Further study of theE/f 1 (1420) meson in central production

We have studied the reactions \(({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})p \to ({{\pi ^ + } \mathord{\left/ {\vphantom {{\pi ^ + } p}} \right. \kern-0em} p})(K\bar K\pi )p\) where the \(K\bar K\pi \) system is centrally produced, at 85 GeV/c and 300 GeV/c using the CERN Omega spectrometer. A spin-parity analysis of theK _S ⁰ K ^± π ^? system shows the presence of a strongJ ^PC=1⁺⁺ signal which we identify as theE/f ₁ (1420) meson. We also find evidence for the decayE/f ₁(1420)→K _S ⁰ K _S ⁰ π ⁰ which determines theC-parity of this state to be positive. Alternative explanations of the data have been tested and ruled out. Hence we obtain the quantum numbers of theE/f ₁ (1420) to beI ^G(J^PC)=0⁺(1⁺).     

Recent results on kaon decays by the NA48/2 experiment at CERN

The NA48/2 experiment reports the first observation of the rare decay K^± → π^±π⁰e⁺e^?, based on about 2000 candidates from 2003 data. The preliminary branching ratio in the full kinematic region is \(\mathcal {B}(K^{\pm } \to \pi ^{\pm }\pi ^{0}e^{+}e^{-})=(4.06\pm 0.17)\cdot 10^{-6}\). A sample of 4.687 × 10⁶\(K^{\pm }\to \pi ^{\pm }{\pi ^{0}_{D}}\) events collected in 2003/4 is analyzed to search for the dark photon (\(A^{\prime }\)) via the decay chain K^± → π^±π⁰, \(\pi ^{0}\to \gamma A^{\prime }\), \(A^{\prime }\to e^{+}e^{-}\). No signal is observed, limits in the plane mixing parameter ε² versus its mass \(m_{A^{\prime }}\) are reported.     

Ds+ → π+ π+ π− decay: The $$1^3 P_0 s\bar s$$ component in scalar-isoscalar mesons

We calculate the processes \(D_s^ + \to \pi ^ + s\bar s\) and D _s ⁺ → π⁺resonance, respectively, in the spectator and W-annihilation mechanisms. The data on the reaction D _s ⁺ → π⁺ρ⁰, which is due to the W-annihilation mechanism only, point to a negligibly small contribution of the W annihilation to the production of scalar-isoscalar resonances D _s ⁺ ?π⁺f₀. As to spectator mechanism, we evaluate the \(1^3 P_0 s\bar s\) component in the resonances f₀(980), f₀(1300), and f₀(1500) and broad state f₀(1200–1600) on the basis of data on the decay ratios D _s ⁺ ?π⁺f₀/(D _s ⁺ ?π⁺_θ). The data point to a large \(s\bar s\) component in the \(f_0 (980):40 \lesssim s\bar s \lesssim 70\% \). Nearly 30% of the \(1^3 P_0 s\bar s\) component flows to the mass region 1300–1500 MeV, being shared by f₀(1300), f₀(1500), and broad state f₀(1200–1600): the interference of these states results in a peak near 1400 MeV with the width around 200 MeV. Our calculations show that the yield of the radial-excitation state\(2^3 P_0 s\bar s\)is relatively suppressed, \({{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} \mathord{\left/ {\vphantom {{\Gamma (D_s^ + \to \pi ^ + (2^3 P_0 s\bar s))} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}}} \right. \kern-\nulldelimiterspace} {\Gamma (D_s^ + \to \pi ^ + (1^3 P_0 s\bar s))}} \lesssim 0.05\).     

