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Yangian代数在混合介子态的纠缠和衰变中的应用

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

Qin Li-Guo, Tian Li-Jun, Wu Shi-Chao
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• #### 摘要

Yangian代数是超出李代数更大的无穷维代数, 是研究非线性量子完全可积系统的新对称特性有力数学工具. 基于介子态中夸克-味su(3)对称性和Yangian代数生成元的跃迁特性, 本文研究了Yangian代数Y(su(3))生成元在三种正反介子态(, K, K0 和K0)各自组成的三种混合介子态(, K和Ki0) 衰变中的作用. 将Y(su(3)) 代数的八个生成元(Ī, Ŭ, V, Ī3和Ī8)作为跃迁算子, 作用在混合介子态上, 研究其可能的衰变道, 以及衰变前后纠缠度的变化. 结果表明: (i)在李代数范围内的生成元Ī3和Ī8作用下, 三种混合介子态衰变后组成成份没有发生变化, 其中混合介子态 在Ī8作用下衰变前后纠缠无变化, 其他衰变纠缠度发生了变化. (ii)在其他的六个(Ī, Ŭ和V)超出李代数的生成元的作用下, 三种混合介子态衰变前后组成成份发生了变化, 其中两个衰变后变成 单态, 纠缠度为零; 两个衰变不存在; 剩余两个衰变后纠缠度发生了变化. 此外在带电(K)和中性(Ki0)两类K型混合介子态的六种可能的衰变中, 两种类型的末态的纠缠度两两相同. (iii)三种混合介子态之间可以通过Ī, Ŭ和V算子循环转化, 具有明显的对称性. 本文从具有的对称性上提供了一种探索混合介子态可能衰变的方法, 并且可以用此方法去预测可能的未知衰变粒子和解释已测得的衰变问题.

#### Abstract

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(, K and Ki0) composed of the three positiVe and negatiVe meson states (, K, K0 and K0). As the transition operators, the eight generators (Ī, Ŭ, V, Ī3 and Ī8) 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: (i) Under the effects of Ī3 and Ī8 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 with the effect of Ī^8, and the others are changed. (ii) Under the effects of the other six generators (Ī, Ŭ and V) 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 (K0, K0) meson states, are the same two by two. (iii) The three mixed meson states can be circularly transferred by the operators Ī, Ŭ and V, 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.

#### 作者及机构信息

###### 通信作者: 秦立国, lgqin@foxmail.com
• 基金项目: 上海远程教育集团学科研究课题量子代数在量子关联和量子保真度中的应用(批准号: JF1406)和国家自然科学基金(批准号: 11347147, 11075101)资助的课题.

#### Authors and contacts

###### Corresponding author: Qin Li-Guo, lgqin@foxmail.com
• Funds: Project supported by the Shanghai Distance Education Group Discipline Research Subject(Grant No. JF1406) and the National Natural Science Foundation of China (Grant Nos. 11347147, 11075101).

#### 参考文献

 [1] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865 [2] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [3] Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 [4] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881 [5] Curty M, Lewenstein M, Lkenhaus N 2004 Phys. Rev. Lett. 92 217903 [6] Beige A, Braun D, Tregenna B, Knight P L 2001 Phys. Rev. Lett. 85 1762 [7] Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 83 4888 [8] Childs A M, Chuang I L 2000 Phys. Rev. A 63 012306 [9] Langford N K, Dalton R B, Harvey M D, Brien J L, Pryde G J, Gilchrist A, Bartlett S D, White A G 2004 Phys. Rev. Lett. 93 053601 [10] Pasquinucci H B, Peres A 2000 Phys. Rev. Lett. 85 3313 [11] Brukner Č, Zukowski M, Zeilinger A 2002 Phys. Rev. Lett. 89 197901 [12] Ralph T C, Resch K, Gilchrist A 2007 Phys. Rev. A 75 022313 [13] Collins D, Gisin N, Linden N, Massar S, Popescu S 2002 Phys. Rev. Lett. 88 040404 [14] Gell-Mann M, Pais A 1955 Phys. Rev. 97 1387 [15] Feldmann T, Kroll P 1998 Phys. Rev. D 58 114006 [16] Magiera A, Machner H 2000 Nucl. Phys. A 674 515 [17] Kroll P 2005 Modern Phys. Lett. A 20 2667 [18] Shi Y 2006 Phys. Lett. B 641 75 [19] Shi Y, Wu Y L 2008 Eur. Phys. J. C 55 477 [20] Tian L J, Jin Y L, Jiang Y, Qin L G, 2011 Eur. Phys. J. C 71 1528 [21] Uglov D 1998 Commun. Math. Phys. 191 663 [22] Kundu A 1998 Phys. Lett. A 249 126 [23] Bernard D 1993 Inter. J. Modern Phys. B 7 3517 [24] Tian L J, Qin L G, Jiang Y, Zhang H B, Xue K 2010 Commun. Theor. Phys. 53 1039 [25] Tian L J, Qin L G 2010 Eur. Phys. J. D 57 123 [26] Polychronakos A 1992 Phys. Rev. Lett. 69 703 [27] Haldane F D M, Ha Z N C, Talstra J C, Bernard D, Pasquier V 1992 Phys. Rev. Lett. 69 2021 [28] Haldane F D M 1994 arXiv:cond-mat/9401001v3 [29] Wadati M 1988 Phys. Rev. Lett. 60 635 [30] Ge M L, Wang Y 1995 Phys. Rev. E 2919 [31] Qin L G, Tian L J, Yang G H 2012 Eur. Phys. J. C 72 1934 [32] Qin L G, Tian L J, Jiang Y, Zhang H B 2012 Chin. Phys. B 21 057101 [33] Tian L J, Jin Y L, Jiang Y 2010 Phys. Lett. B 686 207 [34] Gell-Mann M 1962 Phys. Rev. 125 1067 [35] Neman Y 1961 Nucl. Phys. 26 222 [36] Chari V, Pressley A 1990 Yangian and R-Matrix. L'Enseignement Matematique 36 p267 [37] Chari V, Pressley A 1994 A Guide to Quantum Groups (Cambridge: Cambrige University Press) [38] Bai C M, Ge M L, Xue K 1998 Physical meaning of Yangian representation of Chari and Pressley, TH 1998-07, Tianjin, China [39] Pan F, Lu G Y, Draayer J P 2006 Inter. J. Modern Phys. B 20 1333

