Recent results from BESIII experiment

In this talk, we present recent results from BESIII experiment. This talk covers the studies of charmonium(-like) states, light hadron spectroscopy and charm physics at the BESIII.


Introduction
The Beijing Electron Collider has been upgraded to a double ring collider with a design luminosity of 1 × 10 33 cm −2 s −1 at a center-of-mass energy of 3.78 GeV/c 2 .It is operating between 2.0 and 4.6 GeV/c 2 in the center of mass energy.The BESIII experiment is used to study the charm and τ physics.The BESIII experiment at the BEPCII collider started data taking since 2008, and data samples were accumulated at the peak of the narrow vector charmonium resonances as well as above 4.0 GeV/c 2 .Samples of 13 billion J/ψ decay events and 0.5 billion ψ(2S ) decay events have been collected for the study of charmonium decays and light hadron spectroscopy in the charmonium decays.For the study of charm meson decays, the BESIII experiment acquired about 2.9 fb −1 on the ψ(3770) peak.Between December of 2012 and June of 2013, the BESIII detector collected a total integrated luminosity of 2.9fb −1 of data samples, especially, the largest samples collected at E CM = 4.23 GeV/c 2 (1054 pb −1 ), 4.26 GeV/c 2 (806 pb −1 ), and 4.36 GeV/c 2 (523 pb −1 ), these data samples have provided powerful study of the XYZ states.
In this talk, we present the most recent results on the studies of the charged charmonium-like states, charmonium decays, light hadron spectroscopy and charm physics at the BESIII experiment.

Observations of the charmonium-like states
Many charmonium-like states, "XYZ" particles, have been observed in the initial state radiation (ISR) process and B meson decays.All these states populate the charmonium mass region above open charm threshold.Many strange properties measured from these states make them more like exotic states rather than conventional mesons.The BESIII experiment is unique to use e + e − collision tuned to center of mass energies to directly produce the vector a e-mail: lihb@ihep.ac.cn charmonium-like states, such as Y(4260) or Y(4360), respectively.These data samples can be used not only to study the Y(4260) or Y(4360) states, but also to search for the "charged charmonium-like states", Z c (3900), Z c (4020) and Z c (4025).

2.1
The charged Z c (3900) in e + e − → π + π − J/ψ The BESIII experiment studied the process e + e − → π + π − J/ψ at a center-of-mass (CM) energy of 4.26 GeV/c 2 using 525 pb −1 data sample [1].A structure at around 3.9 GeV/c 2 is observed in the π ± J/ψ mass spectrum, which is referred to as the Z c (2900).This structure couples to charmonium and has an electric charge, which is suggestive of a state containing more quarks than just a charm and anti-charm.A fit to the π ± J/ψ invariant mass spectrum as shown in Fig. 1 (Top), neglecting interference, results in a mass of (3899.0 ± 3.6 ± 4.9) MeV/c 2 and a width of (46 ± 10 ± 20) MeV [1].This structure, was also observed at the same time by the Belle collaboration [2] and was confirmed by the authors of Ref. [3] using CLEO-c data.

Structure in charged
One possible clue for the interpretation of the Z c (3900) is that it has a mass very close to D * D threshold.To investigate, the BESIII experiment studied the processes e + e − → π − D + D * 0 + c.c. and e + e − → π − DD * + + c.c. at the CM of 4.26 GeV/c 2 [4].Clear structure in the mass spectrum of both D + D * 0 + c.c. and DD * + + c.c. was found as shown in Fig. 1 (Bottom).The measured mass and width were (3883.9± 1.5 ± 4.2) MeV/c 2 and (24.8 ± 3.3 ± 11.0) MeV/c 2 , respectively.The structure was named as Z c (3885), and its mass and width are both slightly lower than the ones of Z c (3900) in the π ± J/ψ, but Γ(Z c (3900)→πJ/ψ) = 6.2 ± 1.1 ± 2.7 is determined [4].

