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We consider the problem of motion of a gyrostat under the action of potential and gyroscopic forces in the case where its gyrostatic moment is variable. We analyze the conditions of existence of linear invariant relations for equations of the Kirchhoff–Poisson class. A new solution of these equations is obtained in terms of the elementary functions of time.

Though immensely successful, the standard model of particle physics does not offer any explanation as to why our Universe contains so much more matter than antimatter. A key to a dynamically generated matter–antimatter asymmetry is the existence of processes that violate the combined charge conjugation and parity (CP) symmetry 1 . As such, precision tests of CP symmetry may be used to search for physics beyond the standard model. However, hadrons decay through an interplay of strong and weak processes, quantified in terms of relative phases between the amplitudes. Although previous experiments constructed CP observables that depend on both strong and weak phases, we present an approach where sequential two-body decays of entangled multi-strange baryon–antibaryon pairs provide a separation between these phases. Our method, exploiting spin entanglement between the double-strange Ξ − baryon and its antiparticle 2 Ξ ¯ + , has enabled a direct determination of the weak-phase difference, ( ξ P  −  ξ S ) = (1.2 ± 3.4 ± 0.8) × 10 −2  rad. Furthermore, three independent CP observables can be constructed from our measured parameters. The precision in the estimated parameters for a given data sample size is several orders of magnitude greater than achieved with previous methods 3 . Finally, we provide an independent measurement of the recently debated Λ decay parameter α Λ (refs.  4 , 5 ). The Λ Λ ¯ asymmetry is in agreement with and compatible in precision to the most precise previous measurement 4 . Using spin-entangled baryon–antibaryon pairs, the BESIII Collaboration reports on high-precision measurements of potential charge conjugation and parity (CP)-symmetry-violating effects in hadrons.

A bstract With data samples collected with the BESIII detector at seven energy points at s = 3 . 68 − 3 . 71 GeV, corresponding to an integrated luminosity of 333 pb − 1 , we present a study of the Λ transverse polarization in the e + e − → Λ Λ ¯ reaction. The significance of polarization by combining the seven energy points is found to be 2.6 σ including the systematic uncertainty, which implies a non-zero phase between the transition amplitudes of the Λ Λ ¯ helicity states. The modulus ratio and the relative phase of EM- psionic form factors combined with all energy points are measured to be R Ψ = 0.71 − 0.10 + 0.10 ± 0.03 and ∆Φ Ψ = 23 − 8.0 + 8.8 ± 1.6 ° , where the first uncertainties are statistical and the second systematic.

Using e + e − collision data corresponding to a total integrated luminosity of 12.9 fb − 1 collected with the BESIII detector at the BEPCII collider, the exclusive Born cross sections and the effective form factors of the reaction$$ {e}^{+}{e}^{-}\\to {\\Xi}^{-}{\\overline{\\Xi}}^{+} $$e + e − → Ξ − Ξ ¯ + are measured via the single baryon-tag method at 23 center-of-mass energies between 3.510 and 4.843 GeV. Evidence for the decay$$ \\psi (3770)\\to {\\Xi}^{-}{\\overline{\\Xi}}^{+} $$ψ 3770 → Ξ − Ξ ¯ + is observed with a significance of 4.5 σ by analyzing the measured cross sections together with earlier BESIII results. For the other charmonium(-like) states ψ (4040), ψ (4160), Y (4230), Y (4360), ψ (4415), and Y (4660), no significant signal of their decay to$$ {\\Xi}^{-}{\\overline{\\Xi}}^{+} $$Ξ − Ξ ¯ + is found. For these states, upper limits of the products of the branching fraction and the electronic partial width at the 90% confidence level are provided.

Using a sample of 1.31 × 10 9 J / ψ events collected with the BESIII detector, we perform a study of J / ψ → γ K K ¯ η ′ . X (2370) is observed in the K K ¯ η ′ invariant-mass distribution with a statistical significance of 8.3 σ . Its resonance parameters are measured to be M = 2341.6 ± 6.5 (stat.) ± 5.7 (syst.) MeV / c 2 and Γ = 117 ± 10 (stat.) ± 8 (syst.) MeV . The product branching fractions for J / ψ → γ X ( 2370 ) , X ( 2370 ) → K + K - η ′ and J / ψ → γ X ( 2370 ) , X ( 2370 ) → K S 0 K S 0 η ′ are determined to be ( 1.79 ± 0.23 (stat.) ± 0.65 (syst.) ) × 10 - 5 and ( 1.18 ± 0.32 (stat.) ± 0.39 (syst.) ) × 10 - 5 , respectively. No evident signal for X (2120) is observed in the K K ¯ η ′ invariant-mass distribution. The upper limits for the product branching fractions of B ( J / ψ → γ X ( 2120 ) → γ K + K - η ′ ) and B ( J / ψ → γ X ( 2120 ) → γ K S 0 K S 0 η ′ ) are determined to be 1.49 × 10 - 5 and 6.38 × 10 - 6 at the 90% confidence level, respectively.

