Measurement of the Cross Section for e + e − → Ξ − Ξ̄ + and Observation of an Excited Ξ Baryon

M. Ablikim, M. N. Achasov, P. Adlarson, S. Ahmed, M. Albrecht, M. Alekseev, A. Amoroso, F. F. An, Q. An, Y. Bai, O. Bakina, R. Baldini Ferroli, I. Balossino, Y. Ban, K. Begzsuren, J. V. Bennett, N. Berger, M. Bertani, D. Bettoni, F. Bianchi, J. Biernat, J. Bloms, I. Boyko, R. A. Briere, H. Cai, X. Cai, A. Calcaterra, G. F. Cao, N. Cao, S. A. Cetin, J. Chai, J. F. Chang, W. L. Chang, G. Chelkov, D. Y. Chen, G. Chen, H. S. Chen, J. C. Chen, M. L. Chen, S. J. Chen, Y. B. Chen, W. Cheng, G. Cibinetto, F. Cossio, X. F. Cui, H. L. Dai, J. P. Dai, X. C. Dai, A. Dbeyssi, D. Dedovich, Z. Y. Deng, A. Denig, I. Denysenko, M. Destefanis, F. De Mori, Y. Ding, C. Dong, J. Dong, L. Y. Dong, M. Y. Dong, Z. L. Dou, S. X. Du, J. Z. Fan, J. Fang, S. S. Fang, Y. Fang, R. Farinelli, L. Fava, F. Feldbauer, G. Felici, C. Q. Feng, M. Fritsch, C. D. Fu, Y. Fu, Q. Gao, X. L. Gao, Y. Gao, Y. Gao, Y. G. Gao, Z. Gao, B. Garillon, I. Garzia, E. M. Gersabeck, A. Gilman, K. Goetzen, L. Gong, W. X. Gong, W. Gradl, M. Greco, L. M. Gu, M. H. Gu, S. Gu, Y. T. Gu, A. Q. Guo, L. B. Guo, R. P. Guo, Y. P. Guo, A. Guskov, S. Han, X. Q. Hao, F. A. Harris, K. L. He, F. H. Heinsius, T. Held, Y. K. Heng, M. Himmelreich, Y. R. Hou, Z. L. Hou, H. M. Hu, J. F. Hu, T. Hu, Y. Hu, G. S. Huang, J. S. Huang, X. T. Huang, X. Z. Huang, N. Huesken, T. Hussain, W. Ikegami Andersson, W. Imoehl, M. Irshad, Q. Ji, Q. P. Ji, X. B. Ji, X. L. Ji, H. L. Jiang, X. S. Jiang, X. Y. Jiang, J. B. Jiao, Z. Jiao, D. P. Jin, S. Jin, Y. Jin, T. Johansson, N. Kalantar-Nayestanaki, X. S. Kang, R. Kappert, M. Kavatsyuk, B. C. Ke, I. K. Keshk, A. Khoukaz, P. Kiese, R. Kiuchi, R. Kliemt, L. Koch, O. B. Kolcu, B. Kopf, M. Kuemmel, M. Kuessner, A. Kupsc, M. Kurth, M. G. Kurth, W. Kühn, J. S. Lange, P. Larin, L. Lavezzi, H. Leithoff, T. Lenz, C. Li, Cheng Li, D. M. Li, F. Li, F. Y. Li, G. Li, H. B. Li, H. J. Li, J. C. Li, J. W. Li, Ke Li, L. K. Li, Lei Li, P. L. Li, P. R. Li, Q. Y. Li, W. D. Li, W. G. Li, X. H. Li, X. L. Li, X. N. Li, Z. B. Li, Z. Y. Li, H. Liang, H. Liang, Y. F. Liang, Y. T. Liang, G. R. Liao, L. Z. Liao, J. Libby, C. X. Lin, D. X. Lin, Y. J. Lin, B. Liu, B. J. Liu, C. X. Liu, D. Liu, D. Y. Liu, F. H. Liu, Fang Liu, Feng Liu, H. B. Liu, H. M. Liu, Huanhuan Liu, Huihui Liu, J. B. Liu, J. Y. Liu, K. Liu, K. Y. Liu, Ke Liu, L. Y. Liu, Q. Liu, S. B. Liu, T. Liu, X. Liu, X. Y. Liu, Y. B. Liu, Z. A. Liu, Zhiqing Liu, Y. F. Long, X. C. Lou, H. J. Lu, J. D. Lu, J. G. Lu, Y. Lu, Y. P. Lu, C. L. Luo, M. X. Luo, P.W. Luo, T. Luo, X. L. Luo, S. Lusso, X. R. Lyu, F. C. Ma, H. L. Ma, L. L. Ma, M.M. Ma, Q. M. Ma, X. N. Ma, X. X. Ma, X. Y. Ma, Y. M. Ma, F. E. Maas, M. Maggiora, S. Maldaner, S. Malde, Q. A. Malik, A. Mangoni, Y. J. Mao, Z. P. Mao, S. Marcello, Z. X. Meng, J. G. Messchendorp, G. Mezzadri, J. Min, T. J. Min, R. E. Mitchell, X. H. Mo, Y. J. Mo, C. Morales