Soliton models for the nucleon and predictions for the nucleon spin structure

In these lectures the three flavor soliton approach for baryons is reviewed. Effects of flavor symmetry breaking in the baryon wave functions on axial current matrix elements are discussed. A bosonized chiral quark model is considered to outline the computation of spin dependent nucleon structure functions in the soliton picture.     

Flavor symmetry breaking and strangeness in the nucleon

We suggest that breaking of SU(3) flavor symmetry mainly resides in the baryon wave functions while the charge operators have no (or only small) explicit symmetry-breaking components. We utilize the collective coordinate approach to chiral soliton models to support this picture. In particular we compute the g _A /g _V ratios for hyperon beta-decay and the strangeness contribution to the nucleon axial current matrix elements and analyze their variation with increasing flavor symmetry breaking.Received: 30 September 2002, Published online: 22 October 2003PACS: 12.39.Dc Skyrmions - 12.39.Fe Chiral Lagrangians - 13.30.Ce Leptonic, semileptonic, and radiative decays - 14.20.Jn HyperonsH. Weigel: Heisenberg-Fellow;     

Topologically non-trivial chiral transformations

The role of chiral transformations in effective theories modeling Quantum Chromo Dynamics is reviewed. In the context of the Nambu-Jona-Lasinio model the hidden gauge and massive Yang-Mills approaches to vector mesons are linked by a special chiral transformation which removes the chiral field from the scalar-pseudoscalar sector. The chirally rotated axial vector meson field (à _μ ) transforms homogeneously under flavor rotations and may thus be dropped without violating chiral symmetry. The fermion determinant for static meson field configurations is computed by summing the discretized eigenvalues of the Dirac Hamiltonian. It is discussed how the local chiral transformation loses its unitary character in a finite model space. This technical issue proves to be crucial for the construction of the soliton within the Nambu-Jona-Lasinio model when the chirally rotated axial vector field is neglected. In the background of this soliton the valence quark is strongly bound, and its eigenenergy turns out to be negative. This important feature, which usually is generated by non-vanishing axial vector profiles, is thus maintained by the simplificationà _μ = 0.     

The bose form of two-dimensional quantum chromodynamics

By means of a special choice of gauge QCD₂ [SU(N)] with one flavor of quarks is recast into the Bose form. Weak (g m) and strong (gm) coupling regimes are studied. The former is shown to be the SU(N)-symmetric confining phase in which bound states possess stringlike configurations with strings being represented by electric vortex lines; the ordinary mesons and baryons appear as longitudinal modes of electric strings. The strong coupling regime describes the Higgs phase with the residual symmetry [U(1)]^N−1 S_N where the left and right factors are the maximal abelian subgroup of SU(N) and the permutation group of N quarks, respectively; the particle spectrum consists of S_N multiplets and the [Uw(1)]^N−1 charges are trapped.     

The spectral density of the QCD Dirac operator and patterns of chiral symmetry breaking

We study the spectrum of the QCD Dirac operator for two colors with fermions in the fundamental representation and for two or more colors with adjoint fermions. For N_f flavors, the chiral flavor symmetry of these theories is spontaneously broken according to SU (2N_f → Sp (2N_f) and SU (N_f → O (N_f), respectively, rather than the symmetry breaking pattern SU (N_f) × SU (N_f) → SU (N_f) for QCD with three or more colors and fundamental fermions. In this paper we study the Dirac spectrum for the first two symmetry breaking patterns. Following previous work for the third case we find the Dirac spectrum in the domain λ Λ_QCD by means of partially quenched chiral perturbation theory. In particular, this result allows us to calculate the slope of the Dirac spectrum at λ = 0. We also show that for λ 1/L₂ Λ_QCD (wing L the linear size fo the system) the Dirac spectrum is given by a chiral Random Matrix Theory with the symmetries of the Dirac operator.     

Axially symmetric multi-baryon solutions and their quantization in the chiral quark soliton model

We study axially symmetric solutions with B=2-5 in the chiral quark soliton model. In the background of axially symmetric chiral fields, the quark eigenstates and profile functions of the chiral fields are computed self-consistently. The resultant quark bound spectrum are doubly degenerate due to the symmetry of the chiral field. Upon quantization, various observable spectra of the chiral solitons are obtained. Taking account of the Finkelstein-Rubinstein constraints, we show that the quantum numbers of our solitons coincide with the physical observations for B=2 and 4 while B=3 and 5 do not.     