Charge structures in (D
BESIII studied the process e + e − → (D * D * ) ± π ∓ at a CM energy of 4.26 GeV /c 2 using a 827 pb −1 data sample [5].Based on a partial reconstruction technique, the Born cross section is measured to be (137 ± 9 ± 15) pb.A structure near the (D * D * ) ± threshold in the π ∓ recoil mass spectrum is observed (see Fig. 2 (Top)), which is denoted as the Z ± c (4025) [5].The measured mass and width of the structure are (4026.3± 2.6 ± 3.7) MeV/c 2 and (24.8 ± 5.6 ± 7.7) MeV/c 2 , respectively.Its production ratio is determined to be 0.65 ± 0.09 ± 0.06.Since this structure couples to (D * D * ) ± and has electric charge, the observation suggests that the Z c (4025) may be a loosely bound (D * D * ) ± system [6].
The BESIII experiment also studied e + e − → π + π − h c at CM energies from 3.90 GeV/c 2 to 4.42 GeV/c 2 [7].The Born cross sections are measured at 13 energies, and are found to be of the same order of magnitude as those of e + e − → π + π − J/ψ but with a different line shape.In the π ± h c mass spectrum, a distinct structure, referred to as Z c (4020), is observed at 4.02 GeV/c 2 .The Z c (4020) carries an electric charge and couples to charmonium, which is suggestive of a state containing more quarks than just a charm and an anti-charm quark, as the Z c (3900) observed in the π ± J/ψ system.A fit to the π ± h c invariant mass spectrum (see Fig. 2 (Bottom)), neglecting possible interferences, results in a mass of (4022.9 ± 0.8 ± 2.7) MeV/c 2 and a width of (7.9 ± 2.7 ± 2.6) MeV/c 2 for the Z c (4020), where the first errors are statistical and the second systematic.The difference between the parameters of this structure and the Z c (4025) observed in D * D * final state [5] is within 1.5σ, but whether they are the same state needs further investigation.No significant Z c (3900) signal is observed, and upper limit on the Z c (3900) production cross section in π ± h c at CM energy of 4.26 GeV/c 2 is set to be smaller than 11 pb at the 90% C.L., which is lower than that of e + e − → π ± Z c (3900

Observation of the X(3872)
The X(3872) was observed by Belle in B ± → K ± π + π − J/ψ decays ten years ago [8].It was confirmed subsequently by several other experiments [9][10][11].Since its discovery, it triggered many speculations about its nature, including a hadronic molecule or teraquark state.The CDF and LHCb experiments determined the spin-parity of the X(3872) being J P = 1 + [12,13], and CDF experiment also found that the π + π − system was dominated by a ρ(770) resonance [14].Using data samples at center-of-mass energies from 4.009 to 4.420 GeV/c 2 , the e + e − → γX(3872) was observed for the first time [15].The X(3872) is clearly seen in the M(π + π − J/ψ) (summed over all energy points) displayed in Fig. 3 (Top) .The measured mass, M = 3871.9± 0.7 ± 0.2 MeV/c 2 , is consistent with previous measurements.As shown in Fig. 3 (Bottom), the cross section of this process as a function of center of mass energy, while not conclusive, suggests this observation could arise from the process Y(4260) → γX(3872) [15].
3 Charmonium states: η c (1S ), η c (2S ) and h c in the ψ(2S ) decays The mass and width of the lowest lying charmonium state, the η c (1S ), continue to have large uncertainties when compared to those of other charmonium states [16].The most recent study by the CLEO-c experiment, using both ψ(2S ) → γη c and J/ψ → γη c , pointed out a distortion of the η c line shape in ψ(2S ) decays [17].CLEO-c attributed the η c line-shape distortion to the energy dependence of the "hindered" M1 transition matrix element.
Based on the data sample of 106 M ψ(2S ) decay events, the η c mass and width are measured from the radiative transition ψ(2S ) → γη c [18].The η c candidates are reconstructed from six exclusive decay modes: and 3(π + π − ), where K S is reconstructed in π + π − mode, η and π 0 from γγ final states.For a hindered M1 transition the matrix element acquires terms proportional to E 2 γ , which, when combined with the usual E 3 γ term for the allowed transitions, lead to contributions in the radiative width proportional to E 7 γ [19].Thus, the η c lineshape is described by a BW modified by E 7  γ convoluted with a resolution function.It is important to point out that the interference between η c and non-resonance in the signal region is also considered.The statistical significance of the interference is 15 σ.This affects the η c resonant parameters significantly.Assuming an universal relative phase between the two amplitudes, we obtain η c mass and width, M = 2984.2± 0.6 ± 0.5 MeV/c 2 and Γ = 31.4± 1.2 ± 0.6 MeV/c 2 , respectively.Figure 4 shows the fit results in the six η c decay modes.With precise measurement of the η c mass, one can obtain the hyperfine splitting, ΔM h f (1S ) cc ≡ M(J/ψ)−M(η c ) = 112.5±0.8MeV/c 2 , which agrees with the quark model prediction and lattice computations [20,21], and will be helpful for understanding the spin-dependent interactions in hidden quarkonium states.
The BESIII experiment reported the results on the production and decay of the h c using 106 M of ψ(2S ) decay events in 2010 [27], where we studied the distributions of mass recoiling against a detected π 0 to measure ψ → π 0 h c both inclusively (E1-untagged) and in events tagged as h c → γη c (E1-tagged) by detection of the E1 transition photon.In 2011, 16 specific decay modes of η c were used to reconstruct η c candidates in the decay mode of h c → γη c [28]. Figure 6 shows the π 0 recoiling mass for the sum of the 16 η c decay modes in the decay chain of ψ → π 0 h c , h c → γη c .We fit the 16 π 0 recoil-mass spectra simultaneously that yields M(h c ) = 3525.31± 0.11(stat.)± 0.14(syst.)MeV/c 2 and Γ(h c ) = 0.70 ± 0.28(stat.)± 0.22(syst.)MeV/c 2 .These results are consistent with the previous BESIII inclusive results and CLEO-c exclusive results.

