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构造夸克间的有效的相互作用势函数是强子物理中的重要研究课题,也是学科前沿问题之一.本文对坐标空间中的Breit夸克势函数的完整形式实施消除奇异因子的替代方法,构造出一个有效的夸克势.除了第一项库仑势和第七项常数项势,对其他的项都需进行重新构造,即对第二项和第四项做(r) 3 e-r/8替代,对第三项做1/r(1-e-r)/r替代,对第五项和第六项做1/r3[1-(1+r) e-r]/r3替代,由此重新构造出新的势函数,然后用来计算质量劈裂,检验构造势的有效性.为此计算了一组含重介子和夸克偶素的质量劈裂.计算中屏蔽质量不是简单的常数,而是取与夸克质量mi,mj有关的变量.研究计算发现,只有当屏蔽质量取为关于夸克平均质量a=(mi+mj)/2的洛朗级数形式=c-3(a+0.512)-3+c-2(a+0.512)2+c-1(a+0.512)-1+c0+c1(a+0.512)时重介子c-J/,b-(1s),还有c0-c1-c2等的夸克偶素之间质量劈裂精确达到实验值,同时其他介子尤其是6个D介子质量精度都比以往得到较大幅度的改善.因此,本文构造出一个有效的夸克势模型.Construction of a valid interaction potential function between quarks is a crucial issue in hadronic physics and also one of the frontier issues. Non-relativistic Breit potential is a common model to describe the interaction between quarks. It is used to successfully calculate the bound states of quarks and quark scatterings. These spur people to improve it. As is well known, the full Breit potential function, which includes the color-Coulomb term, the mass term, the orbit-orbit interaction term, the spin-spin interaction term, the spin-orbit interaction term, the tensor force term, and the constant term, contains singularity factors. How to eliminate the singularity factors is the most urgent task for developing Breit potential model. In this paper, we carry out a replacement method to eliminate the singularity factors in the full Breit quark potential function in coordinate space. Except for the color-Coulomb term and the constant term, remaining terms in the Breit quark potential function are all reconstructed. The replacement of (r) 3 e-r/8 is applied to the mass term and the spin-spin interaction term. The replacement of 1/r (1-e-r)/r is applied to the obit-obit interaction term. The replacement of 1/r3[1-(1+r)e-r]/r3 is applied to the spin-obit interaction term and the tensor force term. We calculate mass splits of heavy mesons and quarkonium species by using the reconstructed potential function and test the validity of the reconstructed potential function. The screening mass used in the calculations is not a simple constant but a variable relating to the quark mass mi and mj. It is found that the simple screening-mass expression cannot give the accurate value of B-meson mass, although it may give the mass splits of light mesons. However, the calculated results of the mass splits of the light mesons -, the heavy mesons, c-J/, b-(1s), c0-c2, etc., are highly consistent with the experimental data only when the screening mass is taken to be the Laurent series, =c-3(a+0.512)-3+ c-2(a+0.512)2 +c-1(a+0.512)-1+c0+c1(a+0.512) with respect to the average quark mass a=(mi+mj)/2. In this case, the mass accuracy of other mesons, especially the six D mesons, is improved significantly. Our calculated results indicate that a valid quark potential model, which gives not only the mass values of light mesons accurately but also the mass splits of heavy quarkonium species, is thus constructed in this paper.