2D gravity+1D matter

We consider a formulation of nonperturbative two-dimensional quantum gravity coupled to a single bosonic field (d=1 matter). Starting from a matrix realization of the discretized model, we express the continuum theory as a double scaling limit in which the 2D cosmological constant g tends towards a critical value g_c, and the string coupling 1/N→0, with the scaling parameter ∝1n (g-g_c)/(g-g_c)N held fixed. We find that in this formulation logarithmic corrections already present at tree level persist to all higher genus, suggesting a behavior different from the previously considered cases of d<1 matter.     

Radial excitations of low–lying baryons and the Z + penta–quark

Abstact: Within an extended Skyrme soliton model for baryons the interplay between the collective radial motion and the SU(3)–flavor–rotations is investigated. The coupling between these modes is mediated by flavor symmetry breaking. Collective coordinates which describe the corresponding large amplitude fluctuations are introduced and treated canonically. When diagonalizing the resulting Hamiltonian flavor symmetry breaking is fully taken into consideration. As eigenstates not only the low–lying (1/2)⁺ and (3/2)⁺ baryons but also their radial excitations are obtained and compared to the empirical data. In particular the relevance of radial excitations for the penta–quark baryon Z ⁺ (Y=2, I=0, J ^π=(1/2)⁺) is discussed. In this approach its mass is predicted to be 1.58 GeV. Furthermore the widths for various hadronic decays are estimated which, for example, yields Γ(Z ⁺→NK) ∼ 100 MeV for the only permissible decay process of the Z ⁺. Received: 20 April 1998 / Revised version: 29 May 1998     

ALT in the nucleon-nucleon polarized Drell-Yan process

We present a leading order (LO) estimate for the longitidinal-transverse spin asymmetry (A ) in the nucleon-nucleon polarized Drell-Yan process at RHIC and energies in comparison with A and A . A receives contribution from g₁, the transversity distribution h₁, and the twist-3 distributions g and h . For the twist-3 contribution we use the bag model prediction evolved to a high energy scale by the large-N_c evolution equation. We found that A (normalized by the asymmetry in the parton level) is much smaller than the corresponding A . Twist-3 contribution given by the bag model turned out to be negligible.     

Gauge-Higgs unification in the left–right model

We construct a supersymmetric left–right model in four dimension with gauge-Higgs unification starting from a SU(3)_c×SU(4)_w×U(1)_B−L gauge symmetry in five dimension. The model has several interesting features, such as, the CKM mixings in the quark sector are naturally small while for the neutrino sector it is not, light neutrino masses can be generated via the seesaw mechanism in the usual way, and the model has a U(1)_R symmetry which naturally forbid dimension five proton decay operators. We also discuss the grand unification of our model in SO(12) in five dimensions.     

“Missing moment” and perturbative methods for polynomial iterated function systems

An iterated function system (IFS) over a compact metric space X is defined by a set of contractive maps w_i: X → X, i = 1,…,N, with associated nonzero probabilities p_i > 0, p_i = 1. The “parallel” action of the maps defines a unique compact invariant attractor set A X which supports an invariant measure μ and which is balanced with respect to the p_i. For linear , the invariance of μ yields a relation between the moments g_n = ∫ χⁿ dμ which permits their recursive computation from the initial value g₀ = 1. For nonlinear w_i, however, the moment relations are incomplete and do not permit a recursive computation. This paper describes two methods of obtaining accurate estimates of the moments when the IFS maps w_i are polynomials: (i) application of the necessary Hausdorff conditions on the g_i to obtain convergent upper and lower bounds and (ii) a perturbation expansion approach. The methods are applied to some model problems.     

SU(3) symmetry breaking for masses, magnetic moments and sizes of baryons

We use the SU(3) Skyrme model to investigate the effects of symmetry breaking imposed by different pseudoscalar meson masses on the structure of baryons. Specifically, we calculate their mass splittings, magnetic moments, charge radii, semileptonic decays as well as different strangeness contents of the proton. Since the Skyrme soliton is allowed to deform under the pressure of the symmetry breaking we find significant variations in baryon sizes with respect to strangeness.     

Monte Carlo optimisation of correlated wave functions for normal two-electron systems

A simple, new type of correlated wave function is proposed for the studies of normal two-electron atomic systems: ψ(r₁, r₂) = Σc_mΦ_m(r₁, r₂) with Φ_m(r₁, r₂) = exp[−(r₁ + r₂)]/(br₁₂ + a)^m, where , a, b are non-linear variational parameters. A notable feature of this basis function is that only three terms are required within the framework of the Raleigh-Ritz variational principle to obtain fairly accurate energy eigenvalues and satisfactory cusp conditions. The non-linear variational parameters are optimised by using the Monte Carlo technique.     