Light hadron physics
The BESIII is an idea Lab to study the light hadron spectroscopy in the radiative or hadronic J/ψ/ψ(2S ) decays since both J/ψ and ψ(2S ) decays are OZI suppressed.With huge J/ψ and ψ(2S ) samples, we presented recent results, including the partial wave analyses (PWA) of J/ψ → γp p, γηη, γωφ, and ψ(2S ) → p pπ 0 .We have to mention here that both η and η mesons can be probed in the J/ψ and ψ(2S ) two body decays involving the η/η meson in the final states.It will be highlight for the BESIII to make precision measurements and to search for rare decays of η and η decays [29].
4.1 PWA of J/ψ → γp p, γηη, γωφ, and ψ(2S ) → p pπ 0 For J/ψ → γp p decay, the p p invariant mass distribution is shown in Fig. 7, where strong p p mass threshold enhancement, which denotes as X(p p), is clearly observed [30].To determine its spin, parity, mass, width and production rate with high precision, a full PWA with M p p < 2.2 GeV/c 2 was performed after taking into account the final state interactions using the Julich formulation [31].In the PWA fit the p p threshold enhancement, f 2 (1910) and f 0 (2100) are described by Breit-Wigner propagators, and the parameters of the f 2 (1910) and f 0 (2100) are fixed at PDG values.Figure 7 shows comparisons of the mass and angular distributions between the data and the PWA fit projections.The mass, width and product BR for the X(p p) are measured to be: −13 (syst.)±4(model)MeV/c 2 (a total width of Γ < 76 MeV/c 2 at the 90% C.L) and B(J/ψ → γX)B(X → p p) = (9.0+0.4 −1.1 (stat.)+1.5 −5.0 (syst.)± 2.3(model)) × 10 −5 , respectively.For the spin-parity determination of the X(p p), the 0 −+ assignment fit is better than that for 0 ++ or other J PC assignments with statistical significance that are larger than 6.8σ [30].
Using 225 million J/ψ events, a PWA of J/ψ → γηη has been performed [32], and the results are summarized in Table 1.The scalar contributions are mainly from f 0 (1500), f 0 (1710) and f 0 (2100), while no evident contributions from f 0 (1370) and f 0 (1790) are seen.Recently, the production rate of the pure gauge scalar glueball in J/ψ radiative decays predicted by the lattice QCD [33] was found to be compatible with the production rate of J/ψ radiative decays to f 0 (1710); this suggests that f 0 (1710) has a larger overlap with the glueball compared to other glueball candidates (eg.f 0 (1500)).In this analysis, the production rate of f 0 (1710) and f 0 (2100) are both about one order of Here, the black dots with error bars are data, the solid histograms show the PWA total projection, and the dashed, dotted, dash-dotted and dash-dot-dotted lines show the contributions of the X(p p), 0 ++ phase space, f 0 (2100) and f 2 (1910), respectively [30].
magnitude larger than that of the f 0 (1500) and no clear evidence is found for f 0 (1370), which are both consistent with, at least not contrary to, lattice QCD predictions.The tensor components, which are dominantly from f 2 (1525), f 2 (1810) and f 2 (2340), also have a large contribution in J/ψ → γηη decays.The significant contribution from f 2 (1525) is shown as a clear peak in the ηη mass spectrum; a tensor component exists in the mass region from 1.8 GeV/c 2 to 2 GeV/c 2 , although we cannot distinguish f 2 (1810) from f 2 (1910) or f 2 (1950); and the PWA requires a strong contribution from f 2 (2340), although the possibility of f 2 (2300) cannot be ruled out.For the narrow f J (2220), no evident peak is observed in the ηη mass spectrum.
A study of the doubly OZI suppressed decays of J/ψ → γωφ is performed [34], and a strong deviation (> 30σ) from three-body J/ψ → γωφ phase space is observed near the ωφ mass threshold, which is consistent with the previous observation reported by the BE-SII experiment.A PWA with a tensor covariant amplitude that assumes that the enhancement is due to the presence of a resonance, the X(1810), is performed, and confirms that the spin-parity of the X(1810) is 0 ++ .The mass and width of the X(1810) are determined to be M = 1795 ± 7(stat) +13 −5 (syst)±19(mod) MeV/c 2 and Γ = 95 ± 10(stat) +21 −34 (syst)±75(mod) MeV/c 2 , respectively, and the product branching fraction is measured to

