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We consider a geometric framework for analytical mechanics with external forces. Four versions of this framework are considered. A variational principle with boundary terms and external forces.The second and the third versions are the Lagrangian and Hamiltonian formulations, respectively. The last one is the Poisson formulation. An extensive introductory section presents some well known and some little known geometric constructions to put our formulation in the appropriate setting to make the comparison of the different formulations more easy.

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One dimensional topological kink which has strictly finite size without any exponential or power-like tail is presented. It can be observed in a simple mechanical system akin to the one used in order to demonstrate sinus-Gordon solitons.

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It is proved that symmetry structure of the parity-violating amplitudes of weak radiative hyperon decays in the Vector-Meson Dominance (VMD) approach, and the violation of Hara’s theorem in particular, are also obtained when direct coupling \(e_q~ \bar {q}\gamma _{\mu }q A^{\mu }\) of photon to quarks is used in place of VMD (with calculations performed in the limit of static quarks). Thus, violation of Hara’s theorem in VMD-based models does not result from the lack of gauge invariance. It is further shown that, in the static limit of the quark model, the current-algebra commutator term in the parity-violating amplitudes of nonleptonic hyperon decays and the parity-violating \({\mit \Sigma } ^+ \to p \gamma \) decay amplitude are proportional to each other. As a result, Hara’s theorem may be satisfied in this limit if and only if the contribution from the current-algebra commutator in nonleptonic hyperon decays is zero. Violation of Hara’s theorem is traced back to the nonlocality of quark model states in the static limit. It is argued that the ensuing intrinsic baryon nonlocality does not have to be unphysical. It is stressed that the measurement of the \({\mit \Xi } ^0 \to {\mit \Lambda } \gamma \) asymmetry will provide very important information concerning the presence or absence of nonlocal features in parity-violating photon coupling to baryons at vanishing photon momentum. If the \({\mit \Xi } ^0 \to {\mit \Lambda } \gamma \) asymmetry is found negative, Hara’s theorem is satisfied but the gauge-invariant quark model machinery predicting its violation must miss some contribution, or be modified. If experiment confirms positive \({\mit \Xi } ^0 \to {\mit \Lambda } \gamma \) asymmetry, then, most likely, Hara’s theorem is violated. Although positive \({\mit \Xi } ^0 \to {\mit \Lambda } \gamma \) asymmetry admits of the possibility that Hara’s theorem is satisfied, this alternative is in disagreement with hints suggested by the similarity of photon and vector-meson couplings and the observed size of parity-violating nuclear forces.

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We show, starting from simple differential geometric example, that the partition function of a twisted \({\cal N}=4\) Yang–Mills theory on certain manifold \(X\) is localized on instanton moduli space. Moreover, it equals to the Euler characteristic of this moduli space.

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We investigate the exclusive \(B\rightarrow \gamma \, \ell ^+ \ell ^- \) decay in the general two Higgs Doublet Model (model III) including the neutral Higgs boson effects with an emphasis on possible CP-violating effects. For this decay, we analyze the dependencies of the forward–backward asymmetry of the lepton pair, \(A_{\rm FB}\), CP-violating asymmetry, \(A_{\rm CP}\), and the CP-violating asymmetry in forward–backward asymmetry, \(A_{\rm CP}(A_{\rm FB})\), on the model parameters and also on the neutral Higgs boson effects. We have found that \(A_{\rm FB}\sim 10^{-1},\, 10^{-2}\), \(A_{\rm CP}\sim 10^{-2},\, 10^{-1}\) and \(A_{\rm CP}(A_{\rm FB}) \sim 10^{-2},\, 10^{-1}\) depending on the relative magnitude of the Yukawa couplings \(\bar {\xi }_{N,tt}^{U}\) and \(\bar {\xi }_{N,bb}^{D}\) in the model III. We also observe that these physical quantities are sensitive to the model parameters and neutral Higgs boson effects are quite sizable for some values of the coupling \(\bar {\xi }_{N,\tau \tau }^{D}\).

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We employ QCD sum rules and utilize \(\omega \phi \)-mixing to calculate the coupling constants \(g_{\phi \sigma \gamma }\) and \(g_{\phi a_0\gamma }\) by studying the three point \({\phi \sigma \gamma }\)- and \({\phi a_0\gamma }\)-correlation functions. Our results are consistent with the previous estimations of these coupling constants in the literature.

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This talk was given at the Tunguska-2001 international conference but it is not about the Tunguska event. Instead we tried to give some flavor of mirror matter, which is predicted to exist if parity is an unbroken symmetry of nature, to non-experts. The possible connection of the mirror matter ideas to the Tunguska phenomenon was indicated by Foot and Gninenko some time ago and was elaborated by Foot in the separate talk at this conference. If the mirror world interpretation of the Tunguska like events is indeed correct then the most fascinating (but very speculative) possibility is that some well known celestial bodies with strange properties are in fact made mostly from mirror matter, and so maybe the mirror world was discovered long ago and we just have not suspected this!

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We investigate the potentials of high energy lepton–proton colliders to detect a flavor changing \(l-l'-Z\) or \(l-l'-\gamma \) coupling from the processes \(ep\rightarrow \mu (\tau )\)X and \(\mu p\rightarrow \tau \)X. For the \(l-l'-Z\) coupling we consider string inspired \(E_{6}\) model whereas \(l-l'-\gamma \) coupling is analyzed in the framework of Anomalous Magnetic Moment type Interaction (AMMI) model.

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The observation of one or several Higgs bosons will be fundamental for the understanding of the electroweak symmetry breaking mechanism. In the Standard Model (SM), one scalar doublet is responsible for the electroweak symmetry breaking, leading to the prediction of a single Higgs boson. The simplest extension to the SM Higgs sector is the two Higgs doublet model present in many extensions to the SM itself, including supersymmetry. In such models, symmetry breaking leads to five Higgs particles, three neutral and a charged pair. The sensitivity of the ATLAS detector to the discovery of the charged Higgs has been studied in detail. In this paper, we discuss the expected precisions on the charged Higgs mass and \(\tan \beta \) measurements at the Large Hadron Collider (LHC).

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A generating function for products of Hermite polynomials is used to significantly simplify the evaluation of the integrals \(G_n(p,p')\) occurring in the Gaussian model of multiple particle production. These integrals are crucial for studies of multi-particle effects in Bose–Einstein correlations.