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.     

Meson spectra governed by the Fermi-Breit potential

We calculate the meson mass spectra in a quark potential model by using the complete Fermi-Breit potential including the terms of orbit-orbit interaction, spin-orbit coupling, and tensor force interaction. We find that these terms give nontrivial contributions to the calculated meson spectra. The orbit-orbit coupling term may lead to an instability of the solution of the Schr5dinger equation and should be regularized.     

Breit势的正规化与ηc-J/ψ的劈裂

研究自旋和轨道量子数不同的介子之间的质量劈裂对检验夸克势模型非常重要。 在以往的夸克势模型计算中,η_c-J/ψ的质量劈裂都很难达到实验的值。 用正规化形状因子μ2/(q2+μ2)， 在对完整的动量空间中的Breit夸克势实施一次正规化下研究了η_c-J/ψ和新介子ηb与Υ(1s)之间的质量劈裂。 结果表明， 正规化形状因子中的屏蔽质量μ应与介子折合质量有关， 当将其展开为介子折合质量的三阶多项式时， 上述介子质量劈裂可以精确重现实验的结果。另外， 由于完整的Breit势包含有自旋-轨道耦合相互作用的项，因而还可以研究χc0,χc1和χc2之间的质量劈裂。 The study of the splittings between the masses of mesons with different spin and orbit quantum numbers is important for checking the quark potential model. In the previous calculations with quark potential models, the splitting between ηc and J/ψ is however too small to the experimental result. In this paper the mass splitting of ηc J/ψ and the splitting between the new meson ηb and Υ(1s) are investigated with the complete Breit quark potential regularized by applying the form factor μ2/(q2+μ2) one time in momentum space. In addition, because the complete Breit potential includes the spin orbit interaction, it can be used to investigate the splittings among χc0, χc1 and χc2. The investigated results indicate that the screen mass μ in the form factor of regularization is related to the reduced mass of meson. The splittings of η_c-J/ψ, ηb Υ, and χc0 χc1 χc2 can reproduce the experimental results with high accuracy when the screen mass is expanded to the third order polynomial of meson reduced mass.     

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.     

Chiral symmetry breaking in an instantaneous approximation to Coulomb gauge QCD

We analyze the interplay between explicit and spontaneous chiral-symmetry breaking in Coulomb gauge QCD. Quark and pseudoscalar meson properties are investigated, using an instantaneous approximation to gluon exchange, with momentum-dependent coupling constants and current quark masses in agreement with the full QCD renormalization group equations. We show how a finite momentum-dependent constituent quark mass can be defined even for a confining interaction between the quarks, and derive an integral equation for this constituent mass from the renormalized Dyson-Schwinger equations. This equation is shown to be equivalent to a gap equation derived in a Bogoliubov-Valatin variational method from the model's hamiltonian. Including momentum-dependent current masses also ensures a finite value for the quark condensate. We report numerical results for a purely confining and for a Richardson potential for the Coulombic part of the quark-antiquark potential. Transverse gluons are included in the Breit approximation, neglecting retardation. As a confining Breit interaction leads to an infrared inconsistency in the model, and since there is mounting evidence for a dynamical gluon mass, such a mass is included. Numerical results for the constituent quark mass for one flavour, for different values of the current mass, are reported, together with the corresponding energy densities, quark condensates, pseudoscalar meson masses and pseudoscalar meson decay constants. The results are encouraging from a phenomenological point of view.     

B→f0（980）（π,η^（＇）） decays in the PQCD approach

Based on the assumption of a two-quark structure of the scalar meson f0（980） ,we calculate the branching ratios and CP-violating asymmetries for the four B → f0（980） π and B → f0（980） η^（＇） decays by employing the perturbative QCD（pQCD） factorization approach. The leading order pQCD predictions for branching ratios are,Br（B^-→ f0（980） π^-） ～ 2.5×10^-6,Br（Bˉ^0 → f0（980） π^0） ～ 2.6×10^-7,Br（Bˉ^0 → f0（980） η） ～ 2.5×10^-7 and Br（Bˉ^0 → f0（980） η ） ～ 6.7×10^-7,which are consistent with both the QCD factorization predictions and the experimental upper limits.     