Observation of X(1840) in
We studied the decay J/ψ → γ3(π + π − ) with a 225.3 million J/ψ event sample [36].A structure at 1.84 GeV/c 2 is observed in the 3(π + π − ) mass spectrum with a statistical significance of 7.6σ.As shown in Fig. 8 (Top), fitting the structure X(1840) with a modified Breit-Wigner function yields M = 1842.2± 4.2 +7.1 −2.6 MeV/c 2 and Γ = 83 ± 14 ± 11 MeV/c 2 .The product branching fraction is determined to be B(J/ψ → γX(1840)) × B(X(1840) → 3(π + π − )) = (2.44 ± 0.36 +0.60  −0.74 ) × 10 −5 .The comparison to the BE-SIII results of the masses and widths of the X(p p) [30], X(1810) [34], X(1835) [37] and X(1870) [38] are displayed in Fig. 8 (Bottom), where the mass of X( 1840) is in agreement with those of X(1835) and X(p p), while its width is significantly different from any of them.Therefore, based on these data, one cannot determine whether X(1840) is a new state or the signal of a 3(π + π − ) decay mode of an existing state.Further study, including an amplitude analysis to determine the spin and parity of the X(1840), is needed to establish the relationship between different experimental observations in this mass region and determine the nature of the underlying resonance or resonances.

Potential of charm physics at BESIII
Many of the measurements related to charm decays have been done by other experiments such as BESII and CLEOc, and many are also accessible to the B-factory experiments.What are BESIII's advantages to running at the open charm threshold [42,43]?BESIII will not be able to compete with both BABAR and Belle in statistics on charm physics, especially on the rare and forbidden decays of charm mesons.However, data taken at charm threshold still have powerful advantages over the data at Υ(4S ), which we list here [44]: 1) Charm events produced at threshold are extremely clean; 2) The measurements of absolute branching fraction can be made by using double tag events; 3) Signal/Background is optimal at threshold; 4) Neutrino reconstruction is clean; 5) Quantum coherence allow simple [45] and complex [46] methods to measure the neutral D meson mixing parameters and strong phase difference [47], and to check for direct CP violation.
For charm physics at BESIII, the first physics results will be the measurements of the leptonic and semileptonic decays of charm mesons.Measurements of the leptonic decays at BESIII will benefit from the fully tagged D + and D + S decays available at the ψ(3770) and at √ s ∼ 4170 MeV/c 2 or ∼ 4017 MeV/c 2 [48].The leptonic decay rates for D + and D + S has been measured with a precision of 4.3% and 2.0 % with the final data from CLEOc.It should be noted that the D + → τ + ν decay is reported by CLEOc with an upper limit of 1.2 × 10 −3 at 90% C.L. [49].At BESIII, with 4 times (about 3.0 fb −1 ) of the CLEO-c's luminosity, significant gains on these measurements will be made if the systematic errors remain the same.This will allow the validation of theoretical calculations of the decay constants at the 1-2% level.The neutral D mixing and CP violation in charm sector using quantum correlation are all statistics-starved at CLEO-c, improvement will be made at BESIII experiment.(i) Figure 9.The beam-energy-constrained mass distributions for the different tagged mode combinations, where (a), (b), (c), (d), (e), (f), (g), (h) and (i) are for the modes of , respectively; the two vertical dashed red lines show the tagged D − mass region [50].

