Forward $\pi^\circ$ production and associated transverse energy flow in deep-inelastic scattering at HERA

Deep-inelastic positron-proton interactions at low values of Bjorken-x down to which give rise to high transverse momentum -mesons are studied with the H1 experiment at HERA. The inclusive cross section for -mesons produced at small angles with respect to the proton remnant (the forward region) is presented as a function of the transverse momentum and energy of the and of the four-momentum transfer Q ² and Bjorken-x. Measurements are also presented of the transverse energy flow in events containing a forward -meson. Hadronic final state calculations based on QCD models implementing different parton evolution schemes are confronted with the data.Received: 8 April 2004, Revised: 7 July 2004, Published online: 30 July 2004Dedicated to the memory of Krzysztof Rybicki     

Leptoproduction of $\varrho$ mesons within Regge approach

A model describing the leptoproduction of mesons is considered. For the amplitude of the photon dissociation into a pair, the light-cone wave function is used. Scattering of the colorless pair off the nucleon is computed within reggeon exchange phenomenology. The transition of the scattered quark and antiquark into the final meson is treated with the aid of the parton-hadron duality concept. Numerical calculations of and r⁰⁴₀₀ describe the world data at Q² < 4 GeV² rather reasonably. The calculations of the meson spin density matrix show that the computed matrix elements except r⁰⁴₀₀ are in good agreement with the available experimental data at Q² up to 8 GeV² and the total mass of the system greater than 4 GeV. The Regge phenomenology predictions at the highest experimentally available energies agree with both the HERA data and calculations performed within the perturbative QCD approach even for very high Q² ( -20 GeV²). The predicted scale of the S-channel helicity non-conservation is in reasonable agreement with the experimental data.Received: 18 September 2003, Revised: 17 December 2003, Published online: 13 February 2004     

<Emphasis Type="Italic">T</Emphasis>-dependent Dyson-Schwinger equation in IR regime of QCD: the critical point

The quark mass function in QCD is revisited, using a gluon propagator in the form 1/(k ² + m _g ²) plus , where the second (IR) term gives linear confinement for m _g = 0 in the instantaneous limit, being another scale. To find we propose a new (differential) form of the Dyson-Schwinger equation (DSE) for , based on an infinitesimal subtractive renormalization via a differential operator which lowers the degree of divergence in integration on the RHS, by two units. This warrants in the integrand since its k-dependence is no longer sensitive to the principal term (p-k)² in the quark propagator. The simplified DSE (which incorporates the Ward-Takahashi (WT) identity in the Landau gauge) is satisfied for large p ² by = , except for Log factors. The limit p ² = 0 determines . A third limit, p ² = -m ₀ ², defines the dynamical mass m ₀ via . After two checks ( MeV and = ), for with MeV, the T-dependent DSE is used in the real time formalism to determine the critical index analytically, with the IR term partly serving as the H-field. We find MeV and check the vanishing of and at T _c.Received: 31 August 2004, Published online: 11 January 2005PACS: 24.85. + p, 12.38.Lg, 12.38.AwA.N. Mitra: Permanent address: 244 Tagore Park, Delhi-110009, India.     

Measurement of prompt photon cross sections in photoproduction at HERA

Results are presented on the photoproduction of isolated prompt photons, inclusively and associated with jets, in the center of mass energy range 142 < W < 266 GeV. The cross sections are measured for the transverse momentum range of the photons GeV and for associated jets with E _T ^jet > 4.5 GeV. They are measured differentially as a function of , the pseudorapidities and and estimators of the momentum fractions and x _p of the incident photon and proton carried by the constituents participating in the hard process. In order to further investigate the underlying dynamics, the angular correlation between the prompt photon and the jet in the transverse plane is studied. Predictions by perturbative QCD calculations in next to leading order are about below the inclusive prompt photon data after corrections for hadronisation and multiple interactions, but are in reasonable agreement with the results for prompt photons associated with jets. Comparisons with the predictions of the event generators PYTHIA and HERWIG are also presented.Received: 13 July 2004, Revised: 15 November 2004, Published online: 17 December 2004     

$\overline pp$ annihilation into four charged pions at rest and in flight

The spin-parity analysis of the data on the annihilation reaction at rest in liquid and in gaseous hydrogen at 3 bar pressure and in flight at momentum of MeV/c, collected by the Obelix spectrometer at the LEAR complex of CERN, is presented. The relative branching ratios and are obtained. It is also shown that the inclusion of the exotic meson , J^PC = 1^{- +} , mass and width , GeV/c², in its decay to , improves the fit and some implications of these results are briefly discussed. The relative S and P-wave annihilation percentages in four charged pions at two target densities are obtained.Received: 2 December 2003, Published online: 23 April 2004     

Parton distributions for high energy collisions

Recent data from deep inelastic scattering experiments atx10^–2 are used to fix the parton distributions down tox10^–4 andQ ²0.3 GeV². The predicted extrapolations are uniquely determined by the requirement of avalence-like structure ofall parton distributions at some low resolution scale and are furthermore shown to be insensitive in the small-x region, 10^–4x10^–2, to the detailed experimental input at the presently accessiblex>10^–2. Simple parameterizations of the resulting parton distributions are presented in the range 10^–5x<1 and=">Q ²10⁸ GeV² as obtained from the leading- and higher-order evolution equations.     