A bstract Using 24.1 fb − 1 of e + e − collision data collected with the BESIII detector at the BEPCII collider, the Born cross sections and effective form factors of the e + e − → Σ + Σ ¯ − reaction are measured. The measurements are performed at center-of-mass energies ranging from 3.510 to 4.951 GeV. No significant evidence for the decay of the charmonium(-like) states, ψ (3770), ψ (4040), ψ (4160), Y (4230), Y (4360), ψ (4415), and Y (4660), into a Σ + Σ ¯ − final state is observed. Consequently, upper limits for the products of the branching fractions and the electronic partial widths at the 90% confidence level are reported for these decays.

The decay D→K-π+ is studied in a sample of quantum-correlated DD¯ pairs, based on a data set corresponding to an integrated luminosity of 2.93 fb-1 collected at the ψ(3770) resonance by the BESIII experiment. The asymmetry between CP-odd and CP-even eigenstate decays into K-π+ is determined to be AKπ=0.132±0.011±0.007, where the first uncertainty is statistical and the second is systematic. This measurement is an update of an earlier study exploiting additional tagging modes, including several decay modes involving a KL0 meson. The branching fractions of the KL0 modes are determined as input to the analysis in a manner that is independent of any strong phase uncertainty. Using the predominantly CP-even tag D→π+π-π0 and the ensemble of CP-odd eigenstate tags, the observable AKππππ0 is measured to be 0.130±0.012±0.008. The two asymmetries are sensitive to rDKπcosδDKπ, where rDKπ and δDKπ are the ratio of amplitudes and phase difference, respectively, between the doubly Cabibbo-suppressed and Cabibbo-favoured decays. In addition, events containing D→K-π+ tagged by D→KS,L0π+π- are studied in bins of phase space of the three-body decays. This analysis has sensitivity to both rDKπcosδDKπ and rDKπsinδDKπ. A fit to AKπ, AKππππ0 and the phase-space distribution of the D→KS,L0π+π- tags yields δDKπ=187.6-9.7+8.9-6.4+5.4∘, where external constraints are applied for rDKπ and other relevant parameters. This is the most precise measurement of δDKπ in quantum-correlated DD¯ decays.

A bstract Using e + e − collision data collected by the BESIII detector at BEPCII corresponding to an integrated luminosity of 30 fb − 1 , we measure Born cross sections and effective form factors for the process e + e − → Ξ 0 Ξ ¯ 0 at forty-five center-of-mass energies between 3.51 and 4.95 GeV. The dressed cross section is fitted, assuming a power-law function plus a charmonium(-like) state, i.e., ψ (3770), ψ (4040), ψ (4160), ψ (4230), ψ (4360), ψ (4415) or ψ (4660). No significant charmonium(-like) state decaying into Ξ 0 Ξ ¯ 0 is observed. Upper limits at the 90% confidence level on the product of the branching fraction and the electronic partial width are provided for each decay. In addition, ratios of the Born cross sections and the effective form factors for e + e − → Ξ 0 Ξ ¯ 0 and e + e − → Ξ − Ξ ¯ + are also presented to test isospin symmetry and the vector meson dominance model.

One of the fundamental goals of particle physics is to gain a microscopic understanding of the strong interaction. Electromagnetic form factors quantify the structure of hadrons in terms of charge and magnetization distributions. While the nucleon structure has been investigated extensively, data on hyperons are still scarce. It has recently been demonstrated that electron-positron annihilations into hyperon-antihyperon pairs provide a powerful tool to investigate their inner structure. We present a method useful for hyperon-antihyperon pairs of different types which exploits the cross section enhancement due to the effect of vacuum polarization at the J / ψ resonance. Using the 10 billion J / ψ events collected with the BESIII detector, this allows a precise determination of the hyperon structure function. The result is essentially a precise snapshot of the Λ ¯ Σ 0 ( Λ Σ ¯ 0 ) transition process, encoded in the transition form factor ratio and phase. Their values are measured to be R  = 0.860 ± 0.029(stat.) ± 0.015(syst.), Δ Φ Λ ¯ Σ 0 = ( 1.011 ± 0.094 ( stat. ) ± 0.010 ( syst. ) ) r a d and Δ Φ Λ Σ ¯ 0 = ( 2.128 ± 0.094 ( stat. ) ± 0.010 ( syst. ) ) r a d . Furthermore, charge-parity (CP) breaking is investigated in this reaction and found to be consistent with CP symmetry. Investigating the inner structure of baryons is important to further our understanding of the strong interaction. Here, the BESIII Collaboration extracts the absolute value of the ratio of the electric to magnetic form factors and its relative phase for e + e − → J/ ψ  →  Λ Σ decays, enhancing the signal thanks to the vacuum polarisation effect at the J/ ψ peak.

A bstract Using e + e − collision data collected with the BESIII detector at the BEPCII collider at center-of-mass energies between 3.510 and 4.914 GeV, corresponding to an integrated luminosity of 25 fb − 1 , we measure the Born cross sections for the process e + e − → K − Ξ ¯ + Λ / Σ 0 at thirty-five energy points with a partial-reconstruction strategy. By fitting the dressed cross sections of e + e − → K − Ξ ¯ + Λ / Σ 0 , evidence for ψ 4160 → K − Ξ ¯ + Λ is found for the first time with a significance of 4.4 σ , including systematic uncertainties. No evidence for other possible resonances is found. In addition, the products of electronic partial width and branching fraction for all assumed resonances decaying into K − Ξ ¯ + Λ / Σ 0 are determined.