Electromagnetic form factors of nucleons in a relativistic square-root potential model of independent quarks

The nucleon electromagnetic form factorsG _E ^P (q²),G _M ^P (q²) and the axial-vector form factor G_A(q²) are studied in a relativistic model of independent quarks confined by an equally mixed scalar-vector square root potentialV _q(r)=1/2(1+γ ⁰)(ar ^1/2+ν ₀) taking into account the appropriate centre-of-mass corrections. The respective root-mean-square radii associated withG _E ^P (q²) and G _A (q²) come out as [〈r ²〉 _E ^P ]^1/2=0.86 fm and 〈r _A ² 〉^1/2=0.88 fm. Restoration of chiral symmetry in this model is discussed to derive the pion-nucleon form factorG _πNN(q²) and consequently the pion-nucleon coupling constant is obtained asg _πNN(q²)=12.81 as compared tog _πNN(q²)_exp⋍13.     

Search for possible anapole and electric dipole moments of the proton on the basis of the pp ⇌ e+ e− annihilation reaction

Differential and total cross sections are found for the formation of an electron-positron pair during the annihilation of longitudinally polarized protons and antiprotons (pp e⁺ e^–) and for the inverse reaction (e⁺ e^- pp) in the single-photon approximation, account is taken of the anapole and electric dipole moments of the proton, which violate C, P, and T parity. Possible ways to determine the square moduli of the form factors for the anapole [G₁(q²)] and electric dipole [G₂(q²)] moments and to determine the relative phase of the form factors F_e(q²) and G₂(q²) [F_m(q²) and G₁(q²)] are pointed out. Estimates are found for ¦(G₁q²)¦² and ¦G₂(q²) ¦² with q² = –6.8 (GeV/c)².Translated from Izvestiya VUZ. Fizika, No. 8, pp. 59–65, August, 1970.The authors thank Professor A. A. Sokolov, Professor I. M. Ternov, and Yu. M. Loskutov for discussions of these results.     

Low-energy limit of chiral meson theory

Based on a phenomenologically successful effective chiral theory of pseudoscalar, vector, and axial-vector mesons, all the coefficients of the chiral perturbation theory are predicted. There is no new adjustable parameter in these predictions. Up to O(m ² _q) the formulas of the masses of the pseudoscalar mesons are the same as the ones obtained by ChPT. Received: 31 August 2000 / Accepted: 16 March 2001     

The nucleon axial form factor and the pion-nucleon vertex function

The nucleon axial current and related form factors are investigated in a model of relativistic quarks confined by a scalar potential of the formM(r)=c r ⁿ , with special emphasis on center-of-mass corrections and pionic effects. Pionic contributions to the axial form factorG _A (q ²) from af _π?_μφ term with constantf _π are demonstrated to vanish. The pion-nucleon form factorG _πNN (q ²) is derived and turns out to be longer ranged thanG _A (q ²). The induced pseudo-scalar form factorG _p (q ²) is shown to be connected toG _πNN (q ²) by the standard PCAC relation, contributions from the quark core toG _p (q ²) being negligibly small.     

Electromagnetic form factors for nucleons and pions at positive and negative q 2 in the model of quark-gluon strings

The electromagnetic form factors for pions and nucleons are considered within the model of quark-gluon strings, where the momentum-transfer dependence of hadronic form factors is determined by the intercepts of the corresponding Regge trajectories and by the Sudakov form factor. Analytic expressions found for form factors in the timelike region admit an analytic continuation to the spacelike region. The resulting form factors for pions and nucleons comply well with experimental data both for positive and for negative values of the squared momentum transfer q ². It is shown that the distinctions between the absolute values of the pion and nucleon form factors F _π(q ²), G _m (q ²), and F ₂(q ²) at positive values of q ² and those at negative values of this variable are associated with the analytic properties of the double-logarithmic term in the exponent of the Sudakov form factor. The spin structure of the amplitudes for quark transitions into hadrons that is proposed in the present study makes it possible to describe fairly well available experimental data on the Pauli form factor F ₂ and on the ratio G _e /G _m .     

