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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.
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Keywords:
- Yangian algebra /
- the decay channel /
- quantum entanglement
[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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[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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