pm54$) MeV, respectively, where the first uncertainties are statistical and the second are systematic.

Observation of ψ(3770)→ηJ/ψ

Using a data sample collected with the BESIII detector operating at the BEPCII storage ring, the Born cross section of the process e+e−→ηJ/ψ at a center-of-mass energy s=3.773 GeV is measured to be (8.88±0.87±0.42) pb. We fit the cross section line shape before correcting for the initial state radiation from s=3.773 to 4.600 GeV to obtain the branching fraction B(ψ(3770)→ηJ/ψ). We obtain B(ψ(3770)→ηJ/ψ)=(11.3±5.9±1.1)×10−4 when the ψ(3770) decay amplitude is added coherently to the other contributions, and (8.7±1.0±0.8)×10−4 when it is added incoherently. Here the quoted uncertainties are statistical and systematic, respectively. In both cases, the statistical significance of ψ(3770) resonance is above 7σ. This is the first time the decay ψ(3770)→ηJ/ψ is observed with a statistical significance greater than 5σ.Received 23 December 2022Accepted 18 April 2023DOI:https://doi.org/10.1103/PhysRevD.107.L091101Published 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)Research AreasParticle interactionsParticle productionPhysical SystemsQuarkoniaTechniquesLepton collidersParticles & Fields

Measurement of the cross section of e+e−→ ηπ+π− at center-of-mass energies from 3.872 GeV to 4.700 GeV

Using data samples with an integrated luminosity of 19 fb−1 at twenty-eight center-of-mass energies from 3.872 GeV to 4.700 GeV collected with the BESIII detector at the BEPCII electron-positron collider, the process e+e− → ηπ+π− and the intermediate process e+e− → ηρ0 are studied for the first time. The Born cross sections are measured. No significant resonance structure is observed in the cross section lineshape.

Measurement of e+e−→π+π−D+D− cross sections at center-of-mass energies from 4.190 to 4.946 GeV

Using data samples collected with the BESIII detector operating at the BEPCII storage ring, we measure the cross sections of the $e^{+}e^{-}\rightarrow\pi^{+}\pi^{-}D^{+}D^{-}$ process at center-of-mass energies from 4.190 to 4.946 GeV with a partial reconstruction method. Two resonance structures are seen and the resonance parameters are determined from a fit to the cross section line shape. The first resonance we observe has a mass of (4373.1 $\pm$ 4.0 $\pm$ 2.2) MeV/$c^2$ and a width of (146.5 $\pm$ 7.4 $\pm$ 1.3) MeV, in agreement with those of the $Y(4390)$ state; the other resonance has a mass of (4706 $\pm$ 11 $\pm$ 4) MeV/$c^2$, a width of (45 $\pm$ 28 $\pm$ 9) MeV, and a statistical significance of $4.1$ standard deviations ($\sigma$). This is the first evidence for a vector state at this mass value. The spin-$3$ $D$-wave charmonium state $X(3842)$ is searched for through the $e^{+}e^{-}\rightarrow\pi^{+}\pi^{-}X(3842)\rightarrow\pi^{+}\pi^{-}D^{+}D^{-}$ process, and evidence with a significance of $4.2\sigma$ is found in the data samples with center-of-mass energies from 4.600 to 4.700 GeV.

Observation of Resonance Structures in e^{+}e^{-}→π^{+}π^{-}ψ_{2}(3823) and Mass Measurement of ψ_{2}(3823).

Using a data sample corresponding to an integrated luminosity of 11.3 fb^{-1} collected at center-of-mass energies from 4.23 to 4.70GeV with the BESIII detector, we measure the product of the e^{+}e^{-}→π^{+}π^{-}ψ_{2}(3823) cross section and the branching fraction B[ψ_{2}(3823)→γχ_{c1}]. For the first time, resonance structure is observed in the cross section line shape of e^{+}e^{-}→π^{+}π^{-}ψ_{2}(3823) with significances exceeding 5σ. A fit to data with two coherent Breit-Wigner resonances modeling the sqrt[s]-dependent cross section yields M(R_{1})=4406.9±17.2±4.5 MeV/c^{2}, Γ(R_{1})=128.1±37.2±2.3 MeV, and M(R_{2})=4647.9±8.6±0.8 MeV/c^{2}, Γ(R_{2})=33.1±18.6±4.1 MeV. Though weakly disfavored by the data, a single resonance with M(R)=4417.5±26.2±3.5 MeV/c^{2}, Γ(R)=245±48±13 MeV is also possible to interpret data. This observation deepens our understanding of the nature of the vector charmoniumlike states. The mass of the ψ_{2}(3823) state is measured as (3823.12±0.43±0.13) MeV/c^{2}, which is the most precise measurement to date.