Inclusive production ofK s 0 , K s 0 K s 0 andK *±(892) in\bar pp interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c

InclusiveK _s ⁰ andK _s ⁰ K _s ⁰ production in \(\bar pp\) interactions at 3.0, 3.5, 4.0 and 4.5 GeV/c are studied. Cross sections ofK _s ⁰ , K _s ⁰ K _s ⁰ andK ^*±(892) are presented for each incident momentum. The production ofK _s ⁰ andK ^*±(892) through annihilation process is investigated. It is found that the annihilation process is dominant but decreases with incident momentum. The annihilation process is compared withe ⁺ e ^? interactions. Remarkable similarity between them is found in the \({{x_0 = 2E(K_s^0 )} \mathord{\left/ {\vphantom {{x_0 = 2E(K_s^0 )} {\sqrt s }}} \right. \kern-0em} {\sqrt s }}\) distribution. Events with two detectedK _s ⁰ 's are analyzed. The result shows theK _s ⁰ K _s ⁰ pairs are produced in the central region of c.m. system and there is a clearS ^* signal in theK _s ⁰ K _s ⁰ effective mass distribution.     

Production properties ofD 0,D +,D *+ andD s + in 230 GeV/cπ − andK −-Cu interactions

We have studied the hadronic production of charmed mesons in the NA 32 experiment at CERN. A special trigger together with a high resolution vertex detector consisting of charge coupled devices and silicon microstrip detectors allowed the selection of very clean samples of charmed mesons. We have collected 852 fully reconstructed decays: 60D _s ⁺ →K ⁺ K ^?π⁺, 543D°→K ^?π⁺ andK ^?π⁺π^?π⁺ as well as 249D ⁺→K ^?π⁺π⁺ (or charge conjugate). 147 mesons out of our \({{D^0 } \mathord{\left/ {\vphantom {{D^0 } {\bar D^0 }}} \right. \kern-0em} {\bar D^0 }}\) sample were produced via chargedD ^* state. For all charmed mesons we determine the total production cross-section and study thex _F andp _t ² distributions.     

On the behavior of the πN partial wave amplitudes ats=0

The behavior of theπN partial wave amplitudes in the limitss→+0 ands→? 0 is related to backward scattering in thes- andt-channel, respectively. Assuming Mandelstam analyticity we prove with the aid of the Phragmen-Lindelöf theorem that the amplitudes for high energy backward scattering inπN→πN andππ→N¯N are equal and therefore dominated by the same exchange mechanism, namely Reggeized Fermion exchange. The dominating Regge trajectory is the Δ_δ-trajectory, and it is shown that theπN partial wave amplitudes diverge fors→±0 as \(s^{ - \alpha \Delta _\delta (0) - {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-0em} 2}} \) . — Reduced amplitudes are defined which are regular ats=0. — Using recent results ofπN backward scattering real and imaginary part of thes-wave amplitudef ₀₊ ^(?) are calculated in the interval 0≦s≦7.     

Lightest scalar resonances and the dynamics of the γγ → ππ reactions

The high-statistics Belle data on the γγ → π⁺π^? and γγ → π⁰π⁰ reactions have been jointly analyzed. The main dynamical mechanisms of these reactions for energies below 1.5 GeV have been revealed. It has been shown that the direct coupling constants of the σ(600) and f ₀(980) resonances with a γγ pair are small and that the σ(600) → γγ and f ₀(980) → γγ decays are four-quark transitions due primarily to π⁺π^? and K ⁺ K ^?-loop mechanisms, respectively. The role of the chiral shielding of the σ(600) resonance is emphasized. The widths of the f ₀(980) → γγ and σ(600) → γγ decays averaged over the resonance mass distributions, as well as the width of the f ₂(1270) → γγ decay, are estimated as \(\langle \Gamma _{f_0 \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.19 keV, \langle \Gamma _{\sigma \to \gamma \gamma } \rangle _{\pi \pi } \approx 0.45 keV\), and \(\Gamma _{f_2 \to \gamma \gamma } (m_{f_2 }^2 ) \approx 3.8 keV\).     

