Lüscher公式等价性证明
|
摘要
由于Lüscher’s公式建立了连续空间中的散射相移和格点上能量之间的关系,使用时往往采用非相对论情形下的形式,而格点量子色动力学是基于量子场论也就是相对论性的理论。因此本文利用非相对论性量子力学和量子场论,证明了自旋为0和自旋为1/2的粒子在散射过程中Lüscher公式在非相对论情形下和相对论情形下是完全等价的。所得结果为研究强子-强子散射提供了理论基础,且在格点数值计算中具有非常重要的应用意义。
Lüscher's formula establishes the relationship between the scattering phase shift and the energy levels on lattice,and its non-relativistic form is usually chosen when it is being used.However,the lattice QCD is a relativistic theory based on the quantum field theory.Therefore,in this paper,the quantum mechanism and quantum field theory are used to prove that Lüscher's formulas in both nonrelativistic and relativistic cases are fully equivalent in the scattering of spin-0 and spin-1/2 particles.The obtained results provide a theoretical basis for the study of the hadron-hadron scattering,and have found an important applications in lattice numerical calculations.
Lüscher's formula establishes the relationship between the scattering phase shift and the energy levels on lattice,and its non-relativistic form is usually chosen when it is being used.However,the lattice QCD is a relativistic theory based on the quantum field theory.Therefore,in this paper,the quantum mechanism and quantum field theory are used to prove that Lüscher's formulas in both nonrelativistic and relativistic cases are fully equivalent in the scattering of spin-0 and spin-1/2 particles.The obtained results provide a theoretical basis for the study of the hadron-hadron scattering,and have found an important applications in lattice numerical calculations.
引文
[1]LSCHER M.Volume Dependence of the Energy Spectrum in Massive Quantum Field Theories:II.Scattering States[J].Communications in Mathematical Physics,1986,105(2):153.
[2]LSCHER M.How to Calculate the Elastic Scattering Matrix in Two-Dimensional Quantum Field Theories by Numerical Simulation[J].Nuclear Physics B,1990,339:222.
[3]LSCHER M.Two Particle States on a Torus and Their Relation to the Scattering Matrix[J].Nuclear Physics B,1991,354:531.
[4]LSCHER M.Signatures of Unstable Particles in Finite Volume[J].Nuclear Physics B,1991,364:237.
[5]GUPTA R,PATEL A,SHARPE S R.I=2Pion Scattering Amplitude with Wilson Fermions[J].Physical Review D,1993,48:388.
[6]FUKUGITA M,KURAMASHI Y,OKAWA M,et al.Hadron Scattering Lengths in Lattice QCD[J].Physical Review D,1995,52:3003.
[7]MOIR G,PEARDON M,RYAN S M.Coupled-Channel Dπ,Dηand DSKScattering from Lattice QCD[J].Journal Of High Energy Physics,2016,1610:011.
[8]DUDEK J J.Hadron Scattering and Resonances in QCD[C]//AIP Conference Proceedings.Newport News:AIP,2016:020014.
[9]GUO D,ALEXANDRU A,MOLINA R.Rho Resonance Parameters from Lattice QCD[J].Physical Review D,2016,94(3):034501.
[10]BARABANOV M Y,VODOPYANOV A S.Perspective Study of Exotics Above the D珡D Threshold[J].Physica Scripta,2015,T166:014019.
[11]KIM C,SACHRAJDA C,SHARPE S R.Finite Volume Effects for Two-Hadron States in Moving Frames[J].Nuclear Physics B,2005,727:218.
[12]BEANE S,BEDAQUE P,ORGINOS K,et al.Nucleon-Nucleon Scattering from Fully-Dynamical Lattice QCD[J].Physical Review Letters,2006,97(1):012001.
[13]BEANE S,BEDAQUE P,ORGINOS K,et al.Two Nucleons on a Lattice[J].Physics Letters B,2004,585:106.
[14]MENG G W,MIAO C,DU X N,et al.Lattice Study on Kaon-Nucleon Scattering Length in the I=1Channel[J].International Journal of Modern Physics A,2004,19(26):4401.
[15]LI N,LIU C.Generalized Lüscher Formula in Multichannel Baryon-Meson Scattering[J].Physical Review D,2013,87(1):014502.
[2]LSCHER M.How to Calculate the Elastic Scattering Matrix in Two-Dimensional Quantum Field Theories by Numerical Simulation[J].Nuclear Physics B,1990,339:222.
[3]LSCHER M.Two Particle States on a Torus and Their Relation to the Scattering Matrix[J].Nuclear Physics B,1991,354:531.
[4]LSCHER M.Signatures of Unstable Particles in Finite Volume[J].Nuclear Physics B,1991,364:237.
[5]GUPTA R,PATEL A,SHARPE S R.I=2Pion Scattering Amplitude with Wilson Fermions[J].Physical Review D,1993,48:388.
[6]FUKUGITA M,KURAMASHI Y,OKAWA M,et al.Hadron Scattering Lengths in Lattice QCD[J].Physical Review D,1995,52:3003.
[7]MOIR G,PEARDON M,RYAN S M.Coupled-Channel Dπ,Dηand DSKScattering from Lattice QCD[J].Journal Of High Energy Physics,2016,1610:011.
[8]DUDEK J J.Hadron Scattering and Resonances in QCD[C]//AIP Conference Proceedings.Newport News:AIP,2016:020014.
[9]GUO D,ALEXANDRU A,MOLINA R.Rho Resonance Parameters from Lattice QCD[J].Physical Review D,2016,94(3):034501.
[10]BARABANOV M Y,VODOPYANOV A S.Perspective Study of Exotics Above the D珡D Threshold[J].Physica Scripta,2015,T166:014019.
[11]KIM C,SACHRAJDA C,SHARPE S R.Finite Volume Effects for Two-Hadron States in Moving Frames[J].Nuclear Physics B,2005,727:218.
[12]BEANE S,BEDAQUE P,ORGINOS K,et al.Nucleon-Nucleon Scattering from Fully-Dynamical Lattice QCD[J].Physical Review Letters,2006,97(1):012001.
[13]BEANE S,BEDAQUE P,ORGINOS K,et al.Two Nucleons on a Lattice[J].Physics Letters B,2004,585:106.
[14]MENG G W,MIAO C,DU X N,et al.Lattice Study on Kaon-Nucleon Scattering Length in the I=1Channel[J].International Journal of Modern Physics A,2004,19(26):4401.
[15]LI N,LIU C.Generalized Lüscher Formula in Multichannel Baryon-Meson Scattering[J].Physical Review D,2013,87(1):014502.