Photoproduction of Vector Meson Ф off Deuteron in QCD Inspired Model

Based on the quark-gluon contents of nucleon and strongly believing that the force mediators, Pomeron and its counterpart in the conventional approach of Regge theory, for high energy diffractive process would be the tensor glueball and Odderon respectively, we discuss photo-production of vector meson Ф off the deuteron at energy less than 3 GeV in the QCD inspired model in which the quark gluon degrees of freedom and glueball, Odderon exchange are taken into account. A calculation is performed for γ ＋ D →Ф ＋ D, and the theoretical predictions of the differential cross section dσ^γD/dt, are presented and compared with available experimental data. Our QCD inspired model reproduces data quite well in the whole range of the experimental measurements up to ｜t｜ ≌ 0.4 GeV. Our results can be used to extract γn → Фn data, which cannot be measured in experiment.     

Recoil polarimetry in meson photoproduction at MAMI

The nucleon excitation spectrum remains poorly known, with the masses, widths, EM couplings and even existence of many states not well established. A program of experiments using meson photoproduction off the nucleon is being carried out to improve this situation. A new large acceptance recoil polarimeter has been developed by the Edinburgh group for use in such reactions with the Crystal Ball at MAMI. This work summarizes the procedure used to measure recoil polarization with the new device and presents some preliminary results for the double polarization observable Cx in the reaction γp→pπ, compared to the current partial wave analysis.     

Extraction of resonance parameters from meson production reaction

We have developed an analytic continuation method for extracting parameters of nucleon resonances within a Hamiltonian formulation of meson-nucleon reactions. The method was tested for simple solvable models and then applied for our recent coupled channels model （πN, ηN, π△, ρN, and σN ） of the π＊N and γ＊N reactions. The resonance pole positions and their properties are studied for P11and P11 channels.     

η-production on the proton via electromagnetic and hadronic probes

The reactions π-p →ηn and γ＇p →ηP are investigated within a dynamical coupledJchannels model of meson production reactions in the nucleon resonance region. The meson-baryon channels included are πN, ηN, π△, σN, and pN. The direct wphotoproduction process is studied within a formalism based on a chiral constituent quark model approach, complemented with a one-gluon-exchange mechanism, to take into account the breakdown of the SU（6）0（3） symmetry. In the models search, the following known nucleon resonances are embodied： Sll （1535）, $11（1650）, Pll （1440）, Pl1（1710）, P13（1720）, D13（1520）, D13（1700）, D15（1675）, and F15（1680）. Data for the π-p →ηnreaction from threshold up to a total center-of-mass energy of W ≈ 2 GeV are satisfactorily reproduced. For the photoproduction channel, two additional higher mass known resonances, P13 （1900） and F15 （2000）, are also considered. However, reproducing the data for γ＇p →ηP requires, within our approach, two new nucleon resonances, for which we extract mass and width.     

Next-to-leading-order calculation in kT factorization

We explain the framework for calculating next-to-leading-order （NLO） corrections to exclusive processes in the kT factorization theorem, taking πγ^＊→γ as an example. Patrons off-shell by kT^2 are considered in both the quark diagrams from full QCD and the effective diagrams for the pion wave function. The gauge dependences in the above two sets of diagrams cancel, when deriving the kw-dependent hard kernel as their difference. The light-cone singularities in the kT-dependent pion wave function are regularized by rotating the Wilson lines away from the light cone. Both the large double logarithms In^2 kT and In^2x, x being a parton momentum fraction, arise from the loop correction to the virtual photon vertex, the former being absorbed into the pion wave function, and the latter into a jet function.     

B → ρ（ω, φ）η（＇） Decays and NLO Contributions in pQCD Approach

By employing the perturbative QCD （pQCD） factorization approach, we calculate some important next- to-leading-order （NLO） contributions to the two-body charmless hadronic decays B^＋ →ρ^＋η（＇） and B^0 → ρ^0（ω, φ）η（＇）, induced by the vertex QCD corrections, the quark-loops as well as the chromo-magnetic penguins. From the numerical results and phenomenological analysis we find that （a） for B^± → ρ^±η（＇） （B^0 → ρ^0（ω, φ）η（＇）decays, the partial NLO contributions to branching ratios are small （large） in magnitude; and （b） the pQCD predictions for ACP^dir（B^± → ρ^±η（＇）） are consistent with the data, while the predicted .ACP（B^0 → ρ^0（ω）η（＇）） are generally large in magnitude and could be tested by the forthcoming LHCb experiments.     

