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FCNC processes are expected to offer us a deep insight into the physics at very short distance scales. We present a list of 20 goals in quark and lepton flavour physics that could be reached already in the next decade. This list includes also flavour conserving observables like electric dipole moments of the neutron and leptons and \((g-2)_\mu \). Subsequently we will present some aspects of these goals by concentrating on supersymmetric flavour models. A much more extensive presentation of this material can be found in my recent EPS09 talk [1].

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In this presentation, I review some of the recent findings in hadronic penguin and leptonic decays of \(B\) mesons in regard to search for new physics beyond the Standard Model (SM). Several “tensions” and “puzzles” will be discussed that may indicate effects of new physics.

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A review of experimental results on the radiative penguin decays \(b\to s(d)\gamma \), and the electroweak penguin decays \(b\to s\ell ^+\ell ^-\), emphasising the experimental techniques that have been used at the \(B\) factories by the BaBar and Belle collaborations. World averages are presented for branching fractions, rate asymmetries, and the angular distributions in \(B\to K^*\ell ^+\ell ^-\). The sources of experimental uncertainties are compared with the theoretical uncertainties, and the sensitivity to new physics contributions beyond the Standard Model is briefly discussed.

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We briefly summarize the current status of perturbative calculations at next-to-next-to-leading-order (NNLO) accuracy in the \(\bar B\to X_s\gamma \) decay rate as well as that of non-perturbative power-corrections.

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The Minimal Flavor Violation (MFV) hypothesis is presented in the context of the MSSM. Its fundamental principles are introduced and motivated, and its phenomenological consequences for FCNC and CP-violating observables as well as for \(R\)-parity violating processes are briefly described.

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I give a sketchy overview on aspects related to the lepton–flavour sector in the Standard Model and its possible extensions.

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I review the present Standard Model prediction of the muon anomalous magnetic moment \(a_\mu \). The discrepancy with its experimental determination is \((25.5 \pm 8.0) \times 10^{-10}\), i.e. , 3.2 standard deviations.

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During the last few years the Tevatron has improved the bounds on rare \(B\)-meson decays into two leptons. Sensitivity to this decay is also one of the benchmark goals for LHCb performance. We compute the complete 1-loop MSSM contribution to \(B^0_{s,d}\to \mu ^+\mu ^-\) and study the predictions for arbitrary flavour mixing parameters. We discuss the possibility of both enhancing and suppressing the branching ratios relative to their SM expectations. We find that there are “cancellation regions” in parameter space where the branching ratio is suppressed well below the SM expectation, making it effectively invisible to the LHC.

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Supersymmetry is one of the best options among the possible extensions of the SM that can be found at the LHC. However, most of the phenomenological analysis have been done neglecting flavour structures. In this paper, we show that a realistic flavour symmetry can simultaneously explain the flavour structures in the Yukawa matrices and solve the so-called SUSY flavour problem without ad hoc modifications of the SUSY model. Furthermore, departures from the SM expectations in these models can be used to discriminate among different possibilities. We find that large contributions can be expected in lepton flavour violating decays, as \(\mu \to e \gamma \) and \(\tau \to \mu \gamma \), electric dipole moments, \(d_{e}\) and \(d_{n}\) and kaon CP-violating processes as \(\epsilon _K\). Thus, these flavoured MSSM realizations are phenomenologically sensitive to the experimental searches in the realm of flavour and CP violation physics.

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We present an updated phenomenological analysis of the minimal flavour violating (MFV) effective theory. We evaluate the bounds on the scale of new physics derived mainly from recent measurements of \(B\) meson observables and we use such bounds to derive a series of model-independent predictions within MFV for future experimental searches.

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We investigate the consequences of replacing the continuous flavour symmetry of minimal flavour violation by a discrete group. Goldstone bosons, resulting from the breaking of the continuous flavour symmetry, generically lead to bounds on new flavour structure many orders of magnitude above the TeV-scale. The absence of the latter for discrete symmetries constitute the primary motivation of our work. The four crystal-like groups \({\mit \Sigma }(168)\), \({\mit \Sigma }(72 \varphi )\), \({\mit \Sigma }(216 \varphi )\) and \({\mit \Sigma }(360 \varphi )\) provide enough protection for a discrete TeV-scale MFV scenario in the case where \(\Delta F = 2\) processes are generated by two subsequent \(\Delta F = 1\) transitions.

