夸克模型下的轻介子质量谱

最近,文献[1]将辅助场方法应用于准相对论性夸克模型中,获得了一个解析的非奇异轻介子质量公式。本文将这种方法推广到奇异轻介子的情况,得到了一个味道依赖的轻介子质量公式。结果表明,质量公式预言的低激发态质量谱与实验值吻合良好,平均误差在30 MeV左右。质量公式预言的高激发态质量谱和其他文献（特别是弦模型）的计算相比,也符合较好。Recently, with the help of auxiliary field method, Ref.[1] obtains an analytical mass formula for nonstrange light mesons in quasi-relativistic quark model. In this work, we generalize this method to the case of strange light mesons, and obtain a mesonic mass formula which is flavor-dependent. The results show that the mass of low excitations given by the mass formula are in good agreement with the experimental data and the average error is around 30 MeV. Our mass predictions for the high states also agree well with the other calculations in the literatures, particularly, the string model calculations.     

A static calculation of radiative decay widths of mesons in a potential model of independent quarks

Taking a relativistic potential model of independent quarks with its parameters determined from a fit to the mass splittings of ground state mesons in the strange, charm and bottom flavor sector, we perform a ‘static’ calculation of decay widths for the radiative transitions of mesons within the conventional picture of photon emission by a confined quark and/or antiquark. The results obtained in most of the cases of light mesons are in an overall agreement with the experimental values. The predictions in heavy meson decays are comparable to those of other model calculations.     

Breit夸克势的不同次正规化与ηc-J/ψ等的质量劈裂

用夸克势模型研究结构相同而自旋和轨道量子数不同的介子之间质量劈裂是检验势模型有效性的重要手段之一. 在以往的用各种夸克势模型计算质量劈裂工作中, 当轻介子和重介子一起计算时, π-ρ很容易劈裂, 而η_c-J/ψ等的劈裂都很 难达到实验值. 这里首先用正规化形状因子μ²/(q²+μ²), 对完整的动量空间中的Breit夸克势的第三项实施二次正规化, 除了第一项 库仑势和第七项常数项势, 对其余的项实施一次正规化, 然后用来计算 质量劈裂. 研究计算发现, 只有当屏蔽质量μ取为关于 折合质量μ_r=m_r m_j/(m_r+m_j) 的三阶多项式时, 轻介子π-ρ和重介子η_c-J/ψ, η_b-Υ(1s), 还有χ_c0-χ_c1-χ_c2 等的劈裂 精确达到实验值, 同时其他介子质量也都比以往得到较大的改善. 因此, 本文给出了一个有效的夸克势模型.     

Stable solutions for q(q) bound states with a regularized Breit potential

The Breit interaction contains singular terms which may lead to an instability in quark-antiquark bound state calculations. We regularize the Breit interaction by multiplying the singular terms in momentum space by the form factor μ2/(q2+μ2) such that the interaction is not singular at the origin and the intermediate-and long-range parts of the interaction remain unchanged. The singular terms in the Breit potential find their stable contributions in the calculations after being multiplied by the form factor with different powers. Such a regularized Breit potential with a linear and a relativistically corrected confining potential are applied to the study of qq bound states. The spectra for most familiar mesons are consistently obtained and agree well with the experimental data.     

Spin Effects in Two Quark System and Mixed States

Based on the numeric solution of a system of coupled channels for vector mesons (S-and D-waves mixing)and for tensor mesons (P- and F- waves mixing) mass spectrum and wave functions of a family of vector mesons q in triplet states a e obtained. The calculations are performed using a well-known Cornell potential with a mixed Lorentz- structure of the confinement term. The spin-dependent part of the potential is taken from the Breit-Fermi approach.The effect of irregular terms of the potential is considered within the framework of the perturbation theory and/or of the configuration interaction approach, modified for a system of coupled equations. It is shown that even a small integral contribution of the D-wave to the total wave function of q system is very impotant for the calculation of certain characteristics of the meson states.     