Die absolute Intensität der durch Elektronenstoß in einer dicken Cu-Antikathode erzeugtenKα-Strahlung

The numberN _Kα ^dir (produced) ofKα-photons produced by electron-bombardment in a thick target of copper per incident electron has been measured absolutely with the Ross-filter method and relatively with the crystal-spectrometer method in the energy-region up to the four times theK-ionization energyE _K . The result can be presented in the following empirical form:N _Kα ^dir (produced) = 4π·

     

Characteristics of π−,\bar p,and antinuclei frompp collisions

An investigation of inclusivepp→π^?+? in terms of the covariant Boltzmann factor (BF) including the chemical potential μ indicates a) that the temperatureT increases less rapidly than expected from Stefan's law, b) that a scaling property holds for the fibreball velocity of π^? secondaries, leading to a multiplicity law like ～E _cm ^1/2 at high energy, and c) that μ_π is related to the quark mass: μ_π=2m _q ?m _π the quark massm _q determined by \(T_{\pi ^ - } \) at \(\bar pp\) threshold beingm _q =3T_π?330 MeV. Because ofthreshold effects \(T_{\bar p}< T_{\pi ^ - } \) , whereas \({{\mu _p } \mathord{\left/ {\vphantom {{\mu _p } {\mu _{\pi ^ - } }}} \right. \kern-0em} {\mu _{\pi ^ - } }} \simeq {3 \mathord{\left/ {\vphantom {3 2}} \right. \kern-0em} 2}\) as expected from the quark contents of \(\bar p\) and π. The antinuclei \(\bar d\) and \({{\bar t} \mathord{\left/ {\vphantom {{\bar t} {\overline {He^3 } }}} \right. \kern-0em} {\overline {He^3 } }}\) observed inpp events are formed by coalescence of \(\bar p\) and \(\bar n\) produced in thepp collision. Semi-empirical formulae are proposed to estimate multiplicities of π^?, \(\bar p\) and antinuclei.     

Band interaction in <Superscript>162</Superscript>Dy, <Superscript>168</Superscript>Er,and <Superscript>172</Superscript>Yb

Coriolis interaction between levels of two rotational bands in ¹⁷²Yb with K ^π = 2⁺ and 3⁺ and in ¹⁶⁸Er between levels with K ^π = 0^?, 1^?, and 2^? is studied. The values of the interaction parameters are obtained. The mutual influence of two bands in ¹⁶²Dy with ΔK = 2, K _i ^π = 0 ₂ ⁺ and 2 ₁ ⁺ due to Coriolis interaction is demonstrated.     

In-plane torque and gap symmetry of untwinned YBa<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7</Subscript> crystals

The reversible magnetic torque of untwinned YBa₂Cu₃O₇ single crystals shows the four-fold symmetry in thea-b plane. The irreversible torque indicates evidence for a novel intrinsic pinning along thea andb axes. These facts mean that the free energy of the four-fold symmetry has a minimum when the field is applied along thea orb axis. The results are consistent with those expected from thed _x ²?y ² symmetry and rule out the possibility of thed _xy symmetry. The Fermi surface anisotropy is not responsible for the observed anisotropy. This is firstbulk evidence for thek-dependent gap anisotropy on the Fermi surface. The two-fold anisotropy parameter is found as\(\gamma _{ab} = \sqrt {{{m_a } \mathord{\left/ {\vphantom {{m_a } {m_b }}} \right. \kern-\nulldelimiterspace} {m_b }}} = 1.18 \pm 0.14\).     

Comparison of theK ± p scattering data with the forward dispersion relations

The dispersion relations forK ^± p forward scattering were evaluated in order to test the compatibility with the experimental data and to obtain an estimation of the effective coupling constantG ^2/4π=(G _Λ ² +G _Σ ² )/4π.     

