(Q) corrections to particle multiplicity ratios in gluon and quark jets

The order (Q²) correction to the particle multiplicity ratio in gluon and quark jets is calculated in QCD. Through (Q²) we find

, with r = <n>_{gluon jet}/<n>_{quark jet}. This ratio is independent of the opening angle chosen to define the jets.     

Final-state interactions and single-spin asymmetries in semi-inclusive deep inelastic scattering

Recent measurements from the HERMES and SMC Collaborations show a remarkably large azimuthal single-spin asymmetries A_UL and A_UT of the proton in semi-inclusive pion leptoproduction γ^*(q)p→πX. We show that final-state interactions from gluon exchange between the outgoing quark and the target spectator system lead to single-spin asymmetries in deep inelastic lepton–proton scattering at leading twist in perturbative QCD; i.e., the rescattering corrections are not power-law suppressed at large photon virtuality Q² at fixed x_bj. The existence of such single-spin asymmetries requires a phase difference between two amplitudes coupling the proton target with J^z_p=±1/2 to the same final-state, the same amplitudes which are necessary to produce a nonzero proton anomalous magnetic moment. We show that the exchange of gauge particles between the outgoing quark and the proton spectators produces a Coulomb-like complex phase which depends on the angular momentum L^z of the proton's constituents and is thus distinct for different proton spin amplitudes. The single-spin asymmetry which arises from such final-state interactions does not factorize into a product of distribution function and fragmentation function, and it is not related to the transversity distribution δq(x,Q) which correlates transversely polarized quarks with the spin of the transversely polarized target nucleon.     

How unitarity imposes a steep small-x rise of spin structure function gLT=g1+g2 and breaking of DIS sum rules

We derive a unitarity relationship between the spin structure function g_LT(x,Q²)=g₁(x,Q²)+g₂(x,Q²), the LT interference diffractive structure function and the spin-flip coupling of the pomeron to nucleons. Our diffractive mechanism gives rise to a dramatic small-x rise

Full-size image

, where δ_g is an exponent of small-x rise of the unpolarized gluon density in the proton at a moderate hard scale for light flavour contribution and large hard scale for heavy flavour contribution. It invalidates the Burkhardt–Cottingham sum rule. The found small-x rise of diffraction driven g_LT(x,Q²) is steeper than given by the Wandzura–Wilczek relation under conventional assumptions on small-x behaviour of g₁(x,Q²).     

The contribution of 2N photon absorption in C(γ,2N) reactions for Eγ = 150–400 MeV

The ¹²C(γ,pn) and ¹²C(γ,pp) reactions have been studied using tagged photons of energy E_γ = 150–400 MeV. Recoil momentum distributions are compared to the results of Monte Carlo calculations based on a two-nucleon photon absorption model and two different phase space models. The ¹²C(γ,pn) data at low missing energy are consistent with absorption on 1p² and 1s1p nucleon pairs.     

Complete experiment in eN-elastic scattering, in presence of two-photon exchange

Using a general parametrization of the spin structure of the matrix element for elastic eN-scattering, in terms of three independent complex amplitudes, we found the expressions for all polarization observables, in electron–proton elastic scattering. This allows to suggest possible methods to measure the nucleon electromagnetic form factors, in presence of two-photon exchange. We show that the measurements of the differential cross section for electron and positron nucleon elastic scattering, in the same kinematical conditions, allows to extract the nucleon electromagnetic form factors. The same is correct for the polarization method, with the measurement of the P_x,z components of the final nucleon polarization (for the scattering of longitudinally polarized electrons and positrons). An alternative way, in absence of positron beam, is to measure a definite set of T-odd polarization observables, which includes three different experiments or only T-even observables, with five independent experiments. In both cases, the ratio G_E(Q²)/G_M(Q²) is related to quantities of the order of and requires different polarization experiments with very high accuracy.     

Relative production of vector and pseudoscalar states for light- and heavy-flavour mesons

The relative fractions of vector, V, and pseudoscalar, P, primary mesons produced in and decays, and primary light-flavour mesons produced in fragmentation processes are explained by the hyperfine mass splitting. The difference in corresponding fractions arises from the difference in the constituent quark masses , m_s, m_c and m_b:

The production ratios for strange, charm and beauty mesons evaluated from the ρ/(3π) ratio, measured at LEP for primary produced ρ and π, agree with the results of LEP and lower energy e⁺e⁻ experiments.     

