A more general form of the Bethe Salpater wavefunction for a quark antiquark bound state, in accordance with the spirit of nonrelativistic approximation, is constructed, and the relativistic Salpeter equation is red...A more general form of the Bethe Salpater wavefunction for a quark antiquark bound state, in accordance with the spirit of nonrelativistic approximation, is constructed, and the relativistic Salpeter equation is reduced to two 2×2 matrix equations under an instantaneous approximation, which includes not only the contributions comming from a positive energy state but also ones of a negative energy state, and has no anomalous solution.展开更多
By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction pote...By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.展开更多
A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximat...A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.展开更多
Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coeff...Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.展开更多
Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound s...Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).展开更多
In this study,we investigate possible molecular states composed of two charmed strange baryons from theΞ_(c)^((′,∗))Ξ_(c)^((′,∗))interaction and their hidden-charm hidden-strange partners from theΞ_(c)^((′,∗))Ξ...In this study,we investigate possible molecular states composed of two charmed strange baryons from theΞ_(c)^((′,∗))Ξ_(c)^((′,∗))interaction and their hidden-charm hidden-strange partners from theΞ_(c)^((′,∗))Ξ¯_(c)^((′,∗))interaction.With the aid of heavy quark chiral effective Lagrangians,the interactions of charmed strange baryons are described with light meson exchanges.The potential kernels are constructed and inserted into the quasipotential Bethe–Salpeter equation.The bound states are produced from most interactions considered,which suggests that strong attractions exist widely between the charmed strange baryons.Experimental search for these types of molecular states is suggested in future high-precision measurements.展开更多
The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration.The corresponding scattering length f_(0) is given as Re(f_(0))=0.85±0.34(stat)±0.14(sys...The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration.The corresponding scattering length f_(0) is given as Re(f_(0))=0.85±0.34(stat)±0.14(syst)and Im(f_(0))=0.16±0.10(stat)±0.09(syst)fm.The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of elastic scattering,whereas the inelastic process is less important.In this work,such scattering processes are inspected based on a unitary coupled-channel approach inspired by the Bethe-Salpeter equation.The φp scattering length is calculated based on this approach,and it is found that the experimental value of the φp scattering length can be obtained only if the attractive interaction of the φ meson and the proton is taken into account.A significant outcome of such attractive interaction is a two-pole structure in the φp scattering amplitude.One of the poles,located at(1969−i283)MeV might correspond to N(1895)1/2^(−)or N(1875)3/2^(−)as listed in the review of the Particle Data Group(PDG).The other one,located at 1949−i3 MeV should be a φN bound state,which has no counterpart in the PDG data.展开更多
Taking D^(*)_(s0)(2317)^(+)as a conventional cs meson,we calculate its dominant strong and electromagnetic decays in the framework of the Bethe-Salpeter method.Our results areΓ(D^(∗+)_(s0)→D^(+)_(s)π^(0))=7.83^(+1....Taking D^(*)_(s0)(2317)^(+)as a conventional cs meson,we calculate its dominant strong and electromagnetic decays in the framework of the Bethe-Salpeter method.Our results areΓ(D^(∗+)_(s0)→D^(+)_(s)π^(0))=7.83^(+1.97)_(-1.55)keV andΓ(D^(∗+)_(s0)→D^(∗+)_(s)γ)=2.55^(+0.37)_(-0.45)keV.The contributions of the different partial waves from the initial and final state wave functions to the decay width are also calculated,and we find that the relativistic corrections in both decay processes are very large.展开更多
In this study,we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations.By solving the Bethe-Salpeter equation numerically with the k...In this study,we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations.By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams,we found that the K■,DK,B■,D■,B■,BD,D■,BK,and■systems withI=0 can exist as bound states.We also studied the contributions from heavy meson(J/ψandΥ)exchanges and found that the contributions from heavy meson exchanges cannot be ignored.展开更多