Conserved-vector-current hypothesis and the\bar v_e e^ - \to \pi ^ - \pi ^0 process

Based on the conserved-vector-current (CVC) hypothesis and a four-ρ-resonance unitary and analytic VMD model of the pion electromagnetic form factor, theσ _tot(E _v ^lab ) and dσdE _π ^lab of the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) process are predicted theoretically for the first time. Their experimental approval could verify the CVC hypothesis for all energies above the two-pion threshold. Since, unlike the electromagnetic e⁺e^?→π⁺π^? process, there is no isoscalar vector-meson contribution to the weak \(\bar v_e e^ - \to \pi ^ - \pi ^0\) reaction, accurate measurements of theσ _tot(E _v ^lab ) that moreover is strengthened with energyE _v ^lab linearly could solve now a widely discussed problem of the mass specification of the first excited state of theρ(770) meson. As a by-product, an equality \(\sigma _{tot} (\bar v_e e^ - \to \pi ^ - \pi ^0 ) = \sigma _{tot} (e^ + e^ - \to \pi ^ - \pi ^0 )\) is predicted for \(\sqrt s \approx 70 GeV\) .     

Meson baryon sum rules

The PCAC consistency condition, the Adler-Weisberger sum rule and the dispersion superconvergent sum rule have been saturated with resonance contributions only. Strangeness-changing currents and strangeness-conserving currents have been considered and compared. The results obtained also support PCAC for the strangeness conserving current. While in theπN case PCAC and the Adler-Weisberger sum rule are almost saturated with the famous N ₃₃ ^* resonance only, in the KN caseY ₁ ^* (1385),Y ₀ ^* (1405) andY ₀ ^* (1520) seem to be sufficient. The superconvergent sum rule works very well in the case ofπN scattering, including the contribution of twelve resonances. For KN scattering it can be neither established nor disapproved.     

Absorptive corrections to associated production of strange baryon and meson resonances in πp scattering

Absorptive corrections are calculated for the reactionsπ ⁺ p→K ^*+∑⁺(K ^*+ Y ₁ ^*+ ) mediated byK-exchange andπ ⁺p→K⁺ Y ₁ ^*+ withK ^*-exchange. The effect of the finite width of the resonances is included. Numerical results are given for 5 and 8 GeV/c.     

Searching for signatures around 1920 MeV of a N<Superscript>*</Superscript> state of three hadron nature

We provide a series of arguments which support the idea that the peak seen in the \( \gamma\) p \( \rightarrow\) K ⁺ \( \Lambda\) reaction around 1920MeV should correspond to the recently predicted state of J ^P = 1/2⁺ as a bound state of K \( \bar{{K}}\) N with a mixture of a ₀(980)N and f ₀(980)N components. At the same time we propose polarization experiments in that reaction as a further test of the prediction, as well as a study of the total cross-section for \( \gamma\) p \( \rightarrow\) K ⁺ K ^- p at energies close to threshold and of dσ/dM _inv for invariant masses close to the two-kaon threshold.     

Formfaktor des π-Mesons und Struktur der Nukleonen

Recent measurements of electron-proton scattering at Stanford have shown that the electric and magnetic form factors are not equal. Therefore, the isotopic vector parts of the form factorsG _e ^v andG _m ^v are recalculated with unsubtracted dispersion relations in the 2π-approximation. For the isotopic scalar parts we useG _e ^s (s)≈G _e ^v (s) andG _m ^s (s)≈ 0 which is known to be valid for moderate energy-momentum transfers. We obtain a simple closed expression for the electromagnetic form factor of the pionF _π in terms of the scattering lengtha ₁ and the effective ranger ₁ of the π-π-scattering in the stateL=T=1.a ₁ is roughly known from pion production by pions. With this value and a suitabler ₁,F _π has a resonance in the region of time-like energy-momentum transfer; and the pion rms-radius becomes\(\overline {v_\pi ^2 } = (0.82 \times 10^{ - 13} cm)^2 \). The calculated anomalous magnetic moment, the electric and the magnetic rms-radii of the proton are then within 10% of the experimental values, the electric charge within 30%. Moreover, the proton form factors are different from each other and up to an energy-momentum transfer of\(s = \frac{{ - q^2 }}{{m_\pi ^2 }} = 23\) within the experimental error of the new measurements. The deviations for higher values of the energy-momentum transfer may be explained in terms of the isotopic scalar parts of the form factors. In this case the electric form factor of the neutron will be different from zero in that region and the magnetic form factor of proton and neutron will no longer be equal. For comparison with other experiments we also calculate the π⁺?π^? cross section with neglect of other states thanL=T=1. Under this assumption the π?π cross section has a resonance for low energy-momentum transfer.     