Clusters of cycles

A cluster of cycles (or (r,q)-polycycle) is a simple planar 2-connected finite or countable graph G of girth r and maximal vertex-degree q, which admits an (r,q)-polycyclic realization P(G) on the plane. An (r,q)-polycyclic realization is determined by the following properties: (i) all interior vertices are of degree q; (ii) all interior faces (denote their number by p_r) are combinatorial r-gons; (iii) all vertices, edges and interior faces form a cell-complex.An example of (r,q)-polycycle is the skeleton of (r^q), i.e. of the q-valent partition of the sphere, Euclidean plane or hyperbolic plane by regular r-gons. Call spheric pairs (r,q)=(3,3),(4,3),(3,4),(5,3),(3,5). Only for those five pairs, P((r^q)) is (r^q) without exterior face; otherwise, P((r^q))=(r^q).Here we give a compact survey of results on (r,q)-polycycles. We start with the following general results for any (r,q)-polycycle G: (i) P(G) is unique, except of (easy) case when G is the skeleton of one of the five Platonic polyhedra; (ii) P(G) admits a cell-homomorphism f into (r^q); (iii) a polynomial criterion to decide if given finite graph is a polycycle, is presented.Call a polycycle proper if it is a partial subgraph of (r^q) and a helicene, otherwise. In [ARS Comb. A 29 (1990) 5], all proper spheric polycycles are given. An (r,q)-helicene exists if and only if p_r>(q−2)(r−1) and (r,q)≠(3,3). We list the (4,3)-, (3,4)-helicenes and the number of (5,3)-, (3,5)-helicenes for first interesting p_r. Any outerplanar (r,q)-polycycle G is a proper (r,2q−2)-polycycle and its projection f(P(G)) into (r^2q−2) is convex. Any outerplanar (3,q)-polycycle G is a proper (3,q+2)-polycycle.The symmetry group Aut(G) (equal to Aut(P(G)), except of Platonic case) of an (r,q)-polycycle G is a subgroup of Aut((r^q)) if it is proper and an extension of Aut(f(P(G))), otherwise. Aut(G) consists only of rotations and mirrors if G is finite, so its order divides one of the numbers 2r, 4 or 2q. Almost all polycycles G have trivial AutG.Call a polycycle G isotoxal (or isogonal, or isohedral) if AutG is transitive on edges (or vertices, or interior faces); use notation IT (or IG, or IH), for short. Only r-gons and non-spheric (r^q) are isotoxal. Let T^*(l,m,n) denote Coxeter’s triangle group of a triangle on S², E² or H² with angles π/l, π/m, π/n and let T(l,m,n) denote its subgroup of index 2, excluding motions of 2nd kind. We list all IG- or IH-polycycles for spheric (r,q) and construct many examples of IH-polycycles for general case (with AutG being above two groups for some parameters, including strip and modular groups). Any IG-, but not IT-polycycle is infinite, outerplanar and with same vertex-degree, we present two IG-, but not IH-polycycles with (r,q)=(3,5),(4,4) and AutG=T(2,3,∞)PSL(2,Z), T^*(2,4,∞). Any IH-polycycle has the same number of boundary edges for each its r-gon. For any r≥5, there exists a continuum of quasi-IH-polycycles, i.e. not isohedral, but all r-gons have the same 1-corona.On two notions of extremal polycycles:

1. We found for the spheric (r,q) the maximal number n_int of interior points for an (r,q)-polycycle with given p_r; in general case, (p_r/q)≤n_int<(rp_r/q) if any r-gon contains an interior point.

2. All non-extendible (r,q)-polycycles (i.e. not a proper subgraph of another (r,q)-polycycle) are (r^q), four special ones, (possibly, but we conjecture their non-existence) some other finite (3,5)-polycycles, and, for any (r,q)≠(3,3),(3,4),(4,3), a continuum of infinite ones.

On isometric embedding of polycycles into hypercubes Q_m, half-hypercubes and, if infinite, into cubic lattices Z_m, : for (r,q)≠(5,3),(3,5), there are exactly three non-embeddable polycycles (including (4³)−e, (3⁴)−e); all non-embeddable (5,3)-polycycles are characterized by two forbidden sub-polycycles with p₅=6.     

A Strict Inequality for the Random Triangle Model

The random triangle model on a graph G, is a random graph model where the usual i.i.d. measure is perturbed by a factor q ^t(), where q1 is a constant, and t() is the number of triangles in the random subgraph . Here we consider the case where G is the usual two-dimensional triangular lattice, for which there exists a percolation threshold p _c (q) such that the probability of getting an infinite connected component of retained edges is 0 for p<p _c (q), and 1 for p>p _c (q). It has previously been shown that p _c (q) is a decreasing function of q. Here we strengthen this by showing that p _c (q) is strictly decreasing. This confirms a conjecture by Häggström and Jonasson.     