Morales, N. Yu. Muchnoi, H. Muramatsu, A. Mustafa, S. Nakhoul, Y. Nefedov, F. Nerling, I. B. Nikolaev, Z. Ning, S. Nisar, S. L. Niu, S. L. Olsen, Q. Ouyang, S. Pacetti, Y. Pan, M. Papenbrock, P. Patteri, M. Pelizaeus, H. P. Peng, K. Peters, J. Pettersson, J. L. Ping, R. G. Ping, A. Pitka, R. Poling, V. Prasad, H. R. Qi, M. Qi, T. Y. Qi, S. Qian, C. F. Qiao, N. Qin, X. P. Qin, X. S. Qin, Z. H. Qin, J. F. Qiu, S. Q. Qu, K. H. Rashid, K. Ravindran, C. F. Redmer, M. Richter, A. Rivetti, V. Rodin, M. Rolo, G. Rong, Ch. Rosner, M. Rump, A. Sarantsev, M. Savrié, Y. Schelhaas, K. Schoenning, W. Shan, X. Y. Shan, M. Shao, C. P. Shen, P. X. Shen, X. Y. Shen, H. Y. Sheng, X. Shi, X. D. Shi, J. J. Song, Q. Q. Song, X. Y. Song, S. Sosio, C. Sowa, S. Spataro, F. F. Sui, G. X. Sun, J. F. Sun, L. Sun, S. S. Sun, X. H. Sun, Y. J. Sun, Y. K. Sun, Y. Z. Sun, Z. J. Sun, Z. T. Sun, Y. T. Tan, C. J. Tang, G. Y. Tang, X. Tang, V. Thoren, B. Tsednee, I. Uman, B. Wang, B. L. Wang, C.W. Wang, D. Y. Wang, K. Wang, L. L. Wang, L. S. Wang, M. Wang, M. Z. Wang, Meng Wang, P. L. Wang, R. M. Wang, W. P. Wang, X. Wang, X. F. Wang , X. L. Wang, Y. Wang, Y. Wang, Y. F. Wang, Y. Q. Wang, Z. Wang, Z. G. Wang, Z. Y. Wang, Zongyuan Wang, T. Weber, D. H. Wei, P. Weidenkaff, F. Weidner, H.W. Wen, S. P. Wen, U. Wiedner, G. Wilkinson, M. Wolke, L. H. Wu, L. J. Wu, Z. Wu, L. Xia, Y. Xia, S. Y. Xiao, Y. J. Xiao, Z. J. Xiao, Y. G. Xie, Y. H. Xie, T. Y. Xing, X. A. Xiong, Q. L. Xiu, G. F. Xu, J. J. Xu, L. Xu, Q. J. Xu, W. Xu, X. P. Xu, F. Yan, L. Yan, W. B. Yan, W. C. Yan, Y. H. Yan, H. J. Yang, H. X. Yang, L. Yang, R. X. Yang, S. L. Yang, Y. H. Yang, Y. X. Yang, PHYSICAL REVIEW LETTERS 124, 032002 (2020)

Using a total of 11.0 fb −1 of e þ e − collision data with center-of-mass energies between 4.009 and 4.6 GeV and collected with the BESIII detector at BEPCII, we measure fifteen exclusive cross sections and effective form factors for the process e þ e − → Ξ −Ξþ by means of a single baryon-tag method. After performing a fit to the dressed cross section of e þ e − → Ξ −Ξþ , no significant ψð4230Þ or ψð4260Þ resonance is observed in the Ξ −Ξþ final states, and upper limits at the 90% confidence level on Γ ee B for the processes ψð4230Þ=ψð4260Þ → Ξ −Ξþ are determined. In addition, an excited Ξ baryon at 1820 MeV=c 2 is observed with a statistical significance of 6.2-6.5σ by including the systematic uncertainty, and the mass and width are measured to be M ¼ ð1825. 5  In the last decade, a series of charmonium-like states have been observed at e þ e − colliders. The study of the production of charmonium-like states with the quantum number J PC ¼ 1 −− above the open charm threshold in e þ e − annihilations and their subsequent two-body hadronic decays provides a test for QCD calculations [1,2]. According to potential models, there are five vector charmonium states between the 1D state ½ψð3773Þ and 4.7 GeV=c 2 , namely, the 3S, 2D, 4S, 3D, and 5S states [1]. From experimental studies, besides the three well-established structures observed in the inclusive hadronic cross section [3], i.e., ψð4040Þ, ψð4160Þ, and ψð4415Þ, five new states, i.e., ψð4230Þ, ψð4260Þ, ψð4360Þ, ψð4634Þ, and ψð4660Þ have been reported in initial state radiation (ISR) processes, i.e., e þ e − → γ ISR π þ π − J=ψ or e þ e − → γ ISR π þ π − ψð3686Þ at the BABAR [4] and Belle [5], or in direct production processes at the CLEO [6] and BESIII experiments [7]. Surprisingly, up to now, no evidence for baryon antibaryon pairs above open charm production associated with these states has been found except for the ψð4634Þ resonance observed in Λ þ cΛ − c [8]. Although the BESIII Collaboration previously performed a search for baryonic decays of ψð4040Þ [9], including Ξ −Ξþ final states based on a full reconstruction method, no candidates were observed. The overpopulation of structures in this mass region and the mismatch of the properties between the potential model predictions and experimental measurements make them good candidates for exotic states. Various scenarios, which interpret one or some of them as hybrid states, tetraquark states, or molecular states [10], have been proposed.
The electromagnetic structure of hadrons, parametrized in terms of electromagnetic form factors (EMFFs) [11], provides a key to understanding QCD effects in bound states. While the nucleon has been studied rigorously for more than sixty years, new techniques and the availability of data with larger statistics from modern facilities have given rise to a renewed interest in the field, i.e., the proton radius puzzle [16]. The access to hyperon structure by EMFFs provides an extra dimension that inspires measurements of exclusive cross sections and EMFFs for baryon antibaryon pairs above open charm threshold.
The constituent quark model has been very successful in describing the ground state of the flavor SU(3) octet and decuplet baryons [3,17]. However, some observed excited states do not agree well with the theoretical prediction. It is thus important to study such unusual states, both to probe the limitation of the quark models and to spot unrevealed aspects of the QCD description of the structure of hadron resonances. Intriguingly, the Ξ resonances with strangeness S ¼ −2 may provide important information on the latter aspect. Although there has been significant progress in the experimental studies of charmed baryons by the BABAR [18], LHCb [19], and Belle [20,21] Collaborations, doubly charm baryons by the LHCb Collaboration [22], doubly strange baryons by the Belle Collaboration [23], the studies of excited Ξ states are still sparse [3]. Neither the first radial excitation with spin parity of J P ¼ 1 2 þ nor a first orbital excitation with J P ¼ 1 2 − have been identified. Determination of the resonance parameters of the first excited state is a vital test of our understanding of the structure of Ξ resonances, where one of candidates for the first excited state is Ξð1690Þ with a three-star rating on a four-star scale [3], the second one is Ξð1620Þ with one-star rating, and another excited state is Ξð1820Þ with a three-star rating [3], for which the spin was previously determined to be J ¼ 3 2 [24], and subsequently the parity was determined to be negative and the spin parity confirmed to be J P ¼ 3 2 − by another experiment [25].