坐标空间中构造的Breit夸克势与介子和夸克偶素的质量劈裂

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δ(r)→μ~3e~(-μr)/8π替代,对第三项做1/r→(1-e-μr)/r替代,对第五项和第六项做1/r~3→1-(1+μr)e~(-μr)/r~3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μ不是简单的常数,而是取与夸克质量m_i,m_j有关的变量.研究计算发现,只有当屏蔽质量μ取为关于夸克平均质量μ_a=(m_i+m_j)/2的洛朗级数形式μ=c_(-3)(μ_a+0.512)-3+c_(-2)(μ_a+0.512)~(-2)+c_(-1)(μ_a+0.512)~(-1)+c_0+c_1(μ_a+0.512)时重介子η_c-J/ψ,η_b-Υ(1s),还有χ_(c0)-χ_(c1)-χ_(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.     

Particle trajectories and quarkonium potentials

We examine the compatibility of potential models for quarkonium with conventional Regge trajectories, exploring in particular questions of linearity and the existence of daughter trajectories. Using, for practical calculations, an effective power behaved potential, it is found that linearity of Regge trajectories is not a universal characteristic. It occurs only in a specific range of the effective quark mass, namely in the ordinary mesons. The Regge slope is in fact a decreasing function of the effective quark mass. Linearity of the ? trajectory requires the ?′ to have a mass 1.62 GeV. Altogether our results bring support to the use of quarkonium potentials in the whole range of constituent quark masses. It is argued that relativistic and non-perturbative vacuum effects give an overall shift to the masses of light mesons but do not affect much mass splittings.     

Vector meson photoproduction at high-<Emphasis Type="Italic">t</Emphasis> and comparison to HERA data

We explore QCD calculations for the process where V is a vector meson, in the region and . We compare our calculations for the , and mesons with data from the ZEUS Collaboration at HERA and demonstrate that the BFKL approach is consistent with the data even for light mesons, whereas the two-gluon exchange approach is inadequate. We also predict the differential cross-sections for the and for which no data are currently available. Received: 23 May 2002 / Published online: 9 December 2002     

核子之非正常磁矩

-.引言 核子的磁矩与狄拉克方程所描写的不一样。解释这个不正常性是理论物理学中重要问题之一。一般认为这个不正常性起源于核子和它的介子场的耦合。但是利用攝动方法计算时要遇到目前的量子场论所包含的发散困难,这种困难是由能量极高的虚介子引起的。Frhlich等以“割断”核子和高能介子间的相互作用,曾经得到还合理的磁矩数值。     

Meson electro-magnetic form factors in an extended Nambu–Jona-Lasinio model including heavy quark flavors

Based on an extended NJL model including heavy quark flavors, we calculate the form factors of pseudoscalar and vector mesons. After taking into account the vector-meson-dominance effect, which introduces a form factor correction to the quark vector coupling vertices, the form factors and electric radii of π+and K+pseudo-scalar mesons in the light flavor sector fit the experimental data well. The magnetic moments of the light vector mesonsρ+and K*+are comparable with other theoretical calculations. The form factors in the light-heavy flavor sector are presented to compare with future experiments or other theoretical calculations.     

Subtracted dispersion relations for in-medium meson correlators in QCD sum rules

We analyze subtracted dispersion relations for meson correlators at finite baryon density and temperature. Such relations are needed for QCD sum rules. We point out the importance of scattering terms, as well as finite, well-defined subtraction constants. Both are necessary for consistency, in particular for the equality of the longitudinal and transverse correlators in the limit of vanishing three-momentum of mesons relative to the medium. We present detailed calculations in various mesonic channels for the case of the Fermi gas of nucleons.     

Semileptonic decays of Pseudoscalar mesons in the instant form of relativistic Hamiltonian dynamics

A formalism for describing semileptonic decays of pseudoscalar mesons is developed on the basis of the instant form of relativistic Hamiltonian dynamics. By way of example, this formalism is applied to the decay process $K^ - \to \pi ^0 + \mu ^ - + \bar \nu _\mu $ . Relevant calculations are performed with wave functions that correspond to various models of constituent-quark interactions in mesons. Free parameters that appear in these models are determined from a fit to the root-mean-square radii of the kaons and pions. The results of the calculations agree well with experimental data.     

Dilepton production at SIS energies

In this short review the results of detailed studies for dilepton production from p+A andA+A reactions at SIS energies are presented. The calculations are based on a semi-classical BUU transport model that includes the off-shell propagation of vector mesons and evaluates the width of the vector mesons dynamically. Different scenarios of in-medium modifications of vector mesons, such as collisional broadening and dropping vector meson masses, are investigated and the possibilities for an experimental observation of in-medium effects in p+A reactions at 1–4 GeV are discussed for a variety of nuclear targets.     

