abstract

Recent development in exploring flavour dynamics in the supersymmetric extension of the Standard Model is reviewed. Emphasis is put on possible interesting effects in \(b\)-physics arising for large values of \(\tan \beta \) both in the case of minimal flavour violation and in the case of flavour violation originating in the sfermion sector. The importance of the flavour changing neutral Higgs boson couplings generated by the scalar penguin diagrams and their role in the interplay of neutral \(B\)-meson mixing and \(B^0_{d,s}\rightarrow \mu ^+\mu ^-\) decays is discussed. It is pointed out that observation of the \(B^0_d\rightarrow \mu ^+\mu ^-\) decay with BR at the level \(\gtrsim 3\times 10^{-8}\) would be a strong indication of nonminimal flavour violation in the quark sector. Possible impact of flavour violation in the slepton sector on neutrino physics is also discussed.

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We examine localized kinetic terms for gauge fields which can propagate into compact extra dimensions. We find that such terms are generated by radiative corrections in both theories with matter fields confined to branes and in theories imposing orbifold boundary conditions on bulk matter. In both cases, the radiative corrections are logarithmically divergent, indicating that from an effective field theory point of view they cannot be predicted in terms of other parameters, and should be treated as independent leading order parameters of the theory. Specializing to the five dimensional case, we show that these terms may result in gross distortions of the Kaluza–Klein gauge field masses, wave functions, and couplings to brane and bulk matter. The resulting phenomenological implications are discussed.

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The new idea of deconstruction allows to realize the physics of extra dimensions in a strictly four dimensional set-up. After a short review of these techniques extended to supersymmetry, I will report on an application to build models in which the low energy spectrum shows no sign of supersymmetry but still the radiative corrections to the mass parameters are weakly dependent on the cutoff scale, if this one remains low enough. As a consequence, the Higgs mass dependence in high energy physics is effectively parametrized by the deconstruction scale which also fixes the gauge boson masses through the Higgs vacuum expectation value. In this regard, deconstruction, somehow as gauge invariance, is a dynamical principle that dictates the interactions of particles and gauge fields at low energy and quantum level.

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We emphasize the necessity of a delicate interplay between the gauge and gravitational sectors of five-dimensional brane worlds in creating phenomenologically relevant vacua. We discuss locally supersymmetric brane worlds with unflipped and flipped fermionic boundary conditions and with matter on the branes. We point out that a natural separation between the gauge and gravity sectors, very difficult in models with true extra dimensions, may be achieved in 4d models with deconstructed dimensions.

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In braneworld models the global charges, such as baryon or lepton number, are not conserved. The global-charge non-conservation is a rather model-independent feature which arises due to quantum fluctuations of the brane worldvolume. These fluctuations create “baby branes” that can capture some global charges and carry them away into the bulk of higher-dimensional space. Such processes are exponentially suppressed at low-energies, but can be significant at high enough temperatures or energies. These effects can lead to a new, intrinsically high-dimensional mechanism of baryogenesis. Baryon asymmetry might be produced due either to evaporation into the baby branes, or creation of the baryon number excess in collisions of two Brane Universes.

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We investigate the phenomenon of brane induced supersymmetry breakdown on orbifolds in the presence of a Scherk–Schwarz mechanism. General consistency conditions are derived for arbitrary dimensions and the results are illustrated in the specific example of a 5-dimensional theory compactified on \(S^1\)/\(\mathbb {Z}_2\). This includes a discussion of the Kaluza–Klein spectrum and the possibility of a brane induced supersymmetry restoration.

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It is a great pleasure to be here today and celebrate Stefan Pokorski. Given the breadth of his scientific activity, it is no surprise that this talk touches yet another subject to which Stefan, as well as other younger members of the Warsaw group, have given and are giving important contributions.

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We discuss the phenomenological consequences of large extra dimensions concerning both supersymmetry and electroweak symmetry breaking. We consider separately the fundamental scenarios where this can happen. In particular cases where only the gravitational sector can propagate in the bulk of the large extra dimensions, and cases with longitudinal dimensions where all gauge and matter fields propagate. We briefly comment on the string realization of these ideas and finally present a possible scenario where electroweak breaking is triggered by the Hosotani mechanism and thus a finite Higgs mass does not require supersymmetry.

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An algebraic description of (untwisted) D-branes on compact group manifolds \(G\) using quantum algebras related to \(U_q(\mathfrak {g})\) is discussed. It reproduces the known characteristics of stable branes in the WZW models. A toy model of NCG based on a quiver diagram for branes on orbifold is also presented.

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We discuss Calabi–Yau compactifications with background fluxes at the level of the low energy effective action. For the fluxes in the RR-sector mirror symmetry is manifest at the level of the effective action while for the fluxes in the NS-sector the compactification manifold has to be deformed.