The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari...The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 208-213, 2012, has been removed from this site.展开更多
We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of...We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.展开更多
The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation. In addition to the Weinberg-Tomozawa term, the contri...The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation. In addition to the Weinberg-Tomozawa term, the contribution of the s-and u-channel potentials in the-wave approximation are taken into account. In the sector of isospin I=1/2 and strangeness S =0, a pole is detected in a reasonable region of the complex energy plane of ■ in the center-of-mass frame by analyzing the behavior of the scattering amplitude, which is higher than the ηN threshold and lies on the third Riemann sheet. Thus, it can be regarded as a resonance state and might correspond to the N(1535) particle of the Particle Data Group(PDG) review. The coupling constants of this resonance state to the πN,ηN,KΛ and KΣ channels are calculated, and it is found that this resonance state couples strongly to the hidden strange channels. Apparently, the hidden strange channels play an important role in the generation of resonance states with strangeness zero. The interaction of the pseudoscalar meson and the baryon octet is repulsive in the sector of isospin I = 3/2 and strangeness S = 0, so that no resonance state can be generated dynamically.展开更多
Relativistic corrections are important in hadronic physics since even for the heavy hadrons there are sizable relativistic corrections. Therefore one should use a relativistic model to describe the higher excited stat...Relativistic corrections are important in hadronic physics since even for the heavy hadrons there are sizable relativistic corrections. Therefore one should use a relativistic model to describe the higher excited states. This note summarizes our predictions for the decay constants of the S wave and P wave heavy mesons by means of the instantaneous relativistic Bethe Salpeter equation （Salpeter equation）.展开更多
使用多体摄动理论研究了碱土金属氧化物CaO的电子激发态和光吸收谱.运用GW近似方法来改进DFT对电子交换关联的处理,并计算了CaO电子能带结构.考虑到电子与空穴的相互作用,运用二粒子格林函数理论来求解Bethe-Salpeter方程,计算电子-空...使用多体摄动理论研究了碱土金属氧化物CaO的电子激发态和光吸收谱.运用GW近似方法来改进DFT对电子交换关联的处理,并计算了CaO电子能带结构.考虑到电子与空穴的相互作用,运用二粒子格林函数理论来求解Bethe-Salpeter方程,计算电子-空穴激发态,并在此基础上计算光吸收谱.计算结果 CaO能隙为7.0 e V,与实验结果 7.1 e V符合很好;并且CaO光吸收谱的理论结果与实验数据也相符合.展开更多
It is shown that the virtual states and relative momentum of the constituents of the bound states are very important for the cross section of the process e+e-→J/ψ+ηc with the help of the Bethe-Salpeter wave functio...It is shown that the virtual states and relative momentum of the constituents of the bound states are very important for the cross section of the process e+e-→J/ψ+ηc with the help of the Bethe-Salpeter wave function description of the bound states. The gauge invariance of the cross section is demonstrated. The numerical results can explain the experimental data.展开更多
We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. ...We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.展开更多
文摘A more general form of the Bethe Salpater wavefunction for a quark antiquark bound state, in accordance with the spirit of nonrelativistic approximation, is constructed, and the relativistic Salpeter equation is reduced to two 2×2 matrix equations under an instantaneous approximation, which includes not only the contributions comming from a positive energy state but also ones of a negative energy state, and has no anomalous solution.
文摘By applying an appropriate Pekeris approximation to deal with the centrifugal term, we present an approximate systematic solution of the two-body spinless Salpeter （SS） equation with the Woods-Saxon interaction potential for an arbitrary/-state. The analytical semi-relativistic bound-state energy eigenvalues and the corresponding wave functions are calculated. Two special cases from our solution are studied： the approximated SchrSdinger- Woods-Saxon problem for an arbitrary/-state and the exact s-wave （l=0）.
文摘A generalized Schr¨odinger approximation,due to Ikhdair & Sever,of the semi-relativistic two-body problem with a rectangular barrier in(1+1) dimensions is compared with exact computations.Exact and approximate transmission and reflection coefficients are obtained in terms of local wave numbers.The approximate transmission and reflection coefficients turn out to be surprisingly accurate in an energy range |∈-V0| < 2μc^2,where μ is the reduced mass,∈ the scattering energy,and V_0 the barrier top energy.The approximate wave numbers are less accurate.