First Measurement of the Gerasimov-Drell-Hearn Sum Rule for 1H from 0.7 to 1.8 GeV at ELSA

To verify the fundamental Gerasimov-Drell-Hearn (GDH) sum rule for the first time experimentally, we measured the helicity dependent total photoabsorption cross section with circularly polarized real photons and longitudinally polarized nucleons in the photon energy range 0.68-1.82 GeV with the tagged photon facility at ELSA. The experiment was carried out with a 4pi detection system, a circularly polarized tagged photon beam, and a frozen spin polarized proton target. The contribution to the GDH sum rule in this photon energy range is [49.9+/-2.4(stat)+/-2.2(syst)] microb.     

Nuclear effects in the F3 structure function for finite and asymptotic Q

We study nuclear effects in the structure function F₃ which describes the parity violating part of the charged-current neuitrino nucleon deep inelastic scattering. Starting from a covariant approach we derive a factorized expression for the nuclear structure function in terms of the nuclear spectral function and off-shell nucleon structure functions valid for arbitrary momentum transfer Q and in the limit of weak nuclear binding, i.e. when a nucleus can be treated as a non-relativistic system. We develop a systematic expansion of nuclear structure functions in terms of a Q⁻² series caused by nuclear effects (“nuclear twist” series). Basing ourselves on this expansion we calculate nuclear corrections to the Gross-Llewellyn-Smith sum rule as well as to higher moments of F₃. We show that corrections to the GLS sum rule due to nuclear effects cancel out in the Bjorken limit and calculate the corresponding Q⁻² correction. Special attention is paid to the discussion of the off-shell effects in the structure functions. A sizable impact of these effects both on the Q² and x dependence of nuclear structure functions is found.     

Integral geometry on families of surfaces in the space

A complex {B_ξ} of submanifolds is called admissible in the sense of integral geometry if there are such densities μ_ξ on B_ξ, that the integral transformation

has a local inversion formula. We prove that compact smooth surfaces of an admissible complex in P³ has degree 3 and obtain complete classification of admissible complexes of quadrics. Several general theorems and conjectures about admissible complex of k-dimensional submanifolds are stated.     

Temperature dependence of intensities and widths of N2-broadened lines in the 15 μm CO2 band from tunable laser measurements

Intensities and nitrogen-broadened widths of several low-J lines in the Q-branch of the 15 μm band of CO₂ have been determined over the temperature range 200–300 K. Measurements were made with a tunable infra-red diode laser spectrometer having a spectral resolution 10^-4 cm^-1. Measured intensities are uniformly about 7% lower than available calculations which were based on previous measurements of band intensity. Measured line widths are higher than available calculations and generally followed the relation

b_L⁰(T)=b_L⁰(T₀)(T₀|T)ⁿ

with n = 0.74 (standard deviation 0.08).     

QCD aspects of hadron physics

Several topics in hadron physics at different scales of resolution are discussed. First, deep-inelastic scattering from nucleons and nuclei is viewed in a light-come coordinate space picture. Then the smooth transition from parton to hadron degrees of freedom is demonstrated by analysing generalized Q²-dependent polarizabilities of the nucleon. Turning to low energy QCD we summarize recent developments related to the role of strange quarks in Chiral SU(3) Dynamics, a non-perturbative coupled channel approach to hadronic processes. Finally we elaborate on a unification of QCD Sum Rules with aspects of spontaneous chiral symmetry breaking in the analysis of quark-antiquark excitations of the condensed QCD vacuum and in nuclear matter.     

Linking total cross sections for hard and soft processes through analyticity in Q and sum rules

Using analyticity of the virtual Compton scattering amplitude in Q² sum rules are derived relating meson-nucleon total cross-sections with certain integrals over the large Q² and x0 part of nucleon structure functions. Of preliminary quantitative analysis of the sum rules for both singlet and non-singlet amplitudes is presented. For the singlet amplitude the sum rules relate, in particular, the rise of sea-quark distributions implied by perturbative QCD and the increase of total meson-proton cross sections with energy. Quantitatively, however, nonunitary leading log Q² results for the former give a too rapid increase of the latter.     

Distance functions and statistics

This paper proves that the Riemannian distance function is maximal in the class of distance functions associated with the Riemannian metric tensor.

Secondly, it is proven that there exists a unique minimum of

on a complete Riemannian surface (M,g) with small curvature, small curvature change and injectivity radius +∞. Here p_iM and γ_v is the maximal geodesic with initial velocity v and 0<t₁<<t_m.     