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The scalar sector of the Randall–Sundrum model is discussed. The effective potential for the Standard Model Higgs-boson (\(h\)) interacting with Kaluza–Klein excitations of the graviton (\(h_\mu ^{\nu \, n}\)) and the radion (\(\phi \)) has been derived and it has been shown that only the Standard Model vacuum solution of \(\partial V/\partial h =0\) is allowed. The theoretical and experimental consequences of the curvature-scalar mixing \(\xi \, R\, \widehat H^\dagger \widehat H\) introduced on the visible brane are considered and simple sum rules that relate the couplings of the mass eigenstates \(h\) and \(\phi \) to pairs of vector bosons and fermions are derived. The sum rule for the \(ZZh\) and \(ZZ\phi \) couplings in combination with LEP/LEP2 data implies that not both the \(h\) and \(\phi \) can be light. We present explicit results for the still allowed region in the \((m_{h},{m_\phi })\) plane that remains after imposing the LEP upper limits for non-standard scalar couplings to a \(ZZ\) pair. The phenomenological consequences of the mixing are investigated and, in particular, it is shown that the Higgs-boson decay \(h \to \phi \phi \) would provide an experimental signature for non-zero \(\xi \) and can have a very substantial impact on the Higgs-boson searches, having \({\rm BR}(h \to \phi \phi )\) as large as \(30 \div 40\, \%\).

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We discuss gauge symmetry breaking with Wilson loops in 5 dimensions. We present a simple example with the fifth dimension compactified on an \(S^1\)/\(Z_2\) orbifold. The Wilson loop in this SO\((3)\) example replaces the adjoint Higgs scalar (needed to break SO\((3)\) to U\((1)\)) in the well-known Georgi–Glashow model. We then show that gauge symmetry breaking with a Wilson loop on this \(S^1\)/\(Z_2\) orbifold is gauge equivalent to gauge symmetry breaking on a particular \(S^1\)/\((Z_2 \times Z_2^\prime )\) orbifold. The latter orbifold has been used in many recent constructions with gauge symmetry breaking in five dimensional supersymmetric and non-supersymmetric models. Finally we explicitly construct a magnetic monopole string solution; the analog of the ’t Hooft–Polyakov monopole. The monopole string has finite energy, and length equal to the size of the extra dimension.

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In \(\kappa \)-deformed relativistic framework we consider three different definitions of \(\kappa \)-deformed velocities and introduce corresponding addition laws. We show that one of the velocities has classical relativistic addition law. The relation of velocity formulae with the coproduct for fourmomenta and noncommutative space-time structure is exhibited.

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A new mechanism for generating neutrino masses without a high-energy mass scale is proposed. The mechanism needs a fundamental mass scale \(M\) in the 100–1000 TeV region and a minimal field content beyond the Standard Model one containing a pair of fermion singlets and a pair of weak doublet fermions for each neutrino mass, all of them with a mass of order \(M\). The neutrino mass appears by a multiple seesaw-type tree-level diagram. We provide an explicit model based on supersymmetry and an Abelian symmetry which provides the required fermion mass matrix. The mechanism is natural in the context of string theories with a low fundamental scale. Within an explicit example where the Abelian symmetry is also responsible for the generation of fermion masses and mixings, we give a hint relating the fermion mass matrices and the weak mixing angle. By assuming the weak–strong couplings unification, one naturally finds \(\sin ^2 \theta _{\rm w} = 1/4\) at the fundamental scale.

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The author’s idea of algebraic compositeness of fundamental particles, allowing to understand the existence in Nature of three fermion generations, is revisited. It is based on two postulates. Primo, for all fundamental particles of matter the Dirac square-root procedure \(\sqrt {p^2} \rightarrow {\mit \Gamma }^{(N)}\cdot p\) works, leading to a sequence \(N = 1,2,3,\ldots \) of Dirac-type equations, where four Dirac-type matrices \({\mit \Gamma }^{(N)}_\mu \) are embedded into a Clifford algebra via a Jacobi definition introducing four “centre-of-mass” and \((N-1) \times \)four “relative” Dirac-type matrices. These define one “centre-of-mass” and \(N-1\) “relative” Dirac bispinor indices. Secundo, the “centre-of-mass” Dirac bispinor index is coupled to the Standard Model gauge fields, while \(N-1\) “relative” Dirac bispinor indices are all free indistinguishable physical objects obeying Fermi statistics along with the Pauli principle which requires the full antisymmetry with respect to “relative” Dirac indices. This allows only for three Dirac-type equations with \(N = 1,3,5\) in the case of \(N\) odd, and two with \(N = 2,4\) in the case of \(N\) even. The first of these results implies unavoidably the existence of three and only three generations of fundamental fermions, namely leptons and quarks, as labelled by the Standard Model signature. At the end, a comment is added on the possible shape of Dirac \(3\times 3\) mass matrices for four sorts of spin-1/2 fundamental fermions appearing in three generations. For charged leptons a prediction is \( m_\tau = 1776.80\) MeV, when the input of experimental \(m_e\) and \(m_\mu \) is used.