Measurement of the [formula omitted] cross sections at center-of-mass energies from 2.3864 to 3.0200 GeV

The Born cross sections of e+e−→Σ0Σ¯0 are measured at center-of-mass energies from 2.3864 to 3.0200 GeV using data samples with an integrated luminosity of 328.5 pb−1 collected with the BESIII detector operating at the BEPCII collider. The analysis makes use of a novel reconstruction method for energies near production threshold, while a single-tag method is employed at other center-of-mass energies. The measured cross sections are consistent with earlier results from BaBar, with a substantially improved precision. The cross-section lineshape can be well described by a perturbative QCD-driven energy function. In addition, the effective form factors of the Σ0 baryon are determined. The results provide precise experimental input for testing various theoretical predictions.

Measurement of e+e−→γχc0,c1,c2 cross sections at center-of-mass energies between 3.77 and 4.60 GeV

The e+e−→γχcJ (J=0, 1, 2) processes are studied at center-of-mass energies ranging from 3.773 to 4.600 GeV, using a total integrated luminosity of 19.3 fb−1 e+e− annihilation data accumulated with the BESIII detector at BEPCII. We observe for the first time e+e−→γχc1,c2 signals at s=4.180 GeV with statistical significances of 7.6σ and 6.0σ, respectively. The production cross section of e+e−→γχc1,c2 at each center-of-mass energy is also measured. We find that the line shape of the e+e−→γχc1 cross section can be described with conventional charmonium states ψ(3686), ψ(3770), ψ(4040), ψ(4160). Compared with this, for the e+e−→γχc2 channel, one more additional resonance is added to describe the cross section line shape. Its mass and width are measured to be M=4371.7±7.5±1.8 MeV/c2 and Γtot=51.1±17.6±1.9 MeV, where the first uncertainties are statistical and the second systematic. The significance of this resonance is estimated to be 5.8σ, and its parameters agree with the Y(4360) resonance previously reported in e+e−→π+π−ψ(3686), and the Y(4390) in e+e−→π+π−hc within uncertainties. No significant signal for the e+e−→γχc0 process is observed, and the upper limits of Born cross sections σB(e+e−→γχc0) at 90% confidence level are reported.Received 6 July 2021Accepted 13 September 2021DOI:https://doi.org/10.1103/PhysRevD.104.092001Published 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)Research AreasBranching fractionHadron-hadron interactionsQuark modelParticles & Fields

Measurement of the Born cross sections for e+e−→η′π+π− at center-of-mass energies between 2.00 and 3.08 GeV

The Born cross sections for the process $e^+e^- \to \eta^\prime \pi^{+}\pi^{-}$ at different center-of-mass energies between $2.00$ and $3.08$ GeV are reported with improved precision from an analysis of data samples collected with the BESIII detector operating at the BEPCII storage ring. An obvious structure is observed in the Born cross section line shape. Fit as a Breit-Wigner resonance, it has a statistical significance of $6.3\sigma$ and a mass and width of $M=(2111\pm43\pm25)$~MeV/$c^2$ and $\Gamma=(135\pm34\pm30)$~MeV, where the uncertainties are statistical and systematic, respectively. These measured resonance parameters agree with the measurements of BABAR in $e^+e^- \to \eta^\prime \pi^{+}\pi^{-}$ and BESIII in $e^+e^- \to \omega\pi^0$ within two standard deviations.

