Non-relativistic Limit of a Dirac Polaron in Relativistic Quantum Electrodynamics

A quantum system of a Dirac particle interacting with the quantum radiation field is considered in the case where no external potentials exist. Then the total momentum of the system is conserved and the total Hamiltonian is unitarily equivalent to the direct integral of a family of self-adjoint operators acting in the Hilbert space , where is the Hilbert space of the quantum radiation field. The fiber operator is called the Hamiltonian of the Dirac polaron with total momentum . The main result of this paper is concerned with the non-relativistic (scaling) limit of . It is proven that the non-relativistic limit of yields a self-adjoint extension of a Hamiltonian of a polaron with spin 1/2 in non-relativistic quantum electrodynamics.     

Heavy-to-Light Form Factors in the Quark Model with Infrared Heavy-Quark Propagators

We calculate the heavy-to-light form factors in a relativistic quark model with infrared heavy-quark propagators. Their -dependence in the physical region is defined by two parameters: the “infrared” parameter characterizing the infrared behaviour of the heavy quark and the mass difference of the heavy meson and the heavy quark . It is found that the values of the and form factors at are in excellent agreement with the available experimental data and other approaches whereas for transitions these values are found to be larger than those of several other models. The obtained form factors are used to calculate the widths of the semileptonic decays of and mesons. A comparison of our results with available experimental data and other approaches is presented. Received January 31, 1997; revised July 15, 1997; accepted for publication January 20, 1998     

A Chiral Quark-Confinement Soliton Model for one nucleon and two Nucleons

A chiral quark-meson soliton model with quark-confinement is described in the present work.This model can reasonably produce the static properties of single nucleon,nucleon-nucleon interactions and elastic scattering phase shifts.     

Proton-Proton Virtual Bremsstrahlung in a Relativistic Covariant Model

 Lepton-pair production (virtual bremsstrahlung) in proton-proton scattering is investigated using a relativistic covariant model. The effects of negative-energy states and two-body currents are studied. These are shown to have large effects in some particular structure functions, even at the relatively small energy of a recent experiment at KVI (190 MeV). Received July 1, 1998; accepted for publication November 23, 1998     

相对论夸克模型对重夸克偶素质量谱的研究

介绍了量子场论中基于准势途径的一个相对论夸克模型,并使用这个相对论夸克模型计算了重夸克偶素的质量谱.显示这个相对论夸克模型可较好地拟合实验上肯定的质量谱数据. A relativistic quark model based on the quasipotential approach in quantum field theory is briefly introduced, and by using this model, heavy quarkonium mass spectra are calculated in detail. It is shown that such a model can give results which are in agreement with the observed experimental data on the mass spectra.     

Stability of a Model of Relativistic Quantum Electrodynamics

The relativistic “no pair” model of quantum electrodynamics uses the Dirac operator, D(A) for the electron dynamics together with the usual self-energy of the quantized ultraviolet cutoff electromagnetic field A– in the Coulomb gauge. There are no positrons because the electron wave functions are constrained to lie in the positive spectral subspace of some Dirac operator, D, but the model is defined for any number, N, of electrons, and hence describes a true many-body system. In addition to the electrons there are a number, K, of fixed nuclei with charges ≤Z. If the fields are not quantized but are classical, it was shown earlier that such a model is always unstable (the ground state energy E=−∞) if one uses the customary D(0) to define the electron space, but is stable (E > − const.(N+K)) if one uses D(A) itself (provided the fine structure constant α and Z are not too large). This result is extended to quantized fields here, and stability is proved for α= 1/137 and Z≤ 42. This formulation of QED is somewhat unusual because it means that the electron Hilbert space is inextricably linked to the photon Fock space. But such a linkage appears to better describe the real world of photons and electrons. Received: 8 September 2001 / Accepted: 18 March 2002     

