用手征幺正法研究S=-1，C=+1扇区赝标介子—重子散射
摘要
近年来,随着实验技术突飞猛进地发展,高能量的加速器或对撞机不断的出现并成功运行,极大地推动粒子物理学向前发展。世界各大实验组也相继发现许多新的强子态,如：DsJ、X(3872)、X(1835)、X(1576)、Y(4260)、Y(2175)等介子和∧c+(2940)、Ωc*(2772)、∑。(2800)、三c(2645)、三c(2790)、三c(2815)、三c(2930)、三c(2980)、三c(3055)、三c(3080)、三c(3123)、Ac(2880)、∑b、∑b*以及奇特e(1540)“五夸克态”等重子。这些粒子激起许多科学工作者研究的热情并为此做了大量的工作,但至今为止对于它们的结构和性质目前还存在很大的争议。对这些重味重子的激发态的计算是十分有意义的,它将推动相关的实验与理论研究。重重子系统的性质及研究结果将帮助我们更好地理解量子色动力学,检验囚禁势的味无关性、单胶子交换势的有效性等。它可以帮助我们研究从轻夸克系统到重夸克系统的夸克之间相互作用的变化。另外,它还是检验不同理论方法预言的一个很好的场所。这些共振态的研究对理解强相互作用、重子共振态的动力学产生机制以及强子结构具有重要的理论意义。
强子之间存在着强相互作用,根据QCD理论,强相互作用是通过交换带颜色的胶子进行的。强相互作用耦合常数与与能量成反比的关系,当能量减低到1GeV左右时,即进入到核内部分子之间的相互作用能量范围时,强耦合常数大约是O(1)的量级,这时量子场论计算中赖以使用的微扰论将不再适用。手征有效理论中的手征幺正法在解释强子之间的散射数据方面取得了很大的成功。
本研究工作是利用手征么正法中的耦合道BS方程法研究同位旋I=1／2、奇异数S=-1、粲数C=+1扇区赝标介子-重子散射。我们从满足手征对称性的拉氏量出发,在同位旋体系下计算该扇区赝标介子-重子散射耦合道的玻恩振幅,从而得到散射的全振幅T。利用代数化的BS耦合道方程动力学地产生出了S=-1,C=+1扇区的一些共振态,并计算了这些动力学产生态与各反应道的耦合常数|gi|。在计算过程中我们分别采用了维数正规化方法和动量截断法这两种重整化方法,发现两种方法得到的计算结果比较相近,说明用不同的重整化方法得到计算结果是一致的。当我们取不同的重整化参数时得到的极点略有偏移,但区别不大,说明计算结果对重整化参数的取值不是很敏感。在I=1／2,S=-1,C=+1扇区的赝标介子-重子S波散射中,动力学产生出了3个JP=1／2-的三c共振态：三c(S1)(M=2778.13MeV，Γ=43.44MeV)、三c(S2)(M=2929.48MeV,Γ=105.87MeV)、三c(S3)(M=3014.2MeV,Γ=22.97MeV)；在P波散射中,动力学产生出了3个JP=1／2+,3／2+的三c共振态：三c(P1)(M=2863.82MeV,Γ=150.8MeV)、三c(P2)(M=2964.82MeV,Γ=39.72MeV)、三c(P3)(M=2983.14MeV.Γ=59.22MeV)；在D波散射中,动力学产生出了1个JP=3／2-,5／2-的三c共振态：三c(D1)(M=2907.5MeV,Γ=49.54MeV)。其中三c(S3)(3014)和三c(P2)(2965)与粒子表给出的数据符合得很好,因此我们认定三c(S3)(3014)是三c(3055),三c(P2)(2965)是三。(2980)共振态。三c(S1)(2778)我们也认定它是三c(2790)。三c(S2)(2929)、三c(P1)(2864)、三c(P3)(2983)和三c(D1)(2875)目前还没有相关的三c共振态与之相对应的。因而,我们预言了四个新的三c共振态。三c(S2)(2929)的主要衰变模式是Κ∑c；三c(P1)(2864)的主要衰变模式是Κ∑c和π三c；三c(P3)(2983)的主要衰变模式是η三c和Κ∑c；三c(D1)(2875)衰变模式是π三c'、Κ∧c和Κ∑c。
In recent years, with the rapid development of experimental technology, the emer-gence of high-energy accelerators or colliders and their successful operation have greatly promoted the development of particle physics. The major collaborations in the world also discovered many new hadrons one after the after, such as mesons DSJ、X(3872)、X(1835)、X(1576)、Y(4260)、Y(2175) and baryonsΛc+(2940)、Ωc*(2772)、Σc(2800)、Ξc(2645)、Ξc(2790)、Ξc(2815)、Ξc(2930)、Ξc(2980)、Ξc(3055)、Ξc(3080)、Ξc(3123)、Λc(2880)、Σb、Σb* and bizarreΘ(1540) "pentquarks".These particles have aroused many scientists'enthusiasm about them and they have done a lot of work for them, but so far great controversy still exists as to their structures and properties. It's is very meaningful for the calculation of the excited state of these heavy flavor baryons, which will promote the experimental and theoretical studies. The na-ture and study results of heavy flavor baryons system will help better understand the quantum chromodynamics, test the flavour invariance of confinement potential and the validity of one gluon exchange potential. It can help us study the interaction between quarks between the system lighter quark and heavy quark system. Additionally, It is also a good place to test the prediction according to different theoretical methods. The research on resonances has real theoretical significance for the understanding of the strong interaction, dynamically generated mechanism of the baryon resonances and the structure of hadrons.
