Applications of Yangian algebra in the entanglement and the decay channels of the mixed meson state

作者：Qin Li-Guo^*; Tian Li-Jun; Wu Shi-Chao

来源：Acta Physica Sinica, 2016, 65(2): 020201.

DOI：10.7498/aps.65.020201

• Yangian algebra
• the decay channel
• quantum entanglement

Yangian, as an algebra beyond the Lie algebra, is an infinite dimensional algebra and a powerful mathematical method for investigating the new symmetry of quantum systems which are nonlinear and integrable. Based on the su(3) symmetry of the quark-flavor in the meson states and the transition property of the generators in Yangian algebra, we study the applications of Yangian algebra Y(su(3)) in the decay of three mixed meson states (pi, K and K-i(0)) composed of the three positive and negative meson states (pi(+/-), K-+/-, K-0 and (K) over bar (0)). As the transition operators, the eight generators ((I) over tilde (+/-), (U) over tilde (+/-), (V) over tilde (+/-), (I) over tilde (3) and (I) over tilde (8)) of Yangian algebra Y(su(3)) are acting on the three mixed meson states, respectively. Then, the possible decay channels and the changes of the entanglement are studied. Results show: 1) Under the effects of (I) over tilde (3) and (I) over tilde (8) within the Lie algebra on the three mixed meson states, the compositions of the final states after decays of the three mixed meson states are not changed as compared with the initial state; the entanglement is not changed for the decay of the mixed meson state pi with the effect of (I) over tilde (8), and the others are changed; 2) under the effects of the other six generators ((I) over tilde (+/-), (U) over tilde (+/-) and (V) over tilde (+/-)) beyond the Lie algebra on the three mixed meson states, the compositions of the final states after the decay are changed compared with the initial state; in the six possible decay channels, the two final states become single states without entanglement; two decay channels are absent; and the entanglements of the final states in the remaining two decays are changed. In addition, the entanglement of the final meson states in the possible six decay channels of the two types K mixed meson states, the charged (K+, K-) and neutral (K-0, K-0) meson states, are the same two by two; 3) The three mixed meson states can be circularly transferred by the operators (I) over tilde (+/-), (U) over tilde (+/-) and (V) over tilde (+/-), implying the obvious symmetry. In this paper the Yangian method is presented to study the possible decay channels of the mixed meson states and may be used to present a possible interpretation of the new unknown or known particle in the decay of the mixed meson.

• 单位
  中国科学院; 上海大学