Masses and Widths of Light Scalar Mesons in Chiral Perturbation Theory

Based on the diquark model, we assume that the light scalar mesons are q^2q^-2 states rather than qq^-. The chiral effective Lagrangian for the light scalar meson is constructed, and the mass relations are obtained： the isotriplet （a0） and the isosinglet （f0） are the heaviest and are degenerate, the isodoublets （κ） are heavier and the other isosinglet （σ） is the lightest; and 2Mκ^2 = Mα0^2＋ Mσ^2. Using experimental value for a0 and σ mass, we obtain Mκ=794 MeV, which is consistent with the experimental value. Then taking Г（a0^0 →ηπ^0） = 90 MeV and Г（f0→π^0π^0） = 20 MeV, we get the width of σ is： Г（σ0→π^＋π^-）= 150 MeV.     

B→K0^＊（1430）η（＇） decays in the pQCD approach

Based on the assumption of two-quark structure of the scalar meson K0^＊（1430）, we calculate the CP-averaged branching ratios for B→K0^＊（1430）η（＇） decays in the framework of the perturbative QCD （pQCD） approach here. We perform the evaluations in two scenarios for the scalar meson spectrum. We find that： （a） the pQCD predictions for Br（B→K0^＊（1430）η（＇）） which are about 10^-5 10^-6, basically agree with the data within large theoretical uncertainty; （b） the agreement between the pQCD predictions and the data in Scenario Ⅰ is better than that in Scenario Ⅱ, which can be tested by the forthcoming LHC experiments; （c） the annihilation contributions play an important role for these considered decays.     

Latest results from GRAAL collaboration

The GRAAL experimental set-up consists of a polarized and tagged photon beam that covers an energy range from a minimum of 600 MeV up to a maximum of 1500 MeV, of a liquid Hydrogen or Deuterium target and of the 4π Lagrange detector optimized for photon detection. It allows the study of pseudo-scalar and vector meson photoproduCtion on the nucleon in the energy range corresponding to the second and the third resonance regions. In the following, the ∑ beam asymmetries in η and π0 photoproduction on quasi-free nucleon are shown. Also single and double polarization observables in K＋A photoproduction on free proton are shown; they are important to confirm the role of new or poorly known resonances in the 1900 MeV mass region.     

Study of scalar meson a0（980） from B → a0（980）π decays

In this paper, we calculate the branching ratios and the direct CP-violating asymmetries for decays B^0 → a0^0（980）π^0, a0^＋ （980）π^-, a0^-（980）π^＋ and B^- → a0^0 （980）π^-, a0^- （980）π^0 by employing the perturbative QCD （pQCD） factorization approach at the leading order. We found that （a） the pQCD predictions for the branching ratios are around （0.4-2.8） × 10^-6, consistent with currently available experimental upper limits; （b） the CP asymmetries of B^0→ a0^0（980）π^0 and B^- → a0^- （980）π^0 decays can be large, about （70-80）% for α= 100°.     

Sigma Meson Production in Nuclear Reactions

The sigma meson production in p ＋ ^12C and p A- ^40Ca reactions at the incident energy Ep = 1.5 GeV is investigated within the Quantum Molecular Dynamics model. The simulation results indicate a distinctive A dependence of the sigma production, that is, the increase of A is followed by an increase of the production cross sections. We find that the σ meson production in proton-induced reactions is strongly medium-dependent, and the produced σ mesons decaying in a denser medium experience a stronger mass shift towards lower masses. This mass shift is an experimentally accessible observable in the final state pion pairs, which do not suffer from reabsorption by the surrounding nucleons. It is pointed out that the ratio of measured sigma cross sections as a function of the sigma invariant-mass from various reactions is a good probe to explore the existence of the σ meson in a dense nuclear environment.     

Study of excited nucleon states at EBAC: status and plans

We present an overview of a research program for the excited nucleon states in Excited Baryon Analysis Center （EBAC） at Jefferson Lab. Current status of our analysis of the meson production reactions based on the unitary dynamical coupled-channels model is summarized, and the N＊ pole positions extracted from the constructed scattering amplitudes are presented. Our plans for future developments are also discussed.     

B →πη（′）, η（′）η（′） decays and NLO contributions in the pQCD approach＊

By employing the perturbative QCD （pQCD） factorization approach, we calculate the full leading and the partial next-to-leading order （NLO） contributions to the seven B →πη（′） and η（′）η（′） decays. For B^＋→ π＋η（′） decays, the pQCD predictions for their decay rates agree very well with the data after the inclusion of the small NLO contributions. For neutral decays, the pQCD predictions are also consistent with the experimental upper limits and can be tested by the LHC experiments. The measured value of dir .Acp^dir（π＋η）= 19±7% can also be accommodated by the pQCD approach.