Heavy-Quark Production in the Target Fragmentation Region

Fixed-target experiments permit the study of hadron production in the target fragmentation region. It is expected that the tagging of specific particles in the target fragments can be employed to introduce a bias in the hard scattering process towards a specific flavour content. The case of hadrons containing a heavy quark is particularly attractive because of the clear experimental signatures and the applicability of perturbative QCD. The standard approach to one-particle inclusive processes based on fragmentation functions is valid in the current fragmentation region and for large transverse momenta p_T in the target fragmentation region, but it fails for particle production at small p_T in the target fragmentation region. A collinear singularity, which cannot be absorbed in the standard way into the phenomenological distribution functions, prohibits the application of this procedure. This situation is remedied by the introduction of a new set of distribution functions, the target fragmentation functions. They describe particle production in the target fragmentation region, and can be viewed as correlated distribution functions in the momentum fractions of the observed particle and of the parton initiating the hard scattering process. It is shown in a next-to-leading-order calculation for the case of deeply inelastic lepton-nucleon scattering that the additional singularity can be consistently absorbed into the renormalized target fragmentation functions on the one-loop level. The formalism is derived in detail and is applied to the production of heavy quarks. The renormalization group equation of the target fragmentation functions for the perturbative contribution is solved numerically, and the results of a case study for deeply inelastic lepton-nucleon scattering at DESY (H1 and ZEUS at HERA), at CERN (NA47) and at Fermilab (E665) are discussed. We also comment briefly on the case of an intrinsic heavy-quark content of the proton.     

Monopole Excitation of the Nucleon in a Relativistic Three-Quark Model

The densities and form factors of the proton andthe Roper monopole excitedstate resonance are calculatedusing a relativistic three-quark model. Small currentquark masses are used with the three-body Dirac equation solved in hypercentralapproximation. A QCD-based three-body potential,proportional to a minimum string length between thethree quarks, is used for confinement. The calculatedelectric form factor for the proton reproduces closelya dipole fit to the data. The proton density is morecompact than is the Roper resonance density. The centraldensity of the proton is about five times that for the Roper resonance. The hyperradial nodein the Roper resonance composite three-quark wavefunction shows up as a node in the transition densitybetween the proton and the Roper resonance. This node also causes the calculated transition formfactor to be larger than either the proton or Roperresonance form factors, all evaluated at the same valueof momentum transfer. The Roper resonance form factor is smaller than the proton form factor, asexpected, indicative of the Roper resonance being a morediffuse system than the proton.     

Electromagnetic Form Factors of Nucleons in a Relativistic Three-Quark Model

We study electromagnetic form factors of nucleons within a relativistic three-quark model with a Gaussian shape for the nucleon-quark vertex. The allowed regions for two adjustable parameters, the range parameter Λ _N in the Gaussian and the constituent quark mass m _q , are obtained from fitting the data for magnetic moments and electromagnetic radii of nucleons. It is found that these observables, when calculated with m _q = 420 MeV and Λ _N = 1.25 GeV, agree very well with the experimental data. For these parameter values, however, our model underestimates the electromagnetic form factors of the nucleon at high momentum transfers for the calculated range O ≤ Q²≤ 1 GeV². Received April 10, 1996; revised June 20, 1996; accepted for publication July 19, 1996     

Nucleon Spin Content in a Relativistic Quark Potential Model Approach

Based on a relativistic quark model approach with an effective potential U(r) = (ac/2)(1 + γ0)r2, the spin content of the nucleon is investigated. Pseudo-scalar interaction between quarks and Goldstone bosons is employed to calculate the couplings between the Goldstone bosons and the nucleon. Different approaches to deal with the center of mass correction in the relativistic quark potential model approach are discussed.     

Relativistic Fermi-Gas Model for Nucleus

Spin-half fermions are considered to be limited in a spherical potential well with periodic boundary conditions. The whole system is treated like a relativistic Fermi Gas. Solving the corresponding Dirac equation, the density of states, the Fermi energy, the average energy, the density of states of nucleons and the total energy of the ground-state are obtained.     

Charmed Mesons in Nuclei with Heavy-Quark Spin Symmetry

We study the properties of charmed pseudoscalar and vector mesons in dense matter within a unitary meson–baryon coupled-channel model which incorporates heavy-quark spin symmetry. This is accomplished by extending the SU(3) Weinberg–Tomozawa Lagrangian to incorporate spin-flavor symmetry and implement a suitable flavor symmetry breaking. Several resonances with negative parity are generated dynamically by the s-wave interaction between pseudoscalar and vector meson multiplets with 1/2⁺ and 3/2⁺ baryons. Those states are then compared to experimental data as well as theoretical models. Next, Pauli-blocking effects and meson self-energies are introduced in a self-consistent manner to obtain the open-charm meson spectral functions in a dense nuclear environment. We finally discuss the formation of D-mesic nuclei.     