There is strong interaction between hadrons. According to QCD theory, the strong interaction is made by exchanging the colored gluons. the coupling constant of strong interaction is in inverse proportion to energy, when the energy reduces to about 1GeV, that is, when the energy is in the range of interaction between nuclear molecular, the energy range of strong coupling constant is about O(1), thus the perturbation theory used in the calculation of quantum field theory will not be applicable any more.The Chiral Unitary Approach of the Chiral Effective Theory has achieved great success in explaining the interaction between hadrons.
In this paper,the coupled-channel BS equation of Chiral unitary approach is applied to study the sector pseudoscalar meson-baryon scattering when isospin as I=1／2,strangeness as S=-1,and charm asC=+1. Based on the Lagrangian quantity that meets the chiral symmetry,this study calculates the Born amplitude of the meson-baryon scattering coupling channel under the isospin system,and thus we get the full amplitude of scattering T.And the algebraic BS conpling channel equa-tion is used to get some resonances in the S=-1,C=+lsector and compute the coupling constant |gi|.During the compution,the results by using dimensional reg-ularization method and three-momentum cut-off method respectively turn out to be quite similar,which indicated that using different renormalization method could get the same result.Under different renormalization paramters,the pole has a slight offset, but not very obvious,which indicates the results is not very sensitive to the renormal-ization parameter value.In the pseudoscalar meson-baryon S wave scattering when I=1／2,S=-1,C=+1 dynamics created three JP:1／2-resonances states in-cludingΞc(S1)(M=2778.13MeV,Γ:43.44MeV)、Ξc(S2)(M=2929.48MeV,Γ= 105.87MeV)、Ξc(S3)(M=3014.2MeV,Γ=22.97MeV)；In P wave scattering,dy-namics created three JP=1／2+,3／2+Ξc resonances states includingΞc(P1)(M= 2863.82MeV,Γ=150.8MeV)、Ξc(P2)(M=2964.82MeV,Γ=39.72MeV).Ξc(P3)(M=2983.14MeV,Γ:59.22MeV)；In D wave scattering,dynamics created one JP=3／2-,5／2-Ξc.resonances state asΞc(D1)(M=2875.05MeV,Γ=114MeV).Of them,bothΞc(S2)(3014)andΞc(P2)(2965)have a excellent agreement with the data listed in particle table.Thus It's concluded thatΞc(S3)(3014)andΞc(P2)(2965)the resonances state ofΞc(3055)andΞc(2980),respectively and the fact thatΞc(S1)(2778)is consid-ered asΞc(2790).And so far,there is no counterpart of resonances stateΞc(S2)(2929).Ξc(P1)(2864).Ξc(P3)(2983)andΞc(D1)(2875).Thus,the decay modes of four newΞc res-onances states are predicted as follows:K∑c as the main decay modes ofΞc(S2)(2929)
K∑c andπΞc as the main main decay modes ofΞc(P1)(2864),ηΞc and K∑c as the main decay modes ofΞc(P3)(2983),πΞc、KΛc and K∑c as the main decay modes ofΞc(D1)(2875).