In this Letter, we present a measurement of the Born cross section and the effective form factors (EFF) [11] for the process e þ e − → Ξ −Ξþ , an estimation of the upper limit on Γ ee B[ψð4230Þ=ψð4260Þ → Ξ −Ξþ ] at the 90% confidence level (C.L.), and the observation of an excited Ξ baryon at 1820 MeV=c 2 . The dataset used in this analysis corresponds to a total of 11.0 fb −1 of e þ e − collision data [11] collected at center-of-mass (c.m.) energies from 4.009 to 4.6 GeV with the BESIII detector [26] at BEPCII [27].
The selection of e þ e − → Ξ −Ξþ events with a full reconstruction method has low-reconstruction efficiency. Here, to achieve higher efficiency, a single baryon Ξ − tag technique is employed, i.e., only one Ξ − baryon is reconstructed by the π − Λ decay mode with Λ → pπ − , and the antibaryonΞ þ is extracted from the recoil side (unless otherwise noted, the charge-conjugate state of the Ξ − mode is included by default below). To determine the detection efficiency for the decay e þ e − → Ξ −Ξþ , 100 k simulated events are generated for each of 15 energy points in the range of 4.009 to 4.6 GeVaccording to phase space using the KKMC generator [28], which includes the ISR effect. The Ξ − is simulated in its decay to the π − Λ mode with the subsequent decay Λ → pπ − via EvtGen [29], and the antibaryons are allowed to decay inclusively. The response of the BESIII detector is modeled with Monte Carlo (MC) simulations using a framework based on GEANT4 [30]. Large simulated samples of generic e þ e − → hadrons events ("inclusive MC") are used to estimate background conditions.
Charged tracks are required to be reconstructed in the main drift chamber (MDC) with good helical fits and within the angular coverage of the MDC: j cos θj < 0.93, where θ is the polar angle with respect to the e þ beam direction. Information from the specific energy deposition (dE=dx) measured in the MDC combined with the time of flight (TOF) is used to form particle identification (PID) confidence levels for the hypotheses of a pion, kaon, and proton. Each track is assigned to the particle type with the highest C.L. Events with at least two negatively charged pions and one proton are kept for further analysis.
To reconstruct Λ candidates, a secondary vertex fit is applied to all pπ − combinations; the ones characterized by χ 2 < 500 with 3 degrees of freedom are kept for further analysis. The pπ − invariant mass is required to be within 5 MeV=c 2 of the nominal Λ mass, determined by optimizing the figure of merit S= ffiffiffiffiffiffiffiffiffiffiffiffi S þ B p based on the MC simulation, where S is the number of signal MC events and B is the number of the background events expected from simulation. To further suppress background from non-Λ events, the Λ decay length is required to be greater than zero, where negative decay lengths are caused by the limited detector resolution.
The Ξ − candidates are reconstructed with a similar strategy using a secondary vertex fit, and the candidate with the minimum value of jM π − Λ − m Ξ − j from all π − Λ combinations is selected, where M π − Λ is the invariant mass of the π − Λ pair, and m Ξ − is the nominal mass of Ξ − from the PDG [3]. Further M π − Λ is required to be within 10 MeV=c 2 of the nominal Ξ − mass, and the Ξ − decay length L Ξ − (cm) is required to be greater than zero.
To obtain the antibaryon candidatesΞ þ , we use the distribution of mass recoiling against the selected π − Λ system, where E π − Λ and ⃗p π − Λ are the energy and momentum of the selected π − Λ candidate in the c.m. system, and ffiffi ffi s p is the PHYSICAL REVIEW LETTERS 124, 032002 (2020) 032002-4 c.m. energy. Figure 1 shows the distribution of M π − Λ versus M recoil π − Λ for all 15 considered energy points. The signal yields for the decay e þ e − → Ξ −Ξþ at each energy point are determined by performing an extended maximum likelihood fit to the M recoil π − Λ spectrum in the range from 1.2 to 1.5 GeV=c 2 . In the fit, the signal shape for the decay e þ e − → Ξ −Ξþ at each energy point is represented by the simulated MC shape. After applying the same event selection as the data on the inclusive MC samples at each c.m. energy, it is found that few background events remain at each energy point coming from e þ e − → π þ π − J=ψ, J=ψ → ΛΛ events, and they are distributed smoothly in the region of interest and can be described by a second-order polynomial function. Figure 2 shows the M recoil π − Λ distributions for the decay e þ e − → Ξ −Ξþ at each energy point.