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We present a model of neutrino masses combining the seesaw mechanism and strong Dirac mass hierarchy and at the same time exhibiting a significantly reduced hierarchy at the level of active neutrino masses. The heavy Majorana masses are assumed to be degenerate. The suppression of the hierarchy is due to a symmetric and unitary operator \(R\) whose role is discussed. The model gives realistic mixing and mass spectrum. The mixing of atmospheric neutrinos is attributed to the charged lepton sector whereas the mixing of solar neutrinos is due to the neutrino sector. Small \(U_{e3}\) is a consequence of the model. The masses of the active neutrinos are given by \(\mu _3\approx \sqrt {\Delta m_{@}^2}\) and \(\mu _1\)/\(\mu _2\approx \tan ^2\theta _\odot \).

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We review the propagation of light neutrinos in matter assuming that their mixing with heavy neutrinos is close to present experimental limits. The phenomenological implications of the non-unitarity of the light neutrino mixing matrix for neutrino oscillations are discussed. In particular we show that the resonance effect in neutrino propagation in matter persists, but for slightly modified values of the parameters and with the maximum reduced by a small amount proportional to the mixing between light and heavy neutrinos squared.

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Several years ago, Stefan Pokorski, Manfred Münz and us outlined a program for calculation of the NLO QCD corrections to the weak radiative \(\bar {B}\) meson decay \(\bar {B} \to X_s \gamma \). Very recently, just before the 60th birthday of Stefan Pokorski, this program has been formally completed. In the present paper, we summarize the existing results and discuss perspectives for further improvement of the accuracy of the Standard Model prediction for \({\rm BR}[\bar {B} \to X_s \gamma ]\).

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In supersymmetric extensions of the Standard Model (SM), the Lepton Flavour Violation (LFV) is closely related to the structure of slepton masses and mixing. Allowing for the most general flavour structure of the slepton sector, consistent with the experimental limits on rare lepton decays, large and distinct signals of LFV at future colliders can be expected. A case study of mixing of second and third generation of sleptons at an \(e^+e^-\) collider is presented and compared to that of \(\tau \to \mu \gamma \) rare decay.

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We discuss the implication of recent evaluation of the SM contribution to \((g-2)_{\mu }\) in light of the latest E821 measurement, for the light Higgs-boson scenarios in a Two-Higgs-Doublet-Model (“Model II”). If the constraints from the new \((g-2)_{\mu }\) results are combined with the other existing constraints, one can exclude a light-scalar scenario at 95% CL while a light-pseudoscalar scenario can be realized, for a pseudoscalar mass between 25 and 70 GeV with \(\tan \beta \) in the range \(25 \le \tan \beta \le 115\).

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It is argued that the breakdown of factorization observed recently in the diffractive dijet production in deep inelastic lepton induced and hadron induced processes is naturally explained in the Good–Walker picture of diffraction dissociation. An explicit formula for the hadronic cross-section is given and successfully compared with the existing data.

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Numerous models have been proposed to describe the Bose–Einstein correlations in multiple particle production process. In the present paper we describe a generalization, which includes many previous models as special cases and, therefore, can be useful for work of comparison. We apply the powerful methods of eigenfunction expansions and generating functionals, which often make the calculations much shorter than in the original papers.

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Under certain conditions the number of photons radiated classically by a charged particle following a prescribed trajectory can be finite. An interesting formula for this number is presented and discussed.

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In order to determine polarized parton densities in nucleon we have made fits using all experimental data on spin asymmetries measured in the deep inelastic scattering on different nucleon targets. We have used in our analysis next to leading order QCD corrections in \(\overline {MS}\) renormalization scheme. The functional forms of polarized densities are based on the fit to unpolarized deep inelastic data made by the MRST group (MRST 99). We have concentrated on different models for gluon spin distributions. In the best fit we get for gluon polarization (at \( Q^{2}=1\, {\rm GeV^{2}}\)) \(\Delta G=-1.0 \pm 0.6\). The obtained result does not depend very much on various model assumptions.

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Bose–Einstein correlations (BEC) observed between identical bosons produced in high energy multiparticle collisions are regarded as very important tool in investigations of multiparticle production processes. We present here their stochastic feature stressing the fact that they can be regarded as a reflection of correlations of fluctuations present in hadronizing system. We show in particular that such approach allows for simple modeling of BEC in numerical event generators used to describe the multiparticle production processes at high energy collisions.