Sequential Two-body Decay Research Articles

Probing CP symmetry and weak phases with entangled double-strange baryons

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) symmetry1. 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 antiparticle2{bar{{Xi }}}^{+}, has enabled a direct determination of the weak-phase difference, (ξP − ξS) = (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 methods3. Finally, we provide an independent measurement of the recently debated Λ decay parameter αΛ (refs. 4,5). The {Lambda }bar{{Lambda }} asymmetry is in agreement with and compatible in precision to the most precise previous measurement4.

Nondiagonal pair of Majorana particles at e+e− colliders

We perform a comprehensive and model-independent analysis for characterizing the spin and dynamical structure of the production of a non-diagonal pair of Majorana particles with different masses and arbitrary spins, $e^-e^+\to X_2 X_1$, followed by a sequential two-body decay, $X_2\to Z X_1$, of the heavier particle $X_2$ into a $Z$ gauge boson and the lighter particle $X_1$ escaping undetected at high-energy $e^+e^-$ colliders. Standard leptonic $Z$-boson decays, $Z\to \ell^-\ell^+$ with $\ell=e$ or $\mu$, are employed for precisely diagnosing the $Z$ polarization influenced by the production and decay processes. Based on helicity formalism and Wick helicity rotation for describing the correlated production-decay amplitudes and distributions, we work out the implications on the amplitudes and distributions of discrete CP symmetry and the Majorana condition that two particles are their own anti-particles. For the sake of a concrete illustration, an example of this type in the minimal supersymmetric Standard Model is investigated in detail.

INTERFERENCE EFFECTS, TIME REVERSAL VIOLATION AND SEARCH FOR NEW PHYSICS IN HADRONIC WEAK DECAYS

We propose some methods for studying hadronic sequential two-body decays involving more spinning particles. It relies on the analysis of T-odd and T-even asymmetries, which are related to interference terms. The latter asymmetries turn out to be as useful as the former ones in inferring time reversal violating observables; these in turn may be sensitive, under some particular conditions, to possible contributions beyond the standard model. Our main result is that one can extract such observables even after integrating the differential decay width over almost all of the available angles. Moreover we find that the correlations based exclusively on momenta are quite general, since they provide as much information as those involving one or more spins. We generalize some methods already proposed in the literature for particular decay channels, but we also pick out a new kind of time reversal violating observables. Our analysis could be applied, for example, to data of LHCb experiment.

The 10B+d→ α+ α+ α reaction

The reaction 10B+d→ α+ α+ α is studied at deuteron bombarding energy of 0.40 MeV with the 12C compound nucleus formed at an excitation around the 25 MeV giant resonance. Two of the α-particles in the final state are detected in coincidence by two solid-state detectors. For the presentation of the experimental data, a new method has been employed. The reaction mechanism is found to be sequential two-body decay involving the 0 + ground state and the 2 +, 2.9 MeV first excited state of 8Be. Contributions from simultaneous decay in three alphas or other energetically possible excited states of 8Be up to 17 MeV are not present in the experimental results. The triple differential cross-section d 3σ dS dΩ 1 dΩ 2 is measured.

The 7Li+d → α+ α+n reaction

The reaction 7Li+d → α+ α+n is studied at deuteron bombarding energy 0.380 MeV. The 9Be compound nucleus is formed with an excitation around 17 MeV. The two α-particles are detected in coincidence by two solid state detectors. Thus, the kinematics of the reaction are completely determined and discrimination between sequential two-body decay and direct three-body decay is possible. The reaction mechanism is found to be sequential two-body decay involving the ground and broad first excited states of 5He. Contributions from the direct three-body decay and the sequential two-body decay involving the 8Be, J π = 4 + second excited state, if at all present, are not more than a few percent of the total reaction output. Kinematically possible contributions from the 8Be ground, J π = 0 + and the 2.9 MeV, J π = 2 + excited state fall within the energy region excluded by the apparatus.

Three α-particle decay of C 12

The reaction B 11(p, 2α)He 4 has been studied at proton bombarding energies of 2.0, 2.65, 3.25, 3.73, 4.00, 5.08 and 5.64 MeV. These energies excite several resonantstates in C 12. The kinematics of the reaction were completely determined by detecting in coincidence two of the three final α-particles in solid-state detectors. This determination of the kinematics permitted discrimination between sequential two-body decay and direct three-body decay. The reaction mechanism was found to be sequential two-body decay involving the ground and the broad first-excited states of Be 8, with events involving the latter showing strong interference effects. These interference effects were attributable to the identity of the three final particles and to the ambiguity of the order of their emission. Not more than 5 % of the experimental cross section could be attributed to the direct three-body decay mechanism; indeed, the contribution from the direct process is probably much smaller than the quoted 5 %. Hence, the conclusion must be that, for C 12 with an excitation energy between 17 and 21 MeV, the decay mechanism is predominantly sequential two-body decay. Also the total cross section for this reaction is of the order of 100 to 200 mb; thus it is comparable to the geometric cross section. These two facts imply that, in this energy region, C 12 has a strong cluster configuration of an α-particle plus a Be 8 nucleus in either the ground or the first-excited state.

Evidence for sequential two-body decay in the C 12(d; p, n)C 12 reaction

The C 12(d; p, n) reaction has been studied using the Rice University high resolution 180° magnetic spectrometer for deuteron energies of 4.66, 4.90 and 5.46 MeV. No evidence was found for the existence of a density of states cusp near the neutron threshold similar to that seen in the Be 9(p; p′, n)Be 8 reaction studied by Spencer et al. 1). However, broad proton groups were observed at energies which correspond to the two-body sequential decay C 12+ d→ N 14∗→ N 13∗ + n→ C 12+ n+ p . Two excited states in N 13 involved in this were the known 3.51 and 3.56 MeV states. The proton groups show broadening and energy shifting due to the motion of the intermediate N 13 nucleus. Theoretical line shapes have been calculated to compare with these data. The groups occur at proton energies of approximately 1.01, 1.04 and 1.08 MeV, with each broad group possesing a doublet structure with approximate widths at half height of 60, 50 and 90 keV corresponding to the deuteron bombarding energies of 4.66, 4.90 and 5.46 MeV respectively. No evidence for states at 5.51 and 6.10 MeV in C 13 was observed.