The Born cross section for e þ e − → Ξ −Ξþ is calculated by where N obs is the number of the observed signal events, L is the integrated luminosity related to the c.m. energy, (1 þ δ) is the ISR correction factor [31], 1=ðj1 − Πj 2 Þ is the vacuum polarization correction factor [32], ϵ is the detection efficiency, and BðΞ → π − ΛÞ and BðΛ → pπ − Þ are the branching fractions taken from the PDG [3]. The ISR correction factor is obtained using the QED calculation as described in Ref. [33] and taking the formula used to fit the cross section measured in this analysis parametrized after two iterations as input. The measured cross sections and EFFs are shown in Fig. 3 and summarized in the Supplemental Material [11]. The Supplemental Material also contains the details of the cross section and EFF calculations. A maximum likelihood method is used to fit the dressed cross section σ dressed ¼ σ B =j1 − Πj 2 , for the process e þ e − → Ξ −Ξþ parametrized as the coherent sum of a power-law function plus a Breit-Wigner (BW) function for ψð4230Þ or ψð4260Þ,  where the mass M and total width Γ are fixed to the ψð4230Þ=ψð4260Þ resonance with PDG values [3], ϕ is the relative phase between the BW function, and power function, n is a free fit parameter, and Pð ffiffi ffi s p Þ is the two-body phase space factor. The ψð4230Þ and ψð4260Þ → Ξ −Ξþ processes are found to be not significant. Therefore, upper limits on the products of the twoelectron partial width and the branching fractions of ψð4230Þ and ψð4260Þ → Ξ −Ξþ ðΓ ee BÞ at the 90% credible level are estimated using a Bayesian approach [34] to be Γ ee B ψð4230Þ < 0.33×10 −3 eV and Γ ee B ψð4260Þ < 0.27× 10 −3 eV taking into account the systematic uncertainty described later. Here the masses and widths of ψð4230Þ and ψð4260Þ are changed by all combinations of AE1σ, and the estimation of the upper limits repeated. The largest ones are taken as the final results. Figure 3 shows the fit to the dressed cross section assuming the ψð4230Þ or the ψð4260Þ resonance and without resonance assumption. Including systematic uncertainties, the significance for both resonances is calculated to be ∼2.7σ.
Based on the selected data for the sum of 15 energy points, an excited Ξ baryon is observed in the M recoil π − Λ range from 1.6 to 2.1 GeV=c 2 . Figure 4 shows a fit to the recoil mass spectrum of π − Λ, where the signal is described by a BW function convolved with a double Gaussian function, and the background is described by a 2nd order Chebyshev polynomial, where the resolution width of Gaussian function is fixed according to the MC simulation. The number of signal events is 288 þ125 −85 , and the mass and width are measured to be M ¼ ð1825.5 AE 4.7Þ MeV=c 2 and Γ ¼ ð17.0 AE 15.0Þ MeV, where the uncertainties are statistical only. The statistical significance of the 1820 MeV=c 2 resonance is estimated to be 6.2-6.5σ with including the systematic uncertainty.