Sensitivity of polarization observables in elastic ed scattering to the neutron form factors

The deuteron elastic form factors are calculated within the Bethe-Salpeter approach with separable interaction. The charge, quadrupole, and magnetic form factors [F _C(q ²), F _Q(q ²), and F _M(q ²), respectively]; the structure functions A(q ²) and B(q ²); and the tensor polarization components T ₂₀(q ², T ₂₁(q ²), and T ₂₂(q ²) are investigated up to ?q ²=50 fm^?2. The role of relativistic effects is discussed, and a comparison with nonrelativistic calculations is performed. The effect of the neutron form factors on the deuteron form factors and especially on tensor polarization components is discussed too.     

Some Graded Bialgebras Related to Borcherds Superalgebras

In present paper we define a new kind of weak quantized enveloping algebra of Borcherds superalgebras. We denote this algebra by wU_q^t(G)wU_{q}^{\tau}(\mathcal{G}). It is a noncommutative and noncocommutative weak graded Hopf algebra under some additional condition. It has a homomorphic image which is isomorphic to the usual quantum enveloping algebra U_q(G)U_{q}(\mathcal{G}) of G\mathcal{G}.     

Extraction of the neutron charge form factor G<Superscript>n</Superscript><Subscript>E</Subscript>(Q<Superscript>2</Superscript>) from the charge form factor of deuteron G<Superscript>d</Superscript><Subscript>C</Subscript>(Q<Superscript>2</Superscript>)

We extract the neutron charge form factor G ⁿ _E(Q ²) from the charge form factor of deuteron G ^d _C(Q ²) obtained from T ₂₀(Q ²) data at 0≤Q ²≤ 1.717 (GeV/c)². The extraction is based on the relativistic impulse approximation in the instant form of the relativistic Hamiltonian dynamics. Our results (12 new points) are compatible with existing values of the neutron charge form factor of other authors. We propose a fit for the whole set (36 points) taking into account the data for the slope of the form factor at Q ² = 0. Received: 26 July 2002 / Accepted: 18 September 2002 / Published online: 4 February 2003 RID="a" ID="a"e-mail: krutov@ssu.samara.ru RID="b" ID="b"e-mail: troitsky@theory.sinp.msu.ru Communicated by V.V. Anisovich     

Dispersion approach to quark-binding effects in weak decays of heavy mesons

The dispersion approach based on the constituent quark picture and its applications to weak decays of heavy mesons are reviewed. Meson interaction amplitudes are represented within this approach as relativistic spectral integrals over the mass variables in terms of the meson wave functions and spectral densities of the corresponding Feynman diagrams. Various applications of this approach are discussed:Relativistic spectral representations for meson elastic and transition form factors at spacelike momentum transfers are constructed. Form factors at q² > 0 are obtained by the analytical continuation. As a result of this procedure, form factors are given in the full q² range of the weak decay in terms of the wave functions of the participating mesons.The 1/m_Q expansion of the obtained spectral representations for the form factors for the particular limits of the heavy-to-heavy and heavy-to-light transitions are analysed. Their full consistency with the constraints provided by QCD for these limits is demonstrated.Predictions for form factors for B_(s) and D_(s) decays to light mesons are given.The B → γℓν decay and the weak annihilation in rare radiative decays are considered. Nonfactorizable corrections to the B⁰ mixing are calculated.Inclusive weak B decays are analysed and the differential distributions are obtained in terms of the B meson wave function.     

Implications of the JLab proton polarization data for the behavior of strange nucleon form factors

A special eight-resonance unitary and analytic model of nucleon electromagnetic structure is used to analyze first the classical proton form factor data obtained by the Rosenbluth technique, and then also the contradictory JLab proton polarization data on the ratio μ_p G _Ep(Q ²)/G _Mp(Q ²) , with the aim to investigate the implications of the latter for the behavior of strange nucleon form factors.     

On universalR-matrix for quantized nontwisted rank 3 affine KM algebras

Explicit formulas of the universalR-matrix are given for all quantized nontwisted rank 3 affine KM algebras U _q (A ₂ ⁽¹⁾ ), U _q (C ₂ ⁽¹⁾ ) and U _q (G ₂ ⁽¹⁾ ).     