Ground State Mass Spectrum for Scalar Diquarks with Bethe-Salpeter Equation

In this article,we study the structures of the pseudoscalar mesons π,K and the scalar diquarks Ua,Da,Sa in the framework of the coupled rainbow Schwinger-Dyson equation and ladder Bethe-Salpeter equation with the confining effective potential.The u,d,s quarks have small current masses,and the renormalization is very large,the mass poles in the timelike region are absent which implements confinement naturally.The Bethe-Salpeter wavefunctions of the pseudoscalar mesons π,K,and the scalar diquarks Ua,Da,Sa have the same type (Gaussian type) momentum dependence,center around zero momentum and extend to the energy scale about q2 = 1 GeV2,which happens to be the energy scale for the chiral symmetry breaking,the strong interactions in the infrared region result in bound (or quasi-bound) states.The numerical results for the masses and decay constants of the π and K mesons can reproduce the experimental values,and the ground state masses of the scalar diquarks Ua,Da,Sa are consistent with the existing theoretical calculations.We suggest a new Lagrangian which may explain the uncertainty of the masses of the scalar diquarks.     

A MODEL OF THE STRUCTURE OF MESONS WITH A COVARIANT OSCILLATOR POTENTIAL

In this paper the internal wave functions of mesons are obtained by solving the Bethe-Salpeter equation with a pseudoscalar covariant oscillator potential.The transi-tion probabilities of various weak and electromagnetic processes of mesons are calculat- ed by using these wave functions.The results are qualitatively in agreement with experiments.Quantitatively the results given are in good agreements with experi- ments for processes not involving π mesons,but are not so for processes involving π mesons,for which we give some speculative explanations.     

η-nucleus bound states in nuclei

The binding energies η and widths Γη of η-mesic nuclei are calculated.We parameterize the η self-energy in the nuclear medium as a function of energy and density.We find that the single-particle energies are sensitive to the scattering length,and increase monotonically with the nucleus.The key point for the study of η-nucleus bound states is the η-nuclear optical potential.We study the s-wave interactions of η mesons in a nuclear medium and obtain the optical potential Uη≈ -72 MeV.Comparing our results with the previous results,we find that the ηN scattering length aηN is indeed important to the calculations.With increasing nuclear density the effective mass of the η meson decreases.     

pp̄ Annihilation at rest into mesons in the quark rearrangement model and the quark annihilation modelt

pp? annihilation at rest into mesons is calculated in the quark rearrangement model in which 3 quarks and 3 antiquarks rearrange into 3 mesons and in the quark annihilation model in which one or two quark-antiquark pairs are annihilated and a quark-antiquark pair is created to form two or three mesons. The constants of the quark-meson coupling are adjusted such that the meson-nucleon interactions agree with experiment. The radial dependences of the quark-meson couplings are all assumed to be the same. This is determined by the vector-meson-quark interaction derived from the charge form factor of the proton. In the case of the decay into three mesons both rearrangement and annihilation models explain with similar reliability the branching ratio of the decay products. In the case of the decay into two-meson annihilation gives a better agreement with experiment than rearrangement.     

On the geometric QCD meson spectrum in the strong coupling regime

By giving the explicit calculations in the first order of the strong coupling we extend this method to higher orders and show that there will always appear new excited mesons at higher order, independent of the approximation used. These states are analogous to be bound states of a confining potential, which has an infinite barrier at radiusr=a.     

Radiative decays of radially excited pseudoscalar mesons in the extended Nambu-Jona-Lasinio model

In the extended NJL model the radiative decay widths of the radially excited states of the pseudo-scalar π, η, and η′ mesons are calculated. The predictions for the decay widths of the processes π(1300) → (ρ⁰, ω)γ, η(1295) → (ρ⁰, ω, φ)γ, and η(1475) → (ρ⁰, ω, φ)γ are given. Nowadays, there are no solid experimental data for these processes. The comparison of the results obtained in the framework of the standard and the extended NJL models for decays of the ground states of mesons is given. It is shown that these calculations correspond to each other and are also in satisfactory agreement with experimental data. This allows one to expect that the extended NJL can give reliable predictions for the excited states of mesons.