Measurements of Σ+ and Σ− time-like electromagnetic form factors for center-of-mass energies from 2.3864 to 3.0200 GeV

The Born cross sections of the e+e−→Σ+Σ¯− and e+e−→Σ−Σ¯+ processes are determined for center-of-mass energy from 2.3864 to 3.0200 GeV with the BESIII detector. The cross section lineshapes can be described properly by a pQCD function and the resulting ratio of effective form factors for the Σ+ and Σ− is consistent with 3. In addition, ratios of the Σ+ electric and magnetic form factors, |GE/GM|, are obtained at three center-of-mass energies through an analysis of the angular distributions. These measurements, which are studied for the first time in the off-resonance region, provide precision experimental input for understanding baryonic structure. The observed new features of the Σ± form factors require more theoretical discussions for the hyperons.

Discussions on the line-shape of the X(4660) resonance

A careful reanalysis is made on $e^+e^-\to X(4660)\to (\Lambda_c\bar{\Lambda}_c)/(\psi'\pi\pi)$ processes, aiming at resolving the apparent conflicts between Belle and BESIII data above $\Lambda_c\bar{\Lambda}_c$ threshold. We use a model containing a Breit-Wigner resonance and $\Lambda_c\bar{\Lambda}_c$ four-point contact interactions, with which the enhancement right above the $\Lambda_c\bar{\Lambda}_c$ threshold is well explained by a virtual pole generated by $\Lambda_c\bar{\Lambda}_c$ attractive final state interaction, located at $M_V=4.566\pm0.007$ GeV. Meanwhile, $X(4660)$ remains to be a typical Breit-Wigner resonance, and is hence of confinement nature. Our analysis strongly suggests the existence of the virtual pole with statistical significance of $4.2$ standard deviation ($\sigma$). Nevertheless, the conclusion crucially depends on the line-shape of cross sections which are of limited statistics, hence we urge new experimental analyses from Belle II, BESIII, and LHCb to settle the issue.

Measurement of the phase between strong and electromagnetic amplitudes of J/ψ decays

Using 16 energy points of e+e− annihilation data collected in the vicinity of the J/ψ resonance with the BESIII detector and with a total integrated luminosity of around 100pb−1, we study the relative phase between the strong and electromagnetic amplitudes of J/ψ decays. The relative phase between J/ψ electromagnetic decay and the continuum process (e+e− annihilation without the J/ψ resonance) is confirmed to be zero by studying the cross section lineshape of μ+μ− production. The relative phase between J/ψ strong and electromagnetic decays is then measured to be (84.9±3.6)∘ or (−84.7±3.1)∘ for the 2(π+π−)π0 final state by investigating the interference pattern between the J/ψ decay and the continuum process. This is the first measurement of the relative phase between J/ψ strong and electromagnetic decays into a multihadron final state using the lineshape of the production cross section. We also study the production lineshape of the multihadron final state ηπ+π− with η→π+π−π0, which provides additional information about the phase between the J/ψ electromagnetic decay amplitude and the continuum process. Additionally, the branching fraction of J/ψ→2(π+π−)π0 is measured to be (4.73±0.44)% or (4.85±0.45)%, and the branching fraction of J/ψ→ηπ+π− is measured to be (3.78±0.68)×10−4. Both of them are consistent with the world average values. The quoted uncertainties include both statistical and systematic uncertainties, which are mainly caused by the low statistics.

Measurement of e+e−→K+K− cross section at s=2.00 – 3.08 GeV

The cross section of the process $e^{+} e^{-} \rightarrow K^{+} K^{-}$ is measured at a number of center-of-mass energies $\sqrt{s}$ from 2.00 to 3.08 GeV with the BESIII detector at the Beijing Electron Positron Collider (BEPCII). The results provide the best precision achieved so far. A resonant structure around 2.2 GeV is observed in the cross section line shape. A Breit-Wigner fit yields a mass of $M=2239.2 \pm 7.1 \pm 11.3$~and a width of $\Gamma=139.8\pm12.3\pm20.6$ MeV, where the first uncertainties are statistical and the second ones are systematic. In addition, the time-like electromagnetic form factor of the kaon is determined at the individual center-of-mass energy points.

