Mass matrices and eigenstates for scalars / pseudoscalars; indirect CP violation, mass hierarchies and symmetry breaking

I study indirect CP violation for neutral kaons, and extend it to large values of the CP-violating parameter (taken to be real). I show how and at which condition there can exist a continuous set of basis in which the kinetic and mass terms in the Lagrangian can be diagonalized simultaneously. An ambiguity results for the mass spectrum, which then depends on the basis. In particular, for fixed (positive) (mass)^2 of the CP eigenstates K^0_1, K^0_2, and for certain ranges of values of the CP-violating parameter, a negative (mass)^2 can arise in the CP-violating basis. Under certain conditions, even a small perturbation, by lifting the ambiguity, can strongly alter the pattern of masses. These investigations extend in a natural way to indirect CP violation among a set of Higgs-like doublets. The C-odd commutator [K^0, K^0 bar], or its equivalent for Higgs multiplets, plays an important role. The condition for its vanishing and its consequences are among the main concerns of this work.Comment: LaTeX2e, 35 pages, 10 postscript figures + 1 log

Binary systems of neutral mesons in Quantum Field Theory

Quasi-degenerate binary systems of neutral mesons of the kaon type are investigated in Quantum Field Theory (QFT). General constraints cast by analyticity and discrete symmetries P, C, CP, TCP on the propagator (and on its spectral function) are deduced. Its poles are the physical masses; this unambiguously defines the propagating eigenstates. It is diagonalized and its spectrum thoroughly investigated. The role of ``spurious'' states, of zero norm at the poles, is emphasized, in particular for unitarity and for the realization of TCP symmetry. The K_L-K_S mass splitting triggers a tiny difference between their CP violating parameters \epsilon_L and \epsilon_S, without any violation of TCP. A constant mass matrix like used in Quantum Mechanics (QM) can only be introduced in a linear approximation to the inverse propagator, which respects its analyticity and positivity properties; it is however unable to faithfully describe all features of neutral mesons as we determine them in QFT, nor to provide any sensible parameterization of eventual effects of TCP violation. The suitable way to diagonalize the propagator makes use of a bi-orthogonal basis; it is inequivalent to a bi-unitary transformation (unless the propagator is normal, which cannot occur here). Problems linked with the existence of different ``in'' and ``out'' eigenstates are smoothed out. We study phenomenological consequences of the differences between the QFT and QM treatments. The non-vanishing of semi-leptonic asymmetry \delta_S - \delta_L does not signal, unlike usually claimed, TCP violation, while A_TCP keeps vanishing when TCP is realized. We provide expressions invariant by the rephasing of K0 and K0bar.Comment: 44 pages, 2 figures. Version to appear in Int. J. Mod. Phys.

Next-to-MLLA corrections to single inclusive kt-distributions and 2-particle correlations in a jet

The hadronic kt-spectrum inside a high energy jet is determined including corrections of relative magnitude O{\sqrt{\alpha_s}} with respect to the Modified Leading Logarithmic Approximation (MLLA), in the limiting spectrum approximation (assuming an infrared cut-off Q0 =Lambda_{QCD}) and beyond Q_0\ne\Lambda_{QCD}. The results in the limiting spectrum approximation are found to be, after normalization, in impressive agreement with preliminary measurements by the CDF collaboration, unlike what occurs at MLLA, pointing out small overall non-perturbative contributions. Within the same framework, 2-particle correlations inside a jet are also predicted at NMLLA and compared to previous MLLA calculations.Comment: 35 pages and 39 figures. Comments, appendices, figures, references added. Version to appear in Phys. Rev.

Modification of Coulomb law and energy levels of the hydrogen atom in a superstrong magnetic field

We obtain the following analytical formula which describes the dependence of the electric potential of a point-like charge on the distance away from it in the direction of an external magnetic field B: \Phi(z) = e/|z| [ 1- exp(-\sqrt{6m_e^2}|z|) + exp(-\sqrt{(2/\pi) e^3 B + 6m_e^2} |z|) ]. The deviation from Coulomb's law becomes essential for B > 3\pi B_{cr}/\alpha = 3 \pi m_e^2/e^3 \approx 6 10^{16} G. In such superstrong fields, electrons are ultra-relativistic except those which occupy the lowest Landau level (LLL) and which have the energy epsilon_0^2 = m_e^2 + p_z^2. The energy spectrum on which LLL splits in the presence of the atomic nucleus is found analytically. For B > 3 \pi B_{cr}/\alpha, it substantially differs from the one obtained without accounting for the modification of the atomic potential.Comment: version to be published in Physical Review D (incorrect "Keywords" in previous version have been cancelled

The Schnitzler syndrome

The Schnitzler syndrome is a rare and underdiagnosed entity which is considered today as being a paradigm of an acquired/late onset auto-inflammatory disease. It associates a chronic urticarial skin rash, corresponding from the clinico-pathological viewpoint to a neutrophilic urticarial dermatosis, a monoclonal IgM component and at least 2 of the following signs: fever, joint and/or bone pain, enlarged lymph nodes, spleen and/or liver, increased ESR, increased neutrophil count, abnormal bone imaging findings. It is a chronic disease with only one known case of spontaneous remission. Except of the severe alteration of quality of life related mainly to the rash, fever and pain, complications include severe inflammatory anemia and AA amyloidosis. About 20% of patients will develop a lymphoproliferative disorder, mainly Waldenström disease and lymphoma, a percentage close to other patients with IgM MGUS. It was exceedingly difficult to treat patients with this syndrome until the IL-1 receptor antagonist anakinra became available. Anakinra allows a complete control of all signs within hours after the first injection, but patients need continuous treatment with daily injections

On the Khalfin's improvement of the LOY effective Hamiltonian for neutral meson complex

The general properties of the effective Hamiltonian for neutral meson system improved by L.A. Khalfin in 1980 are studied. It is shown that contrary to the standard result of the Lee--Oehme--Yang (LOY) theory, the diagonal matrix elements of this effective Hamiltonian can not be equal in a CPT invariant system. It is also shown that the scalar product of short, $|K_{S}>$, and long, $|K_{L}>$, living superpositions of neutral kaons can not be real when CPT symmetry is conserved in the system under considerations whereas within the LOY theory such a scalar product is real.Comment: LaTeX2e, 25 pages, new comment and references adde

Low back pain as the presenting sign in a patient with primary extradural melanoma of the thoracic spine - A metastatic disease 17 Years after complete surgical resection

Primary spinal melanomas are extremely rare lesions. In 1906, Hirschberg reported the first primary spinal melanoma, and since then only 40 new cases have been reported. A 47-year-old man was admitted suffering from low back pain, fatigue and loss of body weight persisting for three months. He had a 17-year-old history of an operated primary spinal melanoma from T7-T9, which had remained stable for these 17 years. Routine laboratory findings and clinical symptoms aroused suspicion of a metastatic disease. Multislice computed tomography and magnetic resonance imaging revealed stage-IV melanoma with thoracic, abdominal and skeletal metastases without the recurrence of the primary process. Transiliac crest core bone biopsy confirmed the diagnosis of metastatic melanoma. It is important to know that in all cases of back ore skeletal pain and unexplained weight loss, malignancy must always be considered in the differential diagnosis, especially in the subjects with a positive medical history. Patients who have back, skeletal, or joint pain that is unresponsive to a few weeks of conservative treatment or have known risk factors with or without serious etiology, are candidates for imaging studies. The present case demonstrates that complete surgical resection alone may result in a favourable outcome, but regular medical follow-up for an extended period, with the purpose of an early detection of a metastatic disease, is highly recommended