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The influence of chaos on properties of dilute instanton gas in quantum mechanics is studied. We demonstrate on the example of one-dimensional periodic potential that small perturbation leading to chaos squeezes instanton gas and increases the rate of instanton tunnelling.

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We show that the presently observed anisotropy of the cosmic microwave background radiation already restricts the size of the fundamental domain. It turns out that if the Universe is multiply connected then the size of the fundamental domain is comparable or larger than the diameter of the surface of last scattering.

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The issue of existence of Majorana neutrinos with masses of the order of TeV and substantial couplings is addressed. A general neutrino mass matrix \(M_{\nu }\) with both features is constructed, however, the form of \(M_{\nu }\) is constrained very much by severe relations among the elements of \(m_{\rm D}\) and \(M_{\rm R}\) sub-matrices of \(M_{\nu }\). These general relations follow from the perturbative construction of the light neutrino mass spectrum. To avoid such large correlations between low mass parameters in \(m_{\rm D}\) and large mass parameters in \(M_{\rm R}\), the Jeżabek–Sumino see-saw model of bi-maximal neutrino mixing adopted to the TeV scale and the issue of possible symmetries of the matrix \(M_{\nu }\) are discussed. Results are supported by a few numerical examples which show directly the complexity of the problem.

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It is conjectured that a diagonal and degenerate \(3\times 3\) active–active component (i.e., lefthanded component) dominates in the effective \(6\times 6\) mass matrix for six Majorana neutrinos, three active and three (conventional) sterile, while its \(3\times 3\) active-sterile component (i.e., Dirac component) arises through a bimaximal-mixing unitary transformation from a structure similar to the \(3\times 3\) mass matrices for charged leptons as well as up and down quarks. In such a texture, three neutrino masses are nearly degenerate, \( m_1 \simeq m_2 \simeq m_3 \), though their mass-squared differences appear hierarchical, \(\Delta m^2_{21} \ll \Delta m^2_{32} \simeq \Delta m^2_{31}\), whereas the remaining three neutrino masses can be constructed to vanish, \( m_4 = m_5 = m_6 = 0 \), or to be, as in Appendix A, degenerate in square with the previous masses, \(m_1 = |m_4|, m_2 = |m_5|, m_3 = |m_6|\), in contrast to the familiar seesaw mechanism (in both cases). Appendices B and C are devoted to the author’s idea of the algebraic compositeness of fundamental particles, resulting into three generations of Standard Model fermions and two generations of new bosons.

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The KARMEN experiment at the pulsed neutron facility ISIS is investigating neutrino–nucleus reactions and neutrino oscillations. In this paper we present cross sections for neutrino induced charged and neutral current reactions on \(^{12}\)C. These results allow a precision test of the standard model of weak interaction by imposing new limits on the neutral current isovector axial vector coupling strength \(\beta _{A}\), the strength parameter \(\rho \) measuring the universality of \(W^\pm \) and \(Z^0\) coupling in the low energy regime and by investigating the Lorentz structure of muon decay. Neutrino oscillations \(\bar {\nu }_{\mu }\rightarrow \bar {\nu }_e\) are investigated in the appearance mode by looking for \(p(\bar {\nu }_e,e^+)n\) reactions. An analysis of 3 years running time with the KARMEN\(2\) setup reveals no indication of an oscillation signal excluding most parts of the LSND oscillation evidence.

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Parton distributions of pseudoscalar \(\pi \),\(K\) and \(\eta \) mesons obtained within the NJL model using the Pauli–Villars regularization method are analyzed in terms of LO and NLO evolution, and the valence sea quark and gluon parton distributions for the pion are obtained at \(Q^2 = {\rm 4 GeV}^2 \) and compared to existing parametrizations at that scale. Surprisingly, the NLO order effects turn out to be small compared to the LO ones. The valence distributions are in good agreement with experimental analyses, but the gluon and sea distributions come out to be softer in the high-\(x\) region and harder in the low-\(x\) region than the experimental analyses suggest.

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We utilise the fact that the Catani–Ciafaloni–Fiorani–Marchesini (CCFM) equation in the single loop approximation can be diagonalised by the Fourier–Bessel transform. The analytic solution of the CCFM equation for the moments \(f_{\omega }(b,Q)\) of the scale dependent gluon distribution is obtained, where \(b\) is the transverse coordinate conjugate to the transverse momentum of the gluon. The unintegrated gluon distributions obtained from this solution are analysed. It is shown how the approximate treatment of the exact solution makes it possible to express the unintegrated gluon distributions in terms of the integrated ones. The corresponding approximate expressions for the unintegrated gluon distribution are compared with exact solution of the CCFM equation in the single loop approximation.