A measurement of the photon structure function F2 at Q = 6.8 GeV

The photon structure function F₂^γ has been measured at an average Q² value of 6.8 GeV² using data collected by the AMY detector at the TRISTAN e⁺e⁻ collider. The measured F₂^γ is compared with several QCD-based parton density models.     

The ΔNγ electromagnetic transition form factors GM(q) and GE(q)

A parameter-free, nonperturbative calculation of the ΔNγ electromagnetic transition amplitudes GM*(q2), GE*(q2), and the resonant multipole ratio REM(q2)≡E1+3/2(q2)/M1+3/2(q2) is performed in terms of the well-known nucleon isovector Sachs form factor GMV. Our methods are fully relativistic with conservation of the electromagnetic current guaranteed. We find that GM*(q2) decreases more rapidly than the nucleon dipole form factor when −q21 GeV2/c2 and that REM(q2) remains small even for very high four-momentum transfer implying that the perturbative QCD prediction REM(q2)→1 is purely asymptotic and is valid only for extremely high |q2|.     

Generalized vector dominance and the pion form factor

We have calculated the pion form factor using the bound state Bethe-Salpeter amplitudes and the quark form factor of a relativistic quark model. We obtain a generalized vector dominance structure and an asymptotic behaviour in the space-like region F_π(Q)² −0.33 GeV²/Q².     

Hyperon-Nucleon bound states and electroproduction of strangeness on He

The A(e, e′K⁺)YX reaction has been investigated in Hall C at Jefferson Lab. Data were taken for Q² ≈ 0.35 and 0.5 GeV² at a beam energy of 3.245 GeV for ³He, ⁴He. The missing mass spectra are fitted with Monte Carlo simulations including Λ, Σ⁰, Σ⁻ hyperon production. Models for quasifree production are compared to the data, excess yields close to threshold are attributed to FSI. Evidence for Λ-hypernuclear bound states is seen for ^3,4He targets.     

Magnetic anisotropy in the paramagnetic phase of TbAl2

The magnetic anisotropy of a single crystal of TbAl₂ has been measured by torque magnetometry from below the Curie point up to 170 K, well into the paramagnetic phase. Within a (110) plane the torque can be described by the expression L(θ) = {P sin 2θ} H² + {Q sin 2θ + S sin 4θ} H⁴ + {T sin 4θ} H⁶, where θ is the an gle formed by the magnetization vector with a [001] axis. The first term (in H²) is interpreted as produced by arrays of defects with axial symmetry. The second (in H⁴) and third (in H⁶) terms arise from anisotropic fourth and sixth rank tensor paramagnetic susceptibilities. On the other hand if the anisotropy is described in terms of effective conventional anisotropy constants K₁ and K₂ within the temperature range 90–170 K it is found that both constants change continuously across the Curie temperature and furthermore the [111] direction remains the easy direction in the paramagnetic range. Anisotropy measurements reveal themselves as a sensitive indicator of the level of macroscopic defects in magnetic crystals.     

Saturation and BFKL dynamics in the HERA data at small-x

We show that the HERA data for the inclusive structure function F₂(x,Q²) for x10⁻² and 0.045Q²45 GeV² can be well described within the color dipole picture, with a simple analytic expression for the dipole–proton scattering amplitude, which is an approximate solution to the non-linear evolution equations in QCD. For dipole sizes less than the inverse saturation momentum 1/Q_s(x), the scattering amplitude is the solution to the BFKL equation in the vicinity of the saturation line. It exhibits geometric scaling and scaling violations by the diffusion term. For dipole sizes larger than 1/Q_s(x), the scattering amplitude saturates to one. The fit involves three parameters: the proton radius R, the value x₀ of x at which the saturation scale Q_s equals 1 GeV, and the logarithmic derivative of the saturation momentum λ. The value of λ extracted from the fit turns out to be consistent with a recent calculation using the next-to-leading order BFKL formalism.     

From Planck to GUT via dimensional transmutation

Consider a gauge singlet superfield S coupled to a pair of adjoint fields in a SUSY-GUT. If the tree-level vacuum is flat in S, the vev S which defines the GUT scale will be determined via dimensional transmutation at a scale M where the soft-breaking (mass)² vanishes as a result of running from M_P = (8πG_N)^−1/2. Because of the large number of adjoint fields N_A coupled to S, one finds that M can be generically close to M_GUT = 2 × 10¹⁶GeV:

, where λ is a Yukawa 0.7. This work examines the symmetries and dynamical constraints required in a SUSY-GUT in order that the desired flatness in S is achieved, and that this flatness may survive in a supergravity framework.