强子之间存在着强相互作用,根据QCD理论,强相互作用是通过交换带颜色的胶子进行的。强相互作用耦合常数与与能量成反比的关系,当能量减低到1GeV左右时,即进入到核内部分子之间的相互作用能量范围时,强耦合常数大约是O(1)的量级,这时量子场论计算中赖以使用的微扰论将不再适用。手征有效理论中的手征幺正法在解释强子之间的散射数据方面取得了很大的成功。
本研究工作是利用手征么正法中的耦合道BS方程法研究同位旋I=1／2、奇异数S=-1、粲数C=+1扇区赝标介子-重子散射。我们从满足手征对称性的拉氏量出发,在同位旋体系下计算该扇区赝标介子-重子散射耦合道的玻恩振幅,从而得到散射的全振幅T。利用代数化的BS耦合道方程动力学地产生出了S=-1,C=+1扇区的一些共振态,并计算了这些动力学产生态与各反应道的耦合常数|gi|。在计算过程中我们分别采用了维数正规化方法和动量截断法这两种重整化方法,发现两种方法得到的计算结果比较相近,说明用不同的重整化方法得到计算结果是一致的。当我们取不同的重整化参数时得到的极点略有偏移,但区别不大,说明计算结果对重整化参数的取值不是很敏感。在I=1／2,S=-1,C=+1扇区的赝标介子-重子S波散射中,动力学产生出了3个JP=1／2-的三c共振态：三c(S1)(M=2778.13MeV，Γ=43.44MeV)、三c(S2)(M=2929.48MeV,Γ=105.87MeV)、三c(S3)(M=3014.2MeV,Γ=22.97MeV)；在P波散射中,动力学产生出了3个JP=1／2+,3／2+的三c共振态：三c(P1)(M=2863.82MeV,Γ=150.8MeV)、三c(P2)(M=2964.82MeV,Γ=39.72MeV)、三c(P3)(M=2983.14MeV.Γ=59.22MeV)；在D波散射中,动力学产生出了1个JP=3／2-,5／2-的三c共振态：三c(D1)(M=2907.5MeV,Γ=49.54MeV)。其中三c(S3)(3014)和三c(P2)(2965)与粒子表给出的数据符合得很好,因此我们认定三c(S3)(3014)是三c(3055),三c(P2)(2965)是三。(2980)共振态。三c(S1)(2778)我们也认定它是三c(2790)。三c(S2)(2929)、三c(P1)(2864)、三c(P3)(2983)和三c(D1)(2875)目前还没有相关的三c共振态与之相对应的。因而,我们预言了四个新的三c共振态。三c(S2)(2929)的主要衰变模式是Κ∑c；三c(P1)(2864)的主要衰变模式是Κ∑c和π三c；三c(P3)(2983)的主要衰变模式是η三c和Κ∑c；三c(D1)(2875)衰变模式是π三c'、Κ∧c和Κ∑c。
In recent years, with the rapid development of experimental technology, the emer-gence of high-energy accelerators or colliders and their successful operation have greatly promoted the development of particle physics. The major collaborations in the world also discovered many new hadrons one after the after, such as mesons DSJ、X(3872)、X(1835)、X(1576)、Y(4260)、Y(2175) and baryonsΛc+(2940)、Ωc*(2772)、Σc(2800)、Ξc(2645)、Ξc(2790)、Ξc(2815)、Ξc(2930)、Ξc(2980)、Ξc(3055)、Ξc(3080)、Ξc(3123)、Λc(2880)、Σb、Σb* and bizarreΘ(1540) "pentquarks".These particles have aroused many scientists'enthusiasm about them and they have done a lot of work for them, but so far great controversy still exists as to their structures and properties. It's is very meaningful for the calculation of the excited state of these heavy flavor baryons, which will promote the experimental and theoretical studies. The na-ture and study results of heavy flavor baryons system will help better understand the quantum chromodynamics, test the flavour invariance of confinement potential and the validity of one gluon exchange potential. It can help us study the interaction between quarks between the system lighter quark and heavy quark system. Additionally, It is also a good place to test the prediction according to different theoretical methods. The research on resonances has real theoretical significance for the understanding of the strong interaction, dynamically generated mechanism of the baryon resonances and the structure of hadrons.