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There is a convincing experimental evidence that neutrinos are massive. Therefore we investigate the influence of the neutrino masses on the unification of gauge and Yukawa couplings in the framework of the Minimal Supersymmetric Standard Model. We estimate the contribution of the neutrino Yukawa coupling to the gauge and Yukawa coupling unification. We find that in the case of the gauge coupling unification the effect of massive neutrinos is small and can be neglected. It appears to be much more significant, if we explore \(Y_{b}\) and \(Y_{\tau }\) equality at the GUT scale. The neutrino contribution can change that relation even by \(\sim 12\)%.

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We discuss all contributions from inelastic SU(3)-symmetric rescattering in \(B\) decays into a final pair of pseudoscalar mesons \(PP = \pi \pi \), \(K\bar {K}\), \(\pi K\). FSI-induced modifications of amplitudes obtained from the quark-line approach are described in terms of a few parameters which take care of all possible SU(3)-symmetric forms relevant for final-state interactions. Although in general it appears impossible to uniquely determine FSI effects from the combined set of all \(\pi \pi \), \(K \bar {K}\), and \(\pi K\) data, drawing some conclusions is feasible. In particular, it is shown that in leading order the amplitudes of strangeness-changing \(B\) decays depend on only one additional complex FSI-related parameter apart from those present in the definitions of penguin and tree amplitudes. It is also shown that joint considerations of \(U\)-spin-related \({\mit \Delta } S =0\) and \(|{\mit \Delta } S|=1\) decay amplitudes are modified when non-negligible SU(3)-symmetric FSI are present. In particular, if rescattering in \(B^+ \to K^+\bar {K}^0 \) is substantial, determination of the CP-violating weak angle \(\gamma \) from \(B^+ \to \pi ^+ K^0\), \(B^0_d \to \pi ^-K^+\), \(B^0_s \to \pi ^+ K^-\), and their CP counterparts might be susceptible to important FSI-induced corrections.

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The Nijmegen baryon–baryon interaction models are used to determine the \({\mit \Sigma }^-\) single particle potential in nuclei. For the \({\mit \Sigma } {\mit \Lambda }\) conversion cross section — which appears in the expression for the imaginary part of the \({\mit \Sigma }^-\) potential — two alternative parametrizations are used. With the help of this complex \({\mit \Sigma }^-\) potential the energy shifts and widths of the observed levels of \({\mit \Sigma }^-\) atoms are calculated. Comparison with the 23 existing data shows that the lowest \(\chi ^2\) is obtained with the Nijmegen model F which leads to the \({\mit \Sigma }^-\) potential which is repulsive inside nuclei and has an attractive pocket at the nuclear surface. The reasonable accuracy of the perturbation approximation is discussed. The sensitivity of the results to the tail of the nucleon density distributions is investigated.

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The transverse spin effects may be helpful to distinguish between scalar \((J^{\rm PC}=0^{++})\) or pseudoscalar \((J^{\rm PC}=0^{-+})\) nature of the spin zero (Higgs) particle once discovered in future accelerator experiments. The correlations can manifest themselves e.g. in the distribution of acollinearity angle of \( X^\pm \) in the decay chain \(H/A\to \tau ^+ \tau ^-;~ \tau ^\pm \to \nu X^\pm \). This delicate measurement will require, however, reconstruction of the Higgs boson rest-frame. Then, questions of the combined detection-theoretical effects may be critical to establish the reliability of the method. An appropriate Monte Carlo program is essential. To make such studies possible we have extended the standard universal interface of the TAUOLA \(\tau \)-lepton decay library to include the complete spin effects for \(\tau \) leptons originating from the spin zero particle. The interface is expected to work with any Monte Carlo generator providing Higgs boson production and subsequent decay into a pair of \(\tau \) leptons. Examples of numerical results and cross checks of the program will be also given. In particular, we find that effects of beamstrahlung may be critical to the quality of the measurement of the Higgs boson, unless some improvements of the method can be found.

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A large hierarchy of the Dirac masses can result in a small hierarchy for the low energy masses of the active neutrinos. This can happen even if the Majorana masses of right-handed neutrinos are all equal. A realistic description of the observed neutrino masses and mixing can be obtained starting from a large hierarchy in the Dirac masses. A large mixing for solar neutrinos results from the neutrino sector. The small value of the MNS matrix element \(U_{e3}\) is a natural consequence of the scheme. The masses of the two lighter neutrinos are related to the solar neutrino mixing angle: \(\mu _1\)/\(\mu _2 = \tan ^2\theta _\odot \).