High frequency sound and the boson peak in amorphous silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, i.e. for frequencies ν > 0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J _l(q,ν) and J _t(q,ν), the longitudinal and transverse current correlation function, respectively. For wave-vectors q > 0.4 ?^-1 the spectra are sitting on top of a flat background. The dynamic structure factor S(q,ν) exhibits for q > 0.23 ?^-1 a boson peak which is located nearly independent of q around 1.7 THz and for which the intensity scales approximately linearly with temperature. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q = 1.7 ?^-1, the location of the first sharp diffraction peak in the static structure factor. By studying S(q,ν) for different system sizes we show that strong finite size effects are present in the low frequency part of the boson peak in that for small systems part of its intensity is missing. We discuss the consequences of these finite size effects for the structural relaxation. Received 27 June 2000 and Received in final form 9 January 2001     

Quantum deformation of compactified Minkowski space

The quantum GrassmanianG(2|0; ? _q ^4|0 ) of “quantum 2-planes ? _q ^2|0 in the quantum 4-plane ? _q ^4|0 ”, which provides aq-deformation of compactified complexified Minkowski space, is proposed. A quantum analogue of classical Plücker embedding of the usual GrassmanianG(2; ?²) into a non-degenerate quadric in ??⁵ is found.     

关于B0→π－l+ν l衰变过程分支比的计算

通过构造适当的关联函数,计算B→π跃迁形状因子f⁺_Bπ(q²),f _{Bπ(q²)和标量形状因子f⁰(q²),从而就能研究轻子质量对B⁰→π ^{关键词： B介子半轻衰变 形状因子 分支比}}     

Model-independent analysis of the weak interaction in e− -N elastic scattering experiments

We discuss what model-independent information about the parity non-conserving electron-quark neutral current interaction can be obtained in the experiments on elastic scattering of longitudinally polarized electrons on unpolarized nucleons. Two possible forms of the neutron electric form factor G_E^γn(q²) are used in our analysis. The interpretation of the P-odd asymmetry, measured in these experiments, in terms of electron-quark neutral current coupling constants depends on the form chosen for G_E^γn(q²). We note also that the polarized e^?-p elastic scattering experiments might be used in principle to study the q² dependence of G_E^γn(q²).     

Kl3 form factors at order p of chiral perturbation theory

This paper describes the calculation of the semileptonic K_l3 decay form factors at order p⁶ of chiral perturbation theory, which is the next-to-leading order correction to the well-known p⁴ result achieved by Gasser and Leutwyler. At order p⁶ the chiral expansion contains one- and two-loop diagrams which are discussed in detail. The irreducible two-loop graphs of the sunset topology are calculated numerically. In addition, the chiral Lagrangian produces direct couplings with the W bosons. Due to these unknown couplings, one can always add linear terms in q² to the predictions of the form factor f _- (q ² ). For the form factor f ₊ (q ² ), this ambiguity involves even quadratic terms. Making use of the fact that the pion electromagnetic form factor involves the same q⁴ counterterm, the q⁴ ambiguity can be resolved. Apart from the possibility of adding an arbitrary linear term in q² our calculation shows that chiral perturbation theory converges very well in this application, as the corrections are small. Comparing the predictions of chiral perturbation theory with the recent CPLEAR data, it is seen that the experimental form factor f ₊ (q ² ) is well described by a linear fit, but that the slope is smaller by about 2 standard deviations than the prediction. The unavoidable q² counterterm of the corrections allows one to bring the predictions of chiral perturbation theory into perfect agreement with experiment. Received: 8 January 2002 / Revised version: 27 March 2002 / Published online: 20 September 2002 RID="*" ID="*" Now at Fraunhofer Gesellschaft, Institute for Algorithms and Scientific Computing (SCAI), Schloss Birlinghoven, D-53754 Sankt Augustin, Germany, e-mail: peter.post@scai.fraunhofer.de RID="**"     

Determination of the neutron electric form factor from the reaction 3 He(e,e'n) at medium momentum transfer

The electric form factor of the neutron G_En has been determined in double polarized exclusive ³ He(e,e'n) scattering in quasi–elastic kinematics by measuring asymmetries A _⊥, A _∥ of the cross section with respect to helicity reversal of the electron, with the nuclear spin being oriented perpendicular to the momentum transfer q in case of A_⊥ and parallel in case of A_∥. The experiment was performed at the 855 MeV c. w. microtron MAMI at Mainz. The degree of polarization of the electron beam and of the gaseous ³ He target were each about 50%. Scattered electrons and neutrons were detected in coincidence by detector arrays covering large solid angles. Quasi–elastic scattering events were reconstructed from the measured electron scattering angles ϑ_e, φ_e and the neutron momentum vector p _n ^′ in the plane wave impulse approximation. We obtain the result <G _En>_{(0.27 < Q2c2/GeV2 < 0.5)}= 0.0334 ± 0.0033_stat± 0.0028_syst which is averaged over the indicated range of Q ², the squared momentum transfer. This G _En value is significantly smaller than measured from the D(e,e'n) reaction under similar kinematical conditions. To what extent final state interactions in ³He quench the G _En result is subject of calculations currently in progress elsewhere. Received: 29 April 1999