Measurement of the diffractive structure function in deep inelastic scattering at HERA

This paper presents an analysis of the inclusive properties of diffractive deep inelastic scattering events produced inep interactions at HERA. The events are characterised by a rapidity gap between the outgoing proton system and the remaining hadronic system. Inclusive distributions are presented and compared with Monte Carlo models for diffractive processes. The data are consistent with models where the pomeron structure function has a hard and a soft contribution. The diffractive structure function is measured as a function ofx , the momentum fraction lost by the proton, of , the momentum fraction of the struck quark with respect tox , and ofQ ² in the range 6.3·10^–4x <>^–2, 0.1<0.8 and=">Q ²<100>². The dependence is consistent with the formx wherea=1.30±0.08(stat) _–0.14 ^+0.08 (sys) in all bins of andQ ². In the measuredQ ² range, the diffractive structure function approximately scales withQ ² at fixed . In an Ingelman-Schlein type model, where commonly used pomeron flux factor normalisations are assumed, it is found that the quarks within the pomeron do not saturate the momentum sum rule.supported by Worldlab, Lausanne, Switzerland     

The Homogeneous Hamilton–Jacobi and Bernoulli Equations Revisited

The one-dimensional case of the homogeneous Hamilton–Jacobi and Bernoulli equations S_t S _x ² =0, where S(x, t) is Hamilton's principal function of a free particle and also Bernoulli's momentum potential of a perfect liquid, is considered. Non-elementary solutions are looked for in terms of odd power series in t with x-dependent coefficients and even power series in x with t-dependent coefficients. In both cases, and depending upon initial conditions, unexpected regularities are observed in the terms of these expansions and this suggests that S(^x, ^t) should be written as a product of the elementary solution x²/(2^t) and a function f=f() where =(x, |t|) owing to the symmetry property which is that S(x, –t)=–S(x, t). Requiring that this Ansatz satisfies the said equation and choosing the simplest realization of (x, |t|)=₀ |t/t₀| (x/x ₀)0 with , results in a soluble ordinary differential equation, of first order in u=ln and quadratic in f. This ODE has two fixed points: f=1, obviously, and f=0, a new fixed point which is often called trivial. The phase plane (f_u, f) consists of a family of parabolas, all of which pass through the two fixed points. Explicit solutions of the general case are given close to these fixed points. A one-parameter family of solution is found to emerge from the trivial fixed point with non-trivial initial values S(x, 0). Detailed analyses of these findings will be reported elsewhere, bearing in mind that Bernoulli's equation has to be supplemented by the continuity equation satisfied by the density of the liquid.     

Jet production in <Emphasis Type="Italic">pA</Emphasis> and <Emphasis Type="Italic">AA</Emphasis> collisions in the perturbative QCD pomeron model

Inclusive cross-sections for gluon jet production are studied numerically in the perturbative QCD pomeron model for pA and central AA collisions at high energies. Two forms for the inclusive cross-sections, with and without emission from the triple pomeron vertex, are compared. The difference was found to reduce to a numerical factor for momenta below the saturation momentum Q _s. Above Q _s no difference was found at all. For pA collisions the gluon spectrum was found to be at momenta k below Q _s and above it. For central AA collisions it was found to be at momenta k below Q _s and above it. At large k the spectrum goes like , flattening with energy. The multiplicities turned out to be proportional to A ^0.7 for pA collisions and A for central AA collisions with a good precision. In the latter case they are becoming more peaked at the center with the growth of energy. Their absolute values are high and grow rapidly with energy in accordance with the high value of the BFKL intercept.Received: 12 October 2004, Revised: 22 November 2004, Published online: 21 January 2005     

Excited states in 163,164Ho populated through incomplete-fusion reactions

High-spin states in ^163,164Ho were investigated by means of in-beam -ray spectroscopy techniques using the multidetector array GASP. Excited states in ^163,164Ho were populated predominantly through the incomplete-fusion mechanism in the ¹⁶⁰Gd (¹¹B reaction at a beam energy of 61 MeV. Known rotational bands in ¹⁶³ Ho have been extended to higher spins and a three-quasiparticle band has been observed in this nucleus. Rotational bands have been identified in ¹⁶⁴Ho and their configurations have been discussed. Empirical Gallagher-Moszkowski (GM) splitting energies were extracted from the and GM doublets. Alignments, band crossing frequencies, and electromagnetic properties have been analyzed in the framework of the cranking model.Received: 13 February 2004, Revised: 18 March 2004, Published online: 14 September 2004PACS: 21.10.Re Collective levels - 21.60.Ev Collective models - 23.20.Lv transitions and level energies - 27.70. + q      