文摘Scattering solutions of two-body Spinless Salpeter Equation(SSE) are investigated in the center of mass frame with a repulsive, symmetric Hulth′en potential in one spatial dimension. Transmission and reflection coefficients are calculated and discussed.
基金supported in part by the National Natural Science Foundation of China (Grant Nos.10847001,10875155,10675038 and 10875032)supported in part by the Project of Knowledge Innovation Program of Chinese Academy of Sciences (Grant No.KJCX2.YW.W10)
文摘Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) are still missing in experimental observations and potential applications of the relevant wave functions of the bound states,we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCDinspired kernel.Such a kernel for the heavy quarkonia,relating to potential of the non-relativistic quark model,is instantaneous,so we call the corresponding B.S.equation as BS-In equation throughout the paper.Particularly,a new way to solve the B.S.equation,which is different from the traditional ones,is proposed here,and with it not only the known spectrum for the heavy quarkonia is re-generated,but also an important issue is brought in,i.e.,the obtained solutions of the equation ‘automatically’ include the ‘fine’,‘hyperfine’ splittings and the wave function mixture,such as S-D wave mixing in J PC = 1-states,P-F wave mixing in J PC = 2 ++ states for charmonium,bottomonium etc.It is pointed out that the best place to test the wave mixture probably is at Z-factory (e + e-collider running at Z-boson pole with extremely high luminosity).
基金Supported by the National Natural Science Foundation of China(11675228)。
文摘In this study,we investigate possible molecular states composed of two charmed strange baryons from theΞ_(c)^((′,∗))Ξ_(c)^((′,∗))interaction and their hidden-charm hidden-strange partners from theΞ_(c)^((′,∗))Ξ¯_(c)^((′,∗))interaction.With the aid of heavy quark chiral effective Lagrangians,the interactions of charmed strange baryons are described with light meson exchanges.The potential kernels are constructed and inserted into the quasipotential Bethe–Salpeter equation.The bound states are produced from most interactions considered,which suggests that strong attractions exist widely between the charmed strange baryons.Experimental search for these types of molecular states is suggested in future high-precision measurements.
文摘The strong attractive interaction of the φ meson and the proton has recently been reported by the ALICE Collaboration.The corresponding scattering length f_(0) is given as Re(f_(0))=0.85±0.34(stat)±0.14(syst)and Im(f_(0))=0.16±0.10(stat)±0.09(syst)fm.The fact that the real part is significant in contrast to the imaginary part indicates a dominant role of elastic scattering,whereas the inelastic process is less important.In this work,such scattering processes are inspected based on a unitary coupled-channel approach inspired by the Bethe-Salpeter equation.The φp scattering length is calculated based on this approach,and it is found that the experimental value of the φp scattering length can be obtained only if the attractive interaction of the φ meson and the proton is taken into account.A significant outcome of such attractive interaction is a two-pole structure in the φp scattering amplitude.One of the poles,located at(1969−i283)MeV might correspond to N(1895)1/2^(−)or N(1875)3/2^(−)as listed in the review of the Particle Data Group(PDG).The other one,located at 1949−i3 MeV should be a φN bound state,which has no counterpart in the PDG data.
基金Supported in part by the National Natural Science Foundation of China(12075073,11865001)the Natural Science Foundation of Hebei Province,China(A2021201009)Post-graduate’s Innovation Fund Project of Hebei University(HBU2022BS002)
文摘Taking D^(*)_(s0)(2317)^(+)as a conventional cs meson,we calculate its dominant strong and electromagnetic decays in the framework of the Bethe-Salpeter method.Our results areΓ(D^(∗+)_(s0)→D^(+)_(s)π^(0))=7.83^(+1.97)_(-1.55)keV andΓ(D^(∗+)_(s0)→D^(∗+)_(s)γ)=2.55^(+0.37)_(-0.45)keV.The contributions of the different partial waves from the initial and final state wave functions to the decay width are also calculated,and we find that the relativistic corrections in both decay processes are very large.