There is strong interaction between hadrons. According to QCD theory, the strong interaction is made by exchanging the colored gluons. the coupling constant of strong interaction is in inverse proportion to energy, when the energy reduces to about 1GeV, that is, when the energy is in the range of interaction between nuclear molecular, the energy range of strong coupling constant is about O(1), thus the perturbation theory used in the calculation of quantum field theory will not be applicable any more.The Chiral Unitary Approach of the Chiral Effective Theory has achieved great success in explaining the interaction between hadrons.
In this paper,the coupled-channel BS equation of Chiral unitary approach is applied to study the sector pseudoscalar meson-baryon scattering when isospin as I=1／2,strangeness as S=-1,and charm asC=+1. Based on the Lagrangian quantity that meets the chiral symmetry,this study calculates the Born amplitude of the meson-baryon scattering coupling channel under the isospin system,and thus we get the full amplitude of scattering T.And the algebraic BS conpling channel equa-tion is used to get some resonances in the S=-1,C=+lsector and compute the coupling constant |gi|.During the compution,the results by using dimensional reg-ularization method and three-momentum cut-off method respectively turn out to be quite similar,which indicated that using different renormalization method could get the same result.Under different renormalization paramters,the pole has a slight offset, but not very obvious,which indicates the results is not very sensitive to the renormal-ization parameter value.In the pseudoscalar meson-baryon S wave scattering when I=1／2,S=-1,C=+1 dynamics created three JP:1／2-resonances states in-cludingΞc(S1)(M=2778.13MeV,Γ:43.44MeV)、Ξc(S2)(M=2929.48MeV,Γ= 105.87MeV)、Ξc(S3)(M=3014.2MeV,Γ=22.97MeV)；In P wave scattering,dy-namics created three JP=1／2+,3／2+Ξc resonances states includingΞc(P1)(M= 2863.82MeV,Γ=150.8MeV)、Ξc(P2)(M=2964.82MeV,Γ=39.72MeV).Ξc(P3)(M=2983.14MeV,Γ:59.22MeV)；In D wave scattering,dynamics created one JP=3／2-,5／2-Ξc.resonances state asΞc(D1)(M=2875.05MeV,Γ=114MeV).Of them,bothΞc(S2)(3014)andΞc(P2)(2965)have a excellent agreement with the data listed in particle table.Thus It's concluded thatΞc(S3)(3014)andΞc(P2)(2965)the resonances state ofΞc(3055)andΞc(2980),respectively and the fact thatΞc(S1)(2778)is consid-ered asΞc(2790).And so far,there is no counterpart of resonances stateΞc(S2)(2929).Ξc(P1)(2864).Ξc(P3)(2983)andΞc(D1)(2875).Thus,the decay modes of four newΞc res-onances states are predicted as follows:K∑c as the main decay modes ofΞc(S2)(2929)
K∑c andπΞc as the main main decay modes ofΞc(P1)(2864),ηΞc and K∑c as the main decay modes ofΞc(P3)(2983),πΞc、KΛc and K∑c as the main decay modes ofΞc(D1)(2875).
引文
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