Purely leptonic D decay
With a sample of 2.9 fb −1 taken at open-charm threshold, BESIII experiment measures the decay branching fraction for D + → μ + ν μ and extracts decay constant f D + [50].Decay constant characterizes the strong-interaction physics at the quark-annihilation vertex.In a fully leptonic decay, it parameterizes all of our essential theoretical limitations.Decay constant for B meson also appears in the evaluation of box diagrams, and limits theoretical precision in calculating the neutral B meson mixing.Thus, lack of knowledge of the B 0 and B s decays constants limits the 00011-p.7 Lepton and Hadron Physics at Meson-Factories usefulness of precise measurements of B 0 − B0 and B s − Bs oscillations.These mixing data are our best source of information on the CKM matrix elements V td and V ts , which are difficult to measure directly in top decay.The leptonic decay of charm meson presents an opportunity to check LQCD results for decay constants against precision measurements.
We call an event a tagged one if it has a fullyreconstructed D hadronic decay.A sample of tagged events has a greatly reduced background and constrained kinematics, both of which aid studies of how the other D in the event decays.One can infer neutrinos from energy and momentum conservation, allowing "full" reconstruction of (semi)leptonic D decays.The typical tag rates per D (not per pair) are roughly 15% and 10% for D 0 and D + , respectively.For pure leptonic decay, the single tagged D − meson events are reconstructed in nine nonleptonic decay modes of and K s π − π − π + .Mass peaks for the nine hadronic tag modes are shown in Fig. 9.A maximum likelihood fit to the mass spectrum yields the number of the single tagged D − events for each of the nine modes.The total number of tagged D − events are 170305 ± 3405 [50].
The chosen signal variable for the μ + ν decay is the calculated square of the missing-mass of any undetected decay products, shown in Fig. 10; this should of course peak at M 2 ν = 0 for signal events.The power of D-tagging is evident in the clean, isolated signal peak.The events that peak near M 2 miss 0.25 GeV 2 /c 4 are primarily from D + → K 0 L π + decays, where the K 0 L is undetected.The numbers of the background events from D + → K 0 L π + and D + → π + π 0 , as well as D + → τ + ν τ , are estimated by analyzing Monte Carlo samples that are 10 times larger than the data.The backgrounds from other D decays are corrected considering the difference in the numbers of events from the data and simulated events in the range from 0.15 to 0.60 GeV 2 /c 4 .These studies show that there are 42.0±2.3background events among the 451 D + → μ + ν μ candidates in the signal region indicated in Fig. 10.After subtracting the number of background events, 409.0 ± 21.2 ± 2.3 signal events (N net sig ) for D + → μ + ν μ remain, where the first error is statistical and the second is the systematic associated with the uncertainty of the background estimate.The weighted overall efficiency for detecting D + → μ + ν μ decays is determined to be = 0.6403 ± 0.0012 by analyzing Monte Carlo simulated events for D + → μ + ν μ in each tagged D − mode.We obtain the branching fraction to be where the first error is statistical and the second systematic.The measured branching fraction is consistent within error with world average of B(D + → μ + ν) = (3.82±0.33)× 10 −4 [16], but has better precision.The decay constant f D + is then obtained by using 1040±7 fs as the D + lifetime and 0.2252 as V cd [16].Our result is MeV/c 2 , where the first errors are statistical and the second systematic [50].One of the best ways to measure magnitudes of CKM elements is to use semileptonic decays since they are far simpler to understand than hadronic decays and the decay width is ∼ |V cq | 2 .On the other hand, measurements using other techniques have obtained useful values for V cs and V cd [53], and thus semileptonic D decay measurements are a good laboratory for testing theories of QCD.For a D meson decaying into a single hadron (h), the decay rate can be written exactly in terms of the four-momentum transfer defined as: For decays to pseudoscalar mesons and "virtually massless" leptons, the decay width is given by: where p P is the three-momentum of pseudoscalar meson in the D rest frame, and f + (q 2 ) is a "form-factor" whose normalization must be calculated theoretically, although its shape can be measured.
The BESIII experiment has taken about 2.9 fb −1 data at open-charm threshold during the 2010 and 2011 data runs.Using one-third of the data, a partially-blind analysis has been done with the D 0 → Keν and D 0 → πeν decays.Using the double tag technique, several hadronic D decays are fully reconstructed at first.The following four hadronic D decays are used: D 0 → K − π + , K − π + π 0 , K − π + π 0 π 0 and K − π + π − π + .After hadronic D 0 tags are found, we reconstruct signal decay for the other D0 .The signal events with a missing ν are inferred using the variable U = E miss − |P miss |, similar to missing mass square, where "miss" here refers to the missing energy or momentum.Given the signal yields obtained from fitting U distributions and signal efficiencies obtained from signal Monte Carlo, the absolute branching fractions are obtained.Preliminary results of branching fractions are listed in Table 2, and comparisons with results from PDG2012 [16] and CLEO-c results [54] are also made.In order to measure form factor, partial decay rates are measured in different q 2 bins.D0 → K + e − ν candidates are divided into nine q 2 bins, while D0 → π + e − ν candidates are divided into seven q 2 bins.Signal yields in each q 2 bin are obtained by fitting U distributions in that q 2 range.Using an efficiency matrix versus q 2 , obtained from Monte-Carlo simulation, and combining with tag yields and tag efficiencies, the partial decay rates are obtained, as shown in Fig. 12.The values of q 2 -dependent form factors in each q 2 bin can be extracted from the measured partial decay rates.These data can be fitted with different parameterizations of the form factors, and the fit can distinguish between form factor parameterizations.In general, one may express the form factors in terms of a dispersion relation, an approach that has been well established in the literature (see, for example, Ref. [55] and references therein): where m pole is the mass of the lowest lying (q i q f ) meson with the appropriate quantum numbers: for D → Keν it is D * + s and for D → πeν it is D * + , the parameter α gives the relative contribution from the vector pole at q 2 = 0, m D is the mass of the D meson, and m P is the mass of the final state pseudoscalar meson.The integral term can be expressed in terms of an infinite series [55].Typically it takes only a few terms to describe the data.Three different parameterizations of the form factor f + (q 2 ) are considered.The first parameterization, known as the simple pole model, is dominated by a single pole [56]; the second parameterization is known as the modified pole model [56]; the third parameterization is known as the series expansion [55].Thus minimized χ 2 fits are employed to extract the values of f + (0)|V cd(s) | using each of the parameterizations.The preliminary results for f + (0)|V cd(s) | are shown in Table 3 [57].
00011-p.9In summary for charm physics, the results for the (semi-)leptonic D decays have appeared.However, the BESIII experiment can also measure the strong phase difference between between the doubly Cabibbo-suppressed and and Cabibbo-favored processes, the first preliminary results for D 0 → Kπ were reported [58] recently.We also reported the result on the D + → K S π + π 0 based on a full amplitude analysis [59].More analyses on the D → h 1 h 2 h 3 Dalitz decays and D → h 1 h 2 h 3 h 4 four-body decays are under going at the BESIII, from which one will extract amplitudes from qusi-two-body contributions.Therefore the strong phase difference, neutral D mixing parameters and CP violation asymmetries can be studied.For the rare charm decays, many decay modes including photons and π 0 in the final states can be probed with high sensitivities (with relative smaller integrated luminosity than that at the B factories), for example, the D 0 → γγ decay was reported recently [60].