基金Supported by National Natural Science Foundation of China(12105149,11775024)。
文摘In this study,we systematically investigated two-pseudoscalar meson systems with the Bethe-Salpeter equation in the ladder and instantaneous approximations.By solving the Bethe-Salpeter equation numerically with the kernel containing the one-particle exchange diagrams,we found that the K■,DK,B■,D■,B■,BD,D■,BK,and■systems withI=0 can exist as bound states.We also studied the contributions from heavy meson(J/ψandΥ)exchanges and found that the contributions from heavy meson exchanges cannot be ignored.
文摘The following article has been retracted due to the investigation of complaints received against it. Mr. Mohammadali Ghorbani (corresponding author and also the last author) cheated the author’s name: Alireza Heidari. The scientific community takes a very strong view on this matter and we treat all unethical behavior such as plagiarism seriously. This paper published in Vol.3 No.2, 208-213, 2012, has been removed from this site.
基金The project supported in part by National Natural Science Foundation of China
文摘We have precisely derived a ＂rigorous instantaneous formulation＂ for transitions between two bound states when the bound states are well-described by instantaneous Bethe-Salpeter （BS） equation （i.e. the kernel of the equation is instantaneous ＂occasionally＂）. The obtained rigorous instantaneous formulation, in fact, is expressed as an operator sandwiched by two ＂reduced BS wave functions＂ properly, while the reduced BS wave functions appearing in the formulation are the rigorous solutions of the instantaneous BS equation, and they may relate to Schroedinger wave functions straightforwardly. We also show that the rigorous instantaneous formulation is gauge-invariant with respect to the Uem（1） transformation precisely, if the concerned transitions are radiative. Some applications of the formulation are outlined.
文摘The interaction of the pseudoscalar meson and the baryon octet is investigated by solving the Bethe-Salpeter equation in the unitary coupled-channel approximation. In addition to the Weinberg-Tomozawa term, the contribution of the s-and u-channel potentials in the-wave approximation are taken into account. In the sector of isospin I=1/2 and strangeness S =0, a pole is detected in a reasonable region of the complex energy plane of ■ in the center-of-mass frame by analyzing the behavior of the scattering amplitude, which is higher than the ηN threshold and lies on the third Riemann sheet. Thus, it can be regarded as a resonance state and might correspond to the N(1535) particle of the Particle Data Group(PDG) review. The coupling constants of this resonance state to the πN,ηN,KΛ and KΣ channels are calculated, and it is found that this resonance state couples strongly to the hidden strange channels. Apparently, the hidden strange channels play an important role in the generation of resonance states with strangeness zero. The interaction of the pseudoscalar meson and the baryon octet is repulsive in the sector of isospin I = 3/2 and strangeness S = 0, so that no resonance state can be generated dynamically.
文摘Relativistic corrections are important in hadronic physics since even for the heavy hadrons there are sizable relativistic corrections. Therefore one should use a relativistic model to describe the higher excited states. This note summarizes our predictions for the decay constants of the S wave and P wave heavy mesons by means of the instantaneous relativistic Bethe Salpeter equation （Salpeter equation）.
文摘使用多体摄动理论研究了碱土金属氧化物CaO的电子激发态和光吸收谱.运用GW近似方法来改进DFT对电子交换关联的处理,并计算了CaO电子能带结构.考虑到电子与空穴的相互作用,运用二粒子格林函数理论来求解Bethe-Salpeter方程,计算电子-空穴激发态,并在此基础上计算光吸收谱.计算结果 CaO能隙为7.0 e V,与实验结果 7.1 e V符合很好;并且CaO光吸收谱的理论结果与实验数据也相符合.
文摘It is shown that the virtual states and relative momentum of the constituents of the bound states are very important for the cross section of the process e+e-→J/ψ+ηc with the help of the Bethe-Salpeter wave function description of the bound states. The gauge invariance of the cross section is demonstrated. The numerical results can explain the experimental data.
文摘We apply an approximation to the centrifugal term and solve the two-body spinless-Salpeter equation （SSE） with the Yukawa potential via the supersymmetric quantum mechanics （SUSYQM） for arbitrary quantum numbers. Useful figures and tables are also included.