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Keywords:
- nonrelativistic quark potential model /
- construction of potential function /
- construction of screening mass /
- mass splitting
[1] Barnes T, Black N 1999 Phys. Rev. C 60 045202
[2] Rjla A D, Georgi H, Glashow S L 1975 Phys. Rev. D 12 147
[3] Ebert D, Faustov R N 2000 Phys. Rev. D 62 034014
[4] Chen Y Q, Kuang Y P 1992 Phys. Rev. D 46 1165
[5] Zhou P, Deng C R, Ping J L 2015 Chin. Phys. Lett. 32 101201
[6] Chen J X, Su J C 2001 Phys. Rev. C 64 065201
[7] Wang H J, Yang H, Su J C 2003 Phys. Rev. C 68 055204
[8] Zhao G Q, Jing X G, Su J C 1998 Phys. Rev. D 58 117503
[9] Lucha W, Schoberl F F, Gromes D 1991 Phys. Rep. 200 127
[10] Wong C Y, Swanson E S, Barnes T 2001 Phys. Rev. C 65 014903
[11] Godfrey S, Kokoski R 1991 Phys. Rev. D 43 1679
[12] Godfrey S, Isgur N 1985 Phys. Rev. D 32 189
[13] Godfrey S 1985 Phys. Rev. D 31 2375
[14] Capstick S, Isgur N 1986 Phys. Rev. D 34 2809
[15] Wong C Y, Swanson E S, Barnes T 2000 Phys. Rev. C 62 045201
[16] Wang L, Ping J L 2007 Chin. Phys. Lett. 24 1195
[17] Zhang W N, Wong C Y 2003 Phys. Rev. C 68 035211
[18] Wong C Y 2004 Phys. Rev. C 69 055202
[19] Jirimutu, Wang H J, Zhang W N, Wong C Y 2009 Int. J. Mod. Phys. E 18 729
[20] Jirimutu, Zhang W N 2009 Eur. Phys. J. A 42 63
[21] Jirimutu, Aodeng, Bao tmurbagan 2016 Acta Phys. Sin. 65 041201 (in Chinese) [吉日木图, 敖登, 包特木尔巴根 2016 物理学报 65 041201]
[22] Crater H, Vanalstine P 2004 Phys. Rev. D 70 034026
[23] Landau L D, Lifshitz E M 1958 Quantum Mechanics (London: Pergamon Press)
[24] Vijande J, Fernandez F, Valcarce A 2005 J. Phys. G 31 481
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[1] Barnes T, Black N 1999 Phys. Rev. C 60 045202
[2] Rjla A D, Georgi H, Glashow S L 1975 Phys. Rev. D 12 147
[3] Ebert D, Faustov R N 2000 Phys. Rev. D 62 034014
[4] Chen Y Q, Kuang Y P 1992 Phys. Rev. D 46 1165
[5] Zhou P, Deng C R, Ping J L 2015 Chin. Phys. Lett. 32 101201
[6] Chen J X, Su J C 2001 Phys. Rev. C 64 065201
[7] Wang H J, Yang H, Su J C 2003 Phys. Rev. C 68 055204
[8] Zhao G Q, Jing X G, Su J C 1998 Phys. Rev. D 58 117503
[9] Lucha W, Schoberl F F, Gromes D 1991 Phys. Rep. 200 127
[10] Wong C Y, Swanson E S, Barnes T 2001 Phys. Rev. C 65 014903
[11] Godfrey S, Kokoski R 1991 Phys. Rev. D 43 1679
[12] Godfrey S, Isgur N 1985 Phys. Rev. D 32 189
[13] Godfrey S 1985 Phys. Rev. D 31 2375
[14] Capstick S, Isgur N 1986 Phys. Rev. D 34 2809
[15] Wong C Y, Swanson E S, Barnes T 2000 Phys. Rev. C 62 045201
[16] Wang L, Ping J L 2007 Chin. Phys. Lett. 24 1195
[17] Zhang W N, Wong C Y 2003 Phys. Rev. C 68 035211
[18] Wong C Y 2004 Phys. Rev. C 69 055202
[19] Jirimutu, Wang H J, Zhang W N, Wong C Y 2009 Int. J. Mod. Phys. E 18 729
[20] Jirimutu, Zhang W N 2009 Eur. Phys. J. A 42 63
[21] Jirimutu, Aodeng, Bao tmurbagan 2016 Acta Phys. Sin. 65 041201 (in Chinese) [吉日木图, 敖登, 包特木尔巴根 2016 物理学报 65 041201]
[22] Crater H, Vanalstine P 2004 Phys. Rev. D 70 034026
[23] Landau L D, Lifshitz E M 1958 Quantum Mechanics (London: Pergamon Press)
[24] Vijande J, Fernandez F, Valcarce A 2005 J. Phys. G 31 481
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