Bubbling Solutions for Relativistic Abelian Chern-Simons Model on a Torus

We prove the existence of bubbling solutions for the following Chern-Simons-Higgs equation:

Weak Decays of D and Ds Mesons in a Relativistic Quark Model

The transitions of D and D_s, mesons to light vector states are studied in a relativistic constituent quark model based on the Bethe-Salpeter formalism. The form factors are calculated, and the branching fractions for both semileptonic and nonleptonic decays are given. The results show that the form factors for these transitions deviate substantie from the request of heavy quark symmetry. All the branching ratios for D and D_s semileptonic decays are found to be consistent with data, whereas the calculations of nonleptonic D and D_s decays under the factorization assumption do not agree with experiments. This confirms the conjecture that the factorization scheme is much less applicable in D and D_s decays than in B and B_s decays.     

相对论夸克模型中底奇异介子的辐射衰变(英文)

系统地研究了相对论夸克模型框架下的底奇异介子的辐射衰变。给出了底奇异介子E1 和M1 辐射衰变分宽度。这些结果表明,大多数电偶极辐射衰变宽带能达到数个keV,大多数磁偶极辐射衰变宽度小于1 个keV,这为实验上通过辐射衰变寻找底奇异介子提供了理论依据。建设中的Belle II 上的实验可以进一步验证我们的结果。We systematically study the radiative transitions of bottom-strange mesons in the framework of the relativistic constituent quark model. The partial widths of the E1 and M1 decays are predicted. The results predict that most of E1 decay widths are several keV and most of M1 decay widths are less than 1 keV,which give a roadmap of searching for the higher bottom-strange mesons via radiative decays. The experimental searches by the forthcoming Belle II can in turn provide further tests to our result in the present work.     

Ground State and Charge Renormalization in a Nonlinear Model of Relativistic Atoms

We study the reduced Bogoliubov-Dirac-Fock (BDF) energy which allows to describe relativistic electrons interacting with the Dirac sea, in an external electrostatic potential. The model can be seen as a mean-field approximation of Quantum Electrodynamics (QED) where photons and the so-called exchange term are neglected. A state of the system is described by its one-body density matrix, an infinite rank self-adjoint operator which is a compact perturbation of the negative spectral projector of the free Dirac operator (the Dirac sea). We study the minimization of the reduced BDF energy under a charge constraint. We prove the existence of minimizers for a large range of values of the charge, and any positive value of the coupling constant α. Our result covers neutral and positively charged molecules, provided that the positive charge is not large enough to create electron-positron pairs. We also prove that the density of any minimizer is an L ¹ function and compute the effective charge of the system, recovering the usual renormalization of charge: the physical coupling constant is related to α by the formula α_phys ≃ α(1 + 2α/(3π) log Λ)⁻¹, where Λ is the ultraviolet cut-off. We eventually prove an estimate on the highest number of electrons which can be bound by a nucleus of charge Z. In the nonrelativistic limit, we obtain that this number is  ≤  2Z, recovering a result of Lieb. This work is based on a series of papers by Hainzl, Lewin, Séré and Solovej on the mean-field approximation of no-photon QED.     

相对论重离子碰撞的输运模型研究

美国的布鲁克海文国家实验室相对论重离子对撞机（RHIC）和欧洲核子中心的大型强子对撞机（LHC）的大量实验结果表明,在相对论重离子碰撞中已经产生了一种近似完美流体的强耦合部分子物质。基于一个多相粒子输运模型（AMPT）理论工具,对RHIC和LHC实验上的一些重要结果的开展了三个方面的理论研究工作（集体流、喷注淬火、手征磁效应）,研究结果揭示了初始的夸克胶子等离子体（QGP）能量密度涨落经过部分子输运演化产生末态粒子的各阶次的集体流、喷注和部分子物质的相互作用导致喷注的能量损失、末态相互作用严重影响手征磁效应的大小等物理过程作用机制。The experimental results from the BNL Relativistic Heavy Ion Collider (RHIC) and the CERN Large Hadron Collider (LHC) show that a nearly perfect fluid (i.e. strong-coupling Quark Gluon Plasma) has been created in relativistic heavy-ion collisions. I introduce our theoretical results based on a multi-phase transport (AMPT) model. Several important topics such as collective flow, jet quenching, chiral magnetic effect, are addressed. The simulation results indicate that the initial fluctuations of energy density of the QGP lead to all orders of harmonic flows of final particles via parton cascade, the strong interactions between jet and the QGP make jet lose much energy, and the final state interactions play an important role to affect the initial chiral magnetic effect in relativistic heavy-ion collisions.     

Thermal Dissipation in Two Dimensional Relativistic Fermi Gases with a Relaxation Time Model

Journal of Statistical Physics - The thermal transport properties of a two dimensional Fermi gas are explored, for the full range of temperatures and densities. The heat flux is established by...