Regular Series


Vol. 42 (2011), No. 9, pp. 1891 – 2045


Dressing Method for a Generalized Focusing NLS Equation via Local Riemann–Hilbert Problem

abstract

A generalized focusing NLS equation is studied by the dressing method via local Riemann–Hilbert problem. The associated RH problem with zeros is solved by means of regularization. The explicit solutions, including one-soliton, two-soliton solution and breather solution, are obtained.


Saturation of Uncertainty Relations for Twisted Acceleration-Enlarged Newton–Hooke Space-Times

abstract

Using Fock representation we construct states saturating uncertainty relations for twist-deformed acceleration-enlarged Newton–Hooke space-times.


Novel Ideas about Emergent Vacua

abstract

Arguments for special emergent vacua which generate fermion and weak boson masses are outlined. Limitations and consequences of the concept are discussed. If confirmed, the Australian dipole would give strong support to such a picture. Preliminary support from recent DZero and CDF data is discussed and predictions for LHC are presented.


Reinterpretation of Gluon Condensate in Dynamics of Hadronic Constituents

abstract

We describe an approximate quantum mechanical picture of hadrons in Minkowski space in the context of a renormalization group procedure for effective particles (RGPEP) in a light-front Hamiltonian formulation of QCD. The picture suggests that harmonic oscillator potentials for constituent quarks in lightest mesons and baryons may result from the gluon condensation inside hadrons, rather than from an omnipresent gluon condensate in vacuum. The resulting boost-invariant constituent dynamics at the renormalization group momentum scales comparable with \({\mit \Lambda }_{\rm QCD}\), is identified using gauge symmetry and a crude mean-field approximation for gluons. Besides constituent quark models, the resulting picture also resembles models based on AdS/QCD ideas. However, our hypothetical picture significantly differs from the models by the available option for a systematic analysis in QCD, in which the new picture may be treated as a candidate for a first approximation. This option is outlined by embedding our presentation of the crude and simple hadron picture in the context of RGPEP and a brief outlook on hadron phenomenology. Several appendices describe elements of the formalism required for actual calculations in QCD, including an extension of RGPEP beyond perturbation theory.


\(S\)-, \(P\)- and \(D\)-wave \(\pi \pi \) Final State Interactions and CP Violation in \(B^\pm \to \pi ^\pm \pi ^\mp \pi ^\pm \) Decays

abstract

We study CP violation and the contribution of the strong pion–pion interactions in the three-body \(B^\pm \to \pi ^\pm \pi ^\mp \pi ^\pm \) decays within a quasi two-body QCD factorization approach. The short distance interaction amplitude is calculated in the next-to-leading order in the strong coupling constant with vertex and penguin corrections. The meson–meson final state interactions are described by pion non-strange scalar and vector form factors for the \(S\) and \(P\) waves and by a relativistic Breit–Wigner formula for the \(D\) wave. The pion scalar form factor is calculated from a unitary relativistic coupled-channel model including \(\pi \pi \), \(K \bar K\) and effective \((2\pi )(2\pi )\) interactions. The pion vector form factor results from a Belle Collaboration analysis of \(\tau ^- \to \pi ^- \pi ^0 \nu _\tau \) data. The recent \(B^\pm \to \pi ^\pm \pi ^\mp \pi ^\pm \) BABAR Collaboration data are fitted with our model using only three parameters for the \(S\) wave, one for the \(P\) wave and one for the \(D\) wave. We find not only a sizable contribution of the \(S\) wave just above the \(\pi \pi \) threshold but also under the \(\rho (770)\) peak a significant interference, mainly between the \(S\) and \(P\) waves. For the \(B\) to \(f_2(1270)\) transition form factor, we predict \(F^{Bf_2}(m_\pi ^2)=0.098\pm 0.007\). Our model yields a unified unitary description of the contribution of the three scalar resonances \(f_0(600)\), \(f_0(980)\) and \(f_0(1400)\) in terms of the pion non-strange scalar form factor.


ERRATUM for Acta Phys. Pol. B 40, 1485 (2009)

On the Relation Between Lacunarity and Fractal Dimension


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