Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.Comment: published version, 17 page

Characteristics of difficult-to-treat rheumatoid arthritis: results of an international survey

Objectives: Patients with difficult-to-treat rheumatoid arthritis (RA) remain symptomatic despite treatment according to current European League Against Rheumatism (EULAR) management recommendations. These focus on early phases of the disease and pharmacological management. We aimed to identify characteristics of difficult-to-treat RA and issues to be addressed in its workup and management that are not covered by current management recommendations. Methods: An international survey was conducted among rheumatologists with multiple-choice questions on disease characteristics of difficult-to-treat RA. Using open questions, additional items to be addressed and items missing in current management recommendations were identified. Results: 410 respondents completed the survey: 50% selected disease activity score assessing 28 joints >3.2 OR presence of signs suggestive of active disease as characteristics of difficult-to-treat RA; 42% selected fatigue; 48% selected failure to ≥2 conventional synthetic disease-modifying antirheumatic drugs (DMARDs) AND ≥2 biological/targeted synthetic DMARDs; 89% selected inability to taper glucocorticoids below 5 mg or 10 mg prednisone equivalent daily. Interfering comorbidities, extra-articular manifestations and polypharmacy were identified as important issues missing in current management recommendations. Conclusions: There is wide variation in concepts of difficult-to-treat RA. Several important issues regarding these patients are not addressed by current EULAR recommendations

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Search for Anomalous Couplings in the Higgs Sector at LEP

Anomalous couplings of the Higgs boson are searched for through the processes e^+ e^- -> H gamma, e^+ e^- -> e^+ e^- H and e^+ e^- -> HZ. The mass range 70 GeV < m_H < 190 GeV is explored using 602 pb^-1 of integrated luminosity collected with the L3 detector at LEP at centre-of-mass energies sqrt(s)=189-209 GeV. The Higgs decay channels H -> ffbar, H -> gamma gamma, H -> Z\gamma and H -> WW^(*) are considered and no evidence is found for anomalous Higgs production or decay. Limits on the anomalous couplings d, db, Delta(g1z), Delta(kappa_gamma) and xi^2 are derived as well as limits on the H -> gamma gamma and H -> Z gamma decay rates

Measurement of W Polarisation at LEP

The three different helicity states of W bosons produced in the reaction e+ e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to measure the polarisation of W bosons, and its dependence on the W boson production angle. The fraction of longitudinally polarised W bosons is measured to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model expectation

Bose-Einstein Correlations of Neutral and Charged Pions in Hadronic Z Decays

Bose-Einstein correlations of both neutral and like-sign charged pion pairs are measured in a sample of 2 million hadronic Z decays collected with the L3 detector at LEP. The analysis is performed in the four-momentum difference range 300 MeV < Q < 2 GeV. The radius of the neutral pion source is found to be smaller than that of charged pions. This result is in qualitative agreement with the string fragmentation model

Z Boson Pair-Production at LEP

Events stemming from the pair-production of Z bosons in e^+e^- collisions are studied using 217.4 pb^-1 of data collected with the L3 detector at centre-of-mass energies from 200 GeV up to 209 GeV. The special case of events with b quarks is also investigated. Combining these events with those collected at lower centre-of-mass energies, the Standard Model predictions for the production mechanism are verified. In addition, limits are set on anomalous couplings of neutral gauge bosons and on effects of extra space dimensions

Neutral-Current Four-Fermion Production in e+e- Interactions at LEP

Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of data collected with the L3 detector at LEP at centre-of-mass energies root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and llvv, where l denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e- -> Zgamma* -> ffff process is studied and its total cross section at the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/- 0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqll final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found

Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP

Exclusive rho+rho- production in two-photon collisions between a quasi-real photon, gamma, and a mid-virtuality photon, gamma*, is studied with data collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* -> rho+ rho- process is determined as a function of the photon virtuality, Q^2, and the two-photon centre-of-mass energy, W_gg, in the kinematic region: 0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2 < 30 GeV^2

Measurement of the Running of the Electromagnetic Coupling at Large Momentum-Transfer at LEP

The evolution of the electromagnetic coupling, alpha, in the momentum-transfer range 1800GeV^2 < -Q^2 < 21600GeV^2 is studied with about 40000 Bhabha-scattering events collected with the L3 detector at LEP at centre-of-mass energies 189-209GeV. The running of alpha is parametrised as: alpha(Q^2) = alpha_0/(1-C Delta alpha(Q^2)), where alpha_0=\alpha(Q^2=0) is the fine-structure constant and C=1 corresponds to the evolution expected in QED. A fit to the differential cross section of the e+e- ->e+e- process for scattering angles in the range |cos theta|<0.9 excludes the hypothesis of a constant value of alpha, C=0, and validates the QED prediction with the result: C = 1.05 +/- 0.07 +/- 0.14, where the first uncertainty is statistical and the second systematic