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This is a survey of recent studies of singularity formation in solutions of spherically symmetric Yang–Mills equations in higher dimensions. The main attention is focused on five space dimensions because this case exhibits interesting similarities with Einstein’s equations in the physical dimension, in particular the dynamics at the threshold of singularity formation shares many features (such as universality, self-similarity, and scaling) with critical phenomena in gravitational collapse. The borderline case of four space dimensions is also analysed and the formation of singularities is shown to be intimately tied to the existence of the instanton solution.

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Deviations from an idealized equilibrium phase transition picture in nuclear multifragmentation is studied in terms of the entropic index. We investigate different heat-capacity features in the canonical quantum statistical fragmentation model generalized in the framework of non-extensive thermostatistics, and show that in this model the negative branch of heat capacity in quasi-peripheral Au+Au reactions is consistent with the dominance of non-extensive effects in these reactions.

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We show, by means of a simple compilation of the available experimental results, that the \(p_\perp \)-spectra obtained at RHIC and SPS are strikingly similar up to \(p_\perp \simeq 1.5\)–2 GeV. Our observation is complementary to the well known fact of the equality of the measured \(R_{\rm side}\) and \(R_{\rm out}\) HBT radii at RHIC and SPS. In essence, it points out that the transverse size of the firecylinder and the strength of the transverse flow are not significantly changed between SPS and RHIC. This suggests that a saturation mechanism is effective already at SPS. We also point out that the dominance of protons over \(\pi ^+\) at large \(p_\perp \) can be seen already in the SPS data.

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The directed and elliptic flow of fragments emitted from the excited projectile nuclei has been observed for 158 \(A\) GeV Pb collisions with the lead and plastic targets. For comparison the flow analysis has been performed for 10.6 \(A\) GeV Au collisions with the emulsion target. The strong directed flow of heaviest fragments is found. Light fragments exhibit directed flow opposite to that of heavy fragments. The elliptic flow for all multiply charged fragments is positive and increases with the charge of the fragment. The observed flow patterns in the fragmentation of the projectile nucleus are practically independent of the mass of the target nucleus and the collision energy. Emission of fragments in nuclear multifragmentation shows similar, although weaker, flow effects.

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Fragmentation of 158 \(A\) GeV Pb nucleus after the collision with Pb and plastic targets has been studied using several lead-emulsion chambers irradiated in SPS at CERN. It was found that more than 50% of Pb+Pb interactions at 158 \(A\) GeV are of electromagnetic origin. The distributions of the number of fragments are target dependent while their charges and the shapes of their angular distributions are independent of the target mass. For a given energy transferred to the spectator part of the nucleus the mean values of the number of fragments and their charges as well as angular distributions are the same for light and heavy targets, except for the most central collisions.

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The contribution of the ground state energy of quantum fields to the cosmological constant is estimated from the point of view of the standard Casimir energy calculation scheme. It is shown that the requirement of the renormalization group invariance leads to the value of the effective \({\mit \Lambda }\)-term which is of 11 orders higher than the result extracted from the experimental data.

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There are a number of very puzzling meteoritic events including (a) The Tunguska event. It is the only known example of a low altitude atmospheric explosion. It is also the largest recorded event. Remarkably no fragments or significant chemical traces have ever been recovered. (b) Anomalous low altitude fireballs which (in some cases) have been observed to hit the ground. The absence of fragments is particularly striking in these cases, but this is not the only reason they are anomalous. The other main puzzling feature is the lack of a consistent trajectory: low altitude fireballs, if caused by an ordinary cosmic body penetrating the Earth’s atmosphere, should have been extremely luminous at high altitudes. But in these anomalous cases this is (remarkably) not observed to occur! On the other hand, there is strong evidence that most of our galaxy is made from exotic dark material — ‘dark matter’. Mirror matter is one well motivated dark matter candidate, since it is dark and stable and it is required to exist if particle interactions are mirror symmetric. If mirror matter is the dark matter, then some amount must exist in our solar system. Although there is not much room for a large amount of mirror matter in the inner solar system, numerous small asteroid sized mirror matter objects are a fascinating possibility because they can potentially collide with the Earth. We demonstrate that the mirror matter theory allows for a simple explanation for the puzzling meteoritic events [both (a) and (b)] if they are due to mirror matter space-bodies. A direct consequence of this explanation is that mirror matter fragments should exist in (or on) the ground at various impact sites. The properties of this potentially recoverable material depend importantly on the sign of the photon–mirror photon kinetic mixing parameter, \(\varepsilon \). We argue that the broad characteristics of the anomalous events suggests that \(\varepsilon \) is probably negative. Strategies for detecting mirror matter in the ground are discussed.