Systematic uncertainties on the measurements of the cross section originate from the luminosity measurement, branching fractions of Ξ − → π − Λ and Λ → pπ − , detection efficiency, ISR correction factor, line-shape structure, angular distribution, and the fit procedure. The uncertainty due to the vacuum polarization is negligible. The integrated luminosity is measured with a precision of 1.0% [12]. The branching fraction uncertainties for Ξ − → π − Λ and Λ → pπ − are 0.1% and 0.8% from the PDG [3]. The systematic sources of the uncertainty for the detection efficiency include the Ξ − reconstruction, the mass windows of Ξ − =Λ, and the decay lengths of Ξ − =Λ. The Ξ − reconstruction is studied using the same method as described in Ref. [38], and an uncertainty of 6.6% is found. The mass windows of Ξ − and Λ are studied by varying the nominal requirements by 5.0 MeV=c 2 , which yield uncertainties of 0.7% and 3.2%, respectively. The decay lengths of Λ and Ξ − are studied with and without the nominal requirements, and the uncertainties are estimated to be 1.5% and 1.7%, respectively. For the ISR correction factor, we iterate the cross section measurement until ð1 þ δÞϵ converges as described in Ref. [39]. The change due to the different criteria for convergence is taken as the systematic uncertainty. The uncertainty due to the lineshape structure is estimated to be 4.8% with the assumption of ψð4230Þ=ψð4260Þ → Ξ −Ξþ . The uncertainty due to the angular distribution is estimated to be 4.0% by weighting the cos θ Ξ difference for each bin between the data and the phase space MC model, where the θ Ξ is the angle between Ξ and the beam directions in the e þ e − c.m. system [38]. The systematic sources of the uncertainty in the fit of the M recoil π − Λ spectrum include the fitting range, the polynomial shape, the mass resolution, the signal shape the mass windows of Ξ − =Λ, and the decay lengths of Ξ − =Λ. The uncertainty due to the fit range is estimated to be 3.3% by varying the mass range by AE50 MeV=c 2 . The uncertainty due to the polynomial function is estimated to be 3.3% by alternative fits with a third-or a first-order polynomial function. The mass resolution is studied by varying the nominal signal shape convolved with a Gaussian function, and the yield difference is taken as a systematic uncertainty, which is 4.0%. The effect due to the signal shape is studied by varying the resolution in the convolution of the Breit-Wigner with a Gaussian function. This gives an uncertainty of 3.2%. The effect of the MC statistics on the used signal shape is studied by using a MC sample with only 10% of the events compared to the nominal fit, and the uncertainty is 0.5%. Assuming all sources to be independent, the total systematic uncertainty on the cross section measurement for e þ e − → Ξ −Ξþ is determined to be 12.7% by the quadratic sum of these sources. Systematic uncertainties on the measurements of the mass and width for the excited Ξ state mainly originate from the fit range, the background shape, the mass resolution, and the signal shape. The fit range, the background, and signal shapes are studied with the same method as above with mass uncertainties of 1.5, 1.3, and 1.9 MeV=c 2 , and width uncertainties of 5.6, 3.4, and 4.5 MeV, respectively. The mass uncertainty due to the mass resolution is determined to be 3.8 MeV=c 2 by calibrating the resolution difference in the Ξ − mass region with the full data sample. The total systematic uncertainties of mass and width are calculated to be 4.7 MeV=c 2 and 7.9 MeV, respectively, by summing independent systematic sources in quadrature.
In summary, using a total of 11.0 fb −1 of e þ e − collision data above the open-charm threshold collected with the BESIII detector at the BEPCII collider, we have studied the process e þ e − → Ξ −Ξþ based on a single baryon tag technique. We have measured fifteen exclusive Born cross sections and EFFs in the range from 4.009 to 4.6 GeV=c 2 , where the form factors for the process e þ e − → Ξ −Ξþ have not been previously measured due to limited statistics. A fit to the dressed cross section for e þ e − → Ξ −Ξþ with the assumptions of a power-law dependence for continuum plus a ψð4230Þ or ψð4260Þ resonance is performed, and no significant signal for the processes ψð4230Þ or ψð4260Þ → Ξ −Ξþ is observed. The upper limits on the products of the electronic partial width and the branching fractions of ψð4230Þ and ψð4260Þ → Ξ −Ξþ are measured to be Γ ee B ψð4230Þ < 0.33 × 10 −3 eV and Γ ee B ψð4260Þ <0.27× 10 −3 eV at 90% C.L., which may help to understand the nature of ψð4260Þ [40,41]. In particular, charmless decays of the ψð4260Þ are expected by the hybrid model [41]. In addition, an excited Ξ baryon at ∼1820 MeV=c 2 is observed with a statistical significance of 6.2-6.5σ by including the systematic uncertainty, and the mass and width are measured to be M ¼ ð1825.5 AE 4.7 AE 4.7Þ MeV=c 2 and Γ ¼ ð17.0 AE 15.0 AE 7.9Þ MeV, which are consistent with the mass and width of Ξð1820Þ − obtained from the PDG [3] within 1σ uncertainty. The results shed light on the structure of hyperon resonances with strangeness S ¼ −2.