Impact of S -wave thresholds Ds1D¯s+c.c. and Ds0D¯s*+c.c. on vector charmonium spectrum

By investigating the very closely lied $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ thresholds at about 4.43 GeV we propose that the $\psi(4415)$ and $\psi(4160)$ can be mixing states between the dynamic generated states of the strong $S$-wave $D_{s1}\bar{D}_{s}+c.c.$ and $D_{s0}\bar{D}^*_{s}+c.c.$ interactions and the quark model states $\psi(4S)$ and $\psi(2D)$. We investigate the $J/\psi K\bar{K}$ final states and invariant mass spectrum of $J/\psi K$ to demonstrate that nontrivial lineshapes can arise from such a mechanism. This process, which goes through triangle loop transitions, is located in the vicinity of the so-called "triangle singularity (TS)" kinematics. As a result, it provides a special mechanism for the production of exotic states $Z_{cs}$, which is the strange partner of $Z_c(3900)$, but with flavor contents of $c\bar{c}q\bar{s}$ (or $c\bar{c}s\bar{q}$) with $q$ denoting $u/d$ quarks. The lineshapes of the $e^+e^-\to J/\psi K\bar{K}$ cross sections and $J/\psi K \ (J/\psi \bar{K})$ spectrum are sensitive to the dynamically generated state, and we demonstrate that a pole structure can be easily distinguished from open threshold CUSP effects if an exotic state is created. A precise measurement of the cross section lineshapes can test such a mixing mechanism and provide navel information for the exotic partners of the $Z_c(3900)$ in the charmonium spectrum.

Disentangling the role of the Y(4260) in [formula omitted] and [formula omitted] via line shape studies

Whether the Y(4260) can couple to open charm channels has been a crucial issue for understanding its nature. The available experimental data suggest that the cross section line shapes of exclusive processes in e+e− annihilations have nontrivial structures around the mass region of the Y(4260). As part of a series of studies of the Y(4260) as mainly a D¯D1(2420)+c.c. molecular state, we show that the partial widths of the Y(4260) to the two-body open charm channels of e+e−→D⁎D¯⁎ and Ds⁎D¯s⁎ are much smaller than that to D¯D⁎π+c.c.. The line shapes measured by the Belle Collaboration for these two channels can be well described by the vector charmonium states ψ(4040), ψ(4160) and ψ(4415) together with the Y(4260). It turns out that the interference of the Y(4260) with the other charmonia produces a dip around 4.22 GeV in the e+e−→D⁎D¯⁎ cross section line shape. The data also show an evidence for the strong coupling of the Y(4260) to the DD¯1(2420), in line with the expectation in the hadronic molecular scenario for the Y(4260).

Cross section line shape of e+e− → χc0ω around the Y(4260) mass region

We demonstrate that the recent measurement of the cross section line shapes of e+e−→χc0ω can be naturally explained by the molecular picture for Y(4260) where the Y(4260) is treated as a hadronic molecule dominated by D¯D1(2420)+c.c. This result is consistent with properties extracted for Y(4260) as the D¯D1(2420)+c.c. molecular state in other reactions such as e+e−→J/ψππ, hcππ, D¯D⁎π+c.c., and γX(3872).

Production ofY(4260)as a hadronic molecule state ofD¯D1+c.c.ine+e−annihilations

We study the $Y(4260)$ production mechanism in $e^+e^-$ annihilations in the framework of hadronic molecules and investigate the consequence of such a picture in different decay channels. In the hadronic molecule picture the $Y(4260)$ is described as a mixture state composed of a long-ranged $\bar{D}D_1(2420)+c.c.$ molecule state and a compact $c\bar{c}$ component. We show that the compositeness relation can still provide a reasonable constraint on the wavefunction renormalization parameter due to the dominance of the molecular component. Such a mechanism can be regarded as a natural consequence of the heavy quark spin symmetry (HQSS) breaking. This study elaborates the molecular picture for the $Y(4260)$ in the $e^+e^-$ annihilations and affirms that the cross section lineshape of $e^+e^-\to \bar{D}D^*\pi+c.c.$ in the vicinity of the $Y(4260)$ should have a nontrivial behavior. In this framework we predict that the upper limit of the $Y(4260)$ leptonic decay width is about 500 eV. We also investigate the coupling for $D_1(2420)\to D^*\pi$ in the $^3P_0$ quark model and examine the possible HQSS breaking effects due to the deviation from the $|^1P_1\rangle$ and $|^3P_1\rangle$ ideal mixing. This will in turn provide a constraint on the HQSS breaking coupling for the $Y(4260)$ to $\bar{D}D_1(2420)+c.c.$ via its $c\bar{c}$ component.