Cu1-xHxZr2(PO4)3中Cu2+的EPR谱和局域结构研究

本文采用Cu²⁺斜方对称电子顺磁共振（EPR）参量的高阶微扰公式计算了晶体Cu_1-xH_xZr₂（PO₄）₃中Cu²⁺的EPR参量（g因子和超精细结构常数A因子）．计算结果表明,晶体Cu_1-xH_xZr₂（PO₄）₃中[CuO₆]^10-基团的Cu-O键长分别为R_||≈0.241 nm,R_⊥≈0.215 nm,平面键角τ≈80.1°;由于对称性降低,中心金属离子基态²A_1g（θ）和²A_1g（ε）有一定程度混合,混合系数α≈0.995．所得EPR谱图的理论计算值与实验数据符合得很好．     

Ferromagnetic resonance in Sr doped rare earth orthocobaltites, Ln1−xSrxCoO3†

FMR measurements have been carried out on several members of the Ln_1−xSrxCoO₃ (Ln = Rare earth) system. The results show that g_eff in these systems is around 1.25 independent of x as well as the rare earth ion. It is suggested that this unusual value of g_eff is due to the localized intermediate-spin Co³⁺ ions (t⁵_2g e¹_g) located at the top of the π^* band.     

Double Loops and Pitchfork Symmetry Breaking Bifurcations of Optical Solitons in Nonlinear Fractional Schrödinger Equation with Competing Cubic-Quintic Nonlinearities

Symmetry breaking bifurcations of solitons are investigated in framework of a nonlinear fractional Schrödinger equation (NLFSE) with competing cubic-quintic nonlinearity. Some prototypical characteristics of the symmetry breaking, featured by transformations of symmetric and antisymmetric soliton families into asymmetric ones, are found. Stable asymmetric solitons emerge from unstable symmetric and antisymmetric ones by way of two different symmetry breaking scenarios. A twisting branch, featured with double loops bifurcation, bifurcates off from the base branch of symmetric soliton solutions and crosses it, then merges into the base branch driven by the competitive nonlinear effect. A supercritical pitchfork bifurcation is bifurcated from the branch of antisymmetric soliton solutions and gives rise to a supercritical pitchfork bifurcation. Stability of the soliton families is explored by linear stability analysis. With the increase of the Lévy index, stability region induced by the twisting loops bifurcation is expanded. However, stability region of the pitchfork bifurcation is shrunk on the parameter plane of the Lévy index and the soliton power.     

Continuum limit of finite temperature λφ3 from lattice Monte Carlo

The φ₃⁴ model at finite temperature is simulated on the lattice. For fixed N_t we compute the transition line for N_s → ∞ by means of finite size scaling techniques. The crossings of a renormalization group trajectory with the transition lines of increasing N_t give a well-defined limit for the critical temperature in the continuum. By considering different RG trajectories, we compute T^c/g as a function of the renormalized parameters.     

Raman phonon anomalies in Sr(Fe1-xCox)2As2

Phonon anomalies have been reported in iron-pnictide superconductors indicating a diverse interplay between different orders in the materials.Here,we report Raman scattering measurements on Sr(Fe_1-xCo_x)₂As₂(x=0 and x=0.04)single crystals in the B;symmetry with respect to a 1 Fe unit cell.Upon cooling,we observe a larger split(13 cm;)of Eg Raman phonon modes pertaining to in-plane Fe and As displacements as the crystals undergo the tetragonal-toorthorhombic structural phase transition,although a considerable split(9 cm;)has been reported in BaFe_1-xCo_x)₂As₂.Furthermore,the splitting of E;phonon modes is strongly reduced upon doping.We perform an order-parameter analysis revealing a similar doping dependence of E;phonon splitting as reported in other compounds of the 122 family,indicating these phonon anomalies widely exist in 122 iron-based superconductors and might share the same mechanisms.     

Random bond Potts model: The test of the replica symmetry breaking

The averaged spin-spin correlation function squared is calculated for the ferro-magnetic random bond Potts model in two dimensions. The technique being used is the renormalization group plus conformal field theory. The results are of the E-expansion type fixed point calculation, E being the deviation of the central charge (or the number of components) of the Potts model from the Ising model value. Calculations are done both for the replica symmetric and the replica symmetry broken fixed points. The results obtained allow for numerical simulation tests to decide between the two different criticalities of the random bond Potts model.