#### 施引文献

•  [1] Horodecki R, Horodecki P, Horodecki M, Horodecki K 2009 Rev. Mod. Phys. 81 865 [2] Nielsen M A, Chuang I L 2000 Quantum Computation and Quantum Information (Cambridge: Cambridge University Press) [3] Bennett C H, Brassard G, Crpeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895 [4] Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881 [5] Curty M, Lewenstein M, Lkenhaus N 2004 Phys. Rev. Lett. 92 217903 [6] Beige A, Braun D, Tregenna B, Knight P L 2001 Phys. Rev. Lett. 85 1762 [7] Viola L, Knill E, Lloyd S 1999 Phys. Rev. Lett. 83 4888 [8] Childs A M, Chuang I L 2000 Phys. Rev. A 63 012306 [9] Langford N K, Dalton R B, Harvey M D, Brien J L, Pryde G J, Gilchrist A, Bartlett S D, White A G 2004 Phys. Rev. Lett. 93 053601 [10] Pasquinucci H B, Peres A 2000 Phys. Rev. Lett. 85 3313 [11] Brukner Č, Zukowski M, Zeilinger A 2002 Phys. Rev. Lett. 89 197901 [12] Ralph T C, Resch K, Gilchrist A 2007 Phys. Rev. A 75 022313 [13] Collins D, Gisin N, Linden N, Massar S, Popescu S 2002 Phys. Rev. Lett. 88 040404 [14] Gell-Mann M, Pais A 1955 Phys. Rev. 97 1387 [15] Feldmann T, Kroll P 1998 Phys. Rev. D 58 114006 [16] Magiera A, Machner H 2000 Nucl. Phys. A 674 515 [17] Kroll P 2005 Modern Phys. Lett. A 20 2667 [18] Shi Y 2006 Phys. Lett. B 641 75 [19] Shi Y, Wu Y L 2008 Eur. Phys. J. C 55 477 [20] Tian L J, Jin Y L, Jiang Y, Qin L G, 2011 Eur. Phys. J. C 71 1528 [21] Uglov D 1998 Commun. Math. Phys. 191 663 [22] Kundu A 1998 Phys. Lett. A 249 126 [23] Bernard D 1993 Inter. J. Modern Phys. B 7 3517 [24] Tian L J, Qin L G, Jiang Y, Zhang H B, Xue K 2010 Commun. Theor. Phys. 53 1039 [25] Tian L J, Qin L G 2010 Eur. Phys. J. D 57 123 [26] Polychronakos A 1992 Phys. Rev. Lett. 69 703 [27] Haldane F D M, Ha Z N C, Talstra J C, Bernard D, Pasquier V 1992 Phys. Rev. Lett. 69 2021 [28] Haldane F D M 1994 arXiv:cond-mat/9401001v3 [29] Wadati M 1988 Phys. Rev. Lett. 60 635 [30] Ge M L, Wang Y 1995 Phys. Rev. E 2919 [31] Qin L G, Tian L J, Yang G H 2012 Eur. Phys. J. C 72 1934 [32] Qin L G, Tian L J, Jiang Y, Zhang H B 2012 Chin. Phys. B 21 057101 [33] Tian L J, Jin Y L, Jiang Y 2010 Phys. Lett. B 686 207 [34] Gell-Mann M 1962 Phys. Rev. 125 1067 [35] Neman Y 1961 Nucl. Phys. 26 222 [36] Chari V, Pressley A 1990 Yangian and R-Matrix. L'Enseignement Matematique 36 p267 [37] Chari V, Pressley A 1994 A Guide to Quantum Groups (Cambridge: Cambrige University Press) [38] Bai C M, Ge M L, Xue K 1998 Physical meaning of Yangian representation of Chari and Pressley, TH 1998-07, Tianjin, China [39] Pan F, Lu G Y, Draayer J P 2006 Inter. J. Modern Phys. B 20 1333
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##### 出版历程
• 收稿日期:  2015-09-02
• 修回日期:  2015-10-18
• 刊出日期:  2016-01-20

## Yangian代数在混合介子态的纠缠和衰变中的应用

• 1. 上海开放大学嘉定分校, 上海 201800;
• 2. 中国科学院上海高等研究院, 上海 201210;
• 3. 上海大学物理系, 上海 200444
• ###### 通信作者: 秦立国, lgqin@foxmail.com
基金项目: 上海远程教育集团学科研究课题量子代数在量子关联和量子保真度中的应用(批准号: JF1406)和国家自然科学基金(批准号: 11347147, 11075101)资助的课题.

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