Figure 5 .
Figure5.The invariant-mass spectrum for K s K + π − (top panel), K + K − π 0 (bottom panel), and the simultaneous likelihood fit to the three resonances and combined background sources[22].

Figure 7 .
Figure 7. Comparisons between data and PWA fit projection: (a) the p p invariant mass; (b)-(d) the polar angle θ γ of the radiative photon in the J/ψ center of mass system, the polar angle θ p and the azimuthal angle φ p of the proton in the p p center of mass system with M p p − 2m p < 50 MeV/c 2 , respectively.Here, the black dots with error bars are data, the solid histograms show the PWA total projection, and the dashed, dotted, dash-dotted and dash-dot-dotted lines show the contributions of the X(p p), 0 ++ phase space, f 0 (2100) and f 2 (1910), respectively[30].

Figure 8 .
Figure 8. Top: The fit of mass spectrum of 3(π + π − ).The dots with error bars are data; the solid line is the fit result[36].Bottom: comparisons of observations at BESIII.The error bars include statistical, systematic, and, where applicable, model uncertainties.

Figure 10 .
Figure 10.BESIII missing-mass-squared plot for D + → μ + ν.The insert shows the signal region on a vertical log scale, where dots with error bars are for the data, histograms are sum for the simulated backgrounds from D + → K L π + , D + → π + π 0 , D + → τ + ν and other decays of D mesons as well as from e + e − → non-D D decays.
MeV/c 2 .For the remaining 5 N * intermediate resonances, the analysis yields mass and width values which are consistent with those from established resonances.

Table 2 .
Branching fraction measurement using 923 pb −1 of ψ(3770) data from BESIII experiment, and comparisons with results from CLEO-c and PDG2012.