Einfluß der Pion-Pion-Wechselwirkung auf Pion-Nukleon-Streuphasen

The isospin dependent part of theS-wave pion-nucleon amplitude is calculated according to the CGLN approach, but recoil and projection on the partial waves are treated exactly. Then the difference against the experimental data is approximately a constant up to 100 MeV and amounts to 1/3 of the total value. It is shown, that at low energies the main corrections of the CGLN equations are taken into account by a subtraction of theπ+π→?+\(\overline \Re \),J=I=1 amplitudesf _± ¹ (t) as proposed byMandelstam andFrazer. Calculations have been done forS, P andD pion-nucleon amplitudes. The main result is a prediction of theS-wave amplitude obtained without adjusting free parameters up to 100 MeV. The relations of this method to the equations derived byBowcock, Cottingham andLurié according to the Cini-Fubini approach are discussed.     

Absorptionsspektrum des Ce3+-Ions und Kristallfeld im La(Ce)Cl

The absorption spectrum of single crystals of La_(1?x)Ce _x Cl₃(x=0,05 ... 0,005) has been observed at low temperatures in the region of the 4f→4f infrared transitions. Values for the crystal-field parameters V ₂ ⁰ , V ₄ ⁰ , V ₆ ⁰ , V ₆ ⁶ and for the spin-orbit coupling constant of the ion in the crystalline environment are determined by fitting the observed splittings of the multiplet-components\({}^2F_{\tfrac{5}{2}} \) and\({}^2F_{\tfrac{7}{2}} \) in the crystal-field. The parameters are found to be consistent with values extrapolated from rare earth-ions with neighbouring atomic numbers in the same host-lattice. The only exception is the parameter V ₆ ⁶ , which is found to be smaller in La(Ce)Cl₃ than in other rare-earth-trichlorides (V ₆ ⁶ /V ₆ ⁰ =?6,23 in La(Ce)Cl₃, V ₆ ⁶ /V ₆ ⁰ ≈?10 in other trichlorides). The correct relation V ₆ ⁶ /V ₆ ⁰ in La(Ce)Cl₃ is obtained by fitting the parameters to the observed crystal-field-splitting of the\({}^2F_{\tfrac{5}{2}} \) — component and to the observed Zeeman-splitting-factors taken from the literature. The discrepancies between the two fitting procedures are explained by an effect of nonlinear shielding of the crystal-field.     

Application of the hidden local symmetry effective chiral Lagrangian to evaluation of the <Emphasis Type="Italic">ω</Emphasis>(782), <Emphasis Type="Italic">ϕ</Emphasis>(1020) → 5<Emphasis Type="Italic">π</Emphasis> decay widths

The amplitudes obtained from the effective chiral Lagrangian with anomalous terms based on hidden local symmetry are applied to the evaluation of the partial widths of the decays ω → 2π⁺2π^?π⁰ and ω → π⁺π^?3π⁰. Combining the Okubo-Zweig-Iizuka rule, applied to the five-pion final state, with the Adler condition of vanishing of the amplitude at the vanishing of four-momentum of any final pion in the chiral limit, the ? → 2π⁺2π^?π⁰ and ? → π⁺π^?3π⁰ decay amplitudes are also calculated. The partial widths of the above decays are evaluated, and the resonance excitation curves in e⁺e^? annihilation are obtained, assuming reasonable particular relations among the free parameters characterizing the anomalous terms of the Lagrangian. The evaluated branching ratios \(Br_{\phi \to \pi + \pi - 3\pi ^0 } \approx 2 \times 10^{ - 7} \) and \(Br_{\phi \to 2\pi + 2\pi - \pi ^0 } \approx 5 \times 10^{ - 7} \) are such that with the luminosity L = 500 pb^?1, attained at the DAΦNE ? factory, one may already possess about 1340 events of the decays ? → 5π.