Y(4260)as the firstS-wave open charm vector molecular state?

Since its first observation in 2005, the vector charmonium $Y(4260)$ has turned out to be one of the prime candidates for an exotic state in the charmonium spectrum. It was recently proposed that the $Y(4260)$ should have a prominent ${D}_{1}\overline{D}+\mathrm{c}.\mathrm{c}.$ molecular component that is strongly correlated with the production of the charged ${Z}_{c}(3900)$. In this paper we demonstrate that the nontrivial cross section line shapes of ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}J/\ensuremath{\psi}\ensuremath{\pi}\ensuremath{\pi}$ and ${h}_{c}\ensuremath{\pi}\ensuremath{\pi}$ can be naturally explained by the molecular scenario. As a consequence we find a significantly smaller mass for the $Y(4260)$ than previously studied. In the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}\overline{D}{D}^{*}\ensuremath{\pi}+\mathrm{c}.\mathrm{c}.$ process, with the inclusion of an additional $S$-wave ${\overline{D}}^{*}\ensuremath{\pi}$ contribution constrained from data on the $D{\overline{D}}^{*}$ invariant mass distribution, we obtain a good agreement with the data of the angular distributions. We also predict an unusual line shape of $Y(4260)$ in this channel that may serve as a smoking gun for a predominantly molecular nature of $Y(4260)$. Improved measurements of these observables are therefore crucial for a better understanding of the structure of this famous resonance.

Open charm effects ine+e−→J/ψη,J/ψπ0, andϕηc

We propose to study the open charm effects in $e^+ e^-\to J/\psi\eta$, $J/\psi\pi^0$ and $\phi\eta_c$. We show that the exclusive cross section lineshapes of these processes would be strongly affected by the open charm effects. Since the final state light meson productions are through soft gluon radiations, we assume a recognition of this soft process via charmed meson loops at hadronic level. A unique feature among these three reactions is that the $D\bar{D^*}+c.c.$ open channel is located in a relatively isolated energy, i.e. $\sim 3.876$ GeV, which is sufficiently far away from the known charmonia $\psi(3770)$ and $\psi(4040)$. Therefore, the cross section lineshapes of these reactions may provide an opportunity for singling out the open charm effects with relatively well-defined charmonium contributions. In particular, we find that reaction $e^+ e^-\to J/\psi\pi^0$ is sensitive to the open charm $D\bar{D^*}+c.c.$ Due to the dominance of the isospin-0 component at the charmonium energy region, we predict an enhanced model-independent cusp effect between the thresholds of $D^0\bar{D}^0+c.c.$ and $D^+ D^{*-}+c.c.$ This study can also help us to understand the X(3900) enhancement recently observed by Belle Collaboration in $e^+ e^-\to D\bar{D}+c.c.$

Lineshape ofe+e−→D*D¯+c.c.and electromagnetic form factor ofD*→Dtransition in the timelike region

In this work, we apply the vector meson dominance (VMD) model to extract the electromagnetic time-like form factor of the $D^*\to D$ transition combining the recent Belle data for $e^+ e^-\to D^{*+} D^- + c.c.$ and data for $D^*\to D\gamma$. Two solutions are obtained in the interpretation of the cross section lineshape: i) With a relatively large coupling for $\psi D^*\bar{D}$ determined by experiment, destructive interferences among those charmonium components are required to bring down the overall cross sections, and then account for the cross section lineshape. ii) With a relatively small value for the $\psi D^*\bar{D}$ coupling based on heavy quark theory, an apparent cross section deficit near threshold is observed, and contributions from other mechanisms are needed. It might imply the presence of an additional resonance X(3900). Meanwhile, we also point out that an enhancement like that could be produced by the $D_s^*\bar{D_s}+c.c.$ open channel effects.