Coherent production of pairs of parabosons of order 2

A parameter-free statistical model is used to study multiplicity signatures for coherent production of charged pairs of parabosons of order p = 2 in comparison with those arising in the case of ordinary bosons, p = 1. Two non-negative real parameters arise because ab and ba are fundamentally distinct pair operators of charge + 1, A-quanta and charge -1, B-quanta parabosons. In 3D plots of the probability of m paraboson charged pairs + q positive parabosons versus and , the p = 1 curve is found to lie on the relatively narrow 2D p = 2 surface.Received: 26 December 2003, Published online: 21 December 2004     

Masses and couplings of vector mesonsfrom the pion electromagnetic,weak, and $\pi\gamma$ transition form factors

We analyze the pion electromagnetic, charged-current, and transition form factors at timelike momentum transfers q, GeV², using a dispersion approach. We discuss in detail the propagator matrix of the photon-vector meson system and define certain reduced amplitudes, or vertex functions, describing the coupling of this system to final states. We then apply the derived analytic expressions to the analysis of the recent , , and data. We find the reduced amplitudes for the coupling of the photon and vector mesons to two pseudoscalars to be constant, independent of s, in the range considered, indicating a freezing of the amplitudes for GeV. The fit to the form factor data leads to the following values of the Breit-Wigner resonance masses MeV, MeV and MeV, where the errors are only statistical.Received: 8 December 2003, Published online: 23 March 2004T. Paulus: Now at Philips     

Thermal conductivity of doped $\mathsf{La_2CuO_4}$ as an example for heat transport by optical phonons in complex materials

We investigate the phonon thermal conductivity of doped based on out-of-plane thermal conductivity measurements. When room temperature is approached the temperature dependence of strongly deviates from the T^-1-decrease which is usually expected for heat transport by acoustic phonons. Instead, decreases much weaker or even increases with rising temperature. Simple arguments suggest that such unusual temperature dependencies of are caused by heat transport via dispersive optical phonons.Received: 20 October 2003, Published online: 20 April 2004PACS: 66.70. + f Nonelectronic thermal conduction and heat-pulse propagation in solids; thermal waves - 74.72.Dn La-based cuprates - 44.10. + i Heat conduction     

Statistical mechanics of nonlinear wave equations. 3. Metric transitivity for hyperbolic sine-gordon

McKean and Vaninsky proved that the canonical measuree ^–H d Q d P based upon the Hamiltonian of the wave equation ² Q/t ² - ² Q/x ² +f(Q) = 0 with restoring forcef(Q)=F'(Q) is preserved by the associated flow ofQ andP =Q , and they conjectured that metric transitivity prevails,always on the whole line, and likewise on the circleunless f(Q)=Q orf(Q)=shQ. Here, the metric transitivity is proved for the whole line in the second case. The proof employs the beautiful d'Alembert formula of Krichever.     

The transverse correlation length for randomly rough surfaces

It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx ₃=(x ₁), where the surface profile function (x ₁) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x ₁)(x ₁)/²(x ₁)=W (|x ₁–x ₁|) has the Lorentzian formW(|x ₁|)=a ²/(x ₁ ² +a ²) we find that d=0.9080a; when it has the Gaussian formW(|x ₁|)=exp(–x ₁ ² /a ²), we find that d=1.2837a; and when it has the nonmonotonic formW(|x ₁|)=sin(x ₁/a)/(x ₁/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) [the Fourier transform ofW(|x ₁|)] decays to zero with increasing |Q|. We also obtain the functionP(itx ₁), which is defined in such a way that, ifx ₁=0 is a zero of (x ₁),P(x ₁)dx ₁ is the probability that the nearest zero of (x ₁) for positivex ₁ lies betweenx ₁ andx ₁+dx ₁.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

The $\beta$-function in duality-covariant non-commutative $\phi^4$-theory

We compute the one-loop -functions describing the renormalisation of the coupling constant and the frequency parameter for the real four-dimensional duality-covariant non-commutative -model, which is renormalisable to all orders. The contribution from the one-loop four-point function is reduced by the one-loop wavefunction renormalisation, but the -function remains non-negative. Both and vanish at the one-loop level for the duality-invariant model characterised by . Moreover, also vanishes in the limit , which defines the standard non-commutative -quantum field theory. Thus, the limit exists at least at the one-loop level.Received: 19 March 2004, Published online: 5 May 2004     

\pi\pi correlations in \gamma + A reactions

Preliminary differential cross-sections of the reactions and with A = ¹ H, ¹² C, and ^nat Pb are presented. A significant nuclear-mass dependence of the invariant-mass distribution is found in the channel. The dependence is not observed in the channel. The in-medium observation in the channel is consistent with an in-medium modification of the interaction in the I = J = 0 channel, changing width and pole position of a resonant state.Received: 30 September 2002, Published online: 22 October 2003PACS: 13.60.Le Meson production - 21.65. + f Nuclear matterJ.G. Messchendorp: For the TAPS and A2 Collaborations