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The Littlest Higgs Model with T-parity (LHT) is an interesting alternative model for New Physics at the TeV scale. Although Flavour Physics was not the reason for creating the LHT model, significant effects (such as large CP violation where not predicted by the SM) can be created without violating existing experimental bounds. We study the \(B\)-, \(K\)- and especially the \(D\)-sector.

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Charm processes are usually not considered to be favorable candidates in the search for new physics. Recent disagreement between experimental and lattice QCD results on the \(D_s\) decay constant has motivated us to systematically reinvestigate role of leptoquarks in charm meson decays. We include constraints coming from the light meson decays.

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I present a review of phenomenological implications of the Randall–Sundrum (RS) model with bulk fermions and brane-localised Higgs boson. Modifications to the \(W\)-boson mass, corrections to the Peskin–Takeuchi parameters and to the \(Z b\bar {b}\) couplings will be discussed. From these observables severe bounds on the mass scale of Kaluza–Klein (KK) modes arise. Constraints from all three observables are very sensitive to the exact value of the Higgs boson mass and the bounds can be significantly lowered by allowing for a heavy Higgs boson (\(m_h\sim 1\) TeV). Consequences thereof, as well as other approaches like “little RS” models and models with custodial symmetry will also be briefly discussed.

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In these proceedings we present the main results for particle–antipar- ticle mixing and rare decays in the Randall–Sundrum (RS) model with custodial symmetry. To investigate the strong bound on the Kaluza–Klein (KK) mass scale \(M_{\rm KK}\gtrsim \mathcal O(20)\,\textrm {TeV}\) implied by the measurement of \(\varepsilon _K\) we perform a fine-tuning analysis that, on the one hand, confirms the quoted bound on the KK mass scale but, on the other hand, reveals that consistence with experiment can still be achieved for small or moderate fine-tuning. In our analysis of rare decays of \(K\) and \(B\) mesons we find that due to the custodial symmetry the coupling of the \(Z\) boson to right handed quarks yields the dominant contribution. This feature of the model leads to distinct patterns and correlations that allow to distinguish the model from other frameworks of physics beyond the Standard Model (SM).

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The rare decay \(B \to K^* (\to K \pi ) \mu ^+ \mu ^-\) is regarded as one of the crucial channels for \(B\) physics since its angular distribution gives access to many observables that offer new important tests of the Standard Model (SM) and its extensions. We point out a number of correlations among various observables which will allow a clear distinction between different New Physics (NP) scenarios. Furthermore, we discuss the decay \(B \to K^* \nu \bar \nu \) which allows for a transparent study of \(Z\) penguin effects in NP frameworks in the absence of dipole operator contributions and Higgs penguin contributions. We study all possible observables in \(B \to K^* \nu \bar \nu \) and the related \(b \to s\) transitions \(B \to K \nu \bar \nu \) and \(B \to X_s \nu \bar \nu \) in the context of the SM and various NP models.

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We study the \(K^*\) polarization states in the exclusive 4-body B meson decay \(B^0 \to K^{*0}(\to K^- \pi ^+)l^+ l^-\) in the low dilepton mass region working in the framework of QCDF. We review the construction of the CP-conserving transverse and transverse/longitudinal observables \(A_{\rm T}^2\), \(A_{\rm T}^3\) and \(A_{\rm T}^4\). We focus here on analyzing their behaviour at large recoil energy in the presence of right-handed currents.

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Through an effective field theory approach, we analyse the new physics (NP) corrections to muon and beta decays and their effects on the extractions of \(V_{ud}\) and \(V_{us}\). Assuming nearly flavour blind NP interactions, we find that the only quantity sensitive to NP is \({\mit \Delta }_{\rm CKM} \equiv |V_{ud}|^2 + |V_{us}|^2 + |V _{ub}|^2 - 1\), that receives contributions from four short distance operators. The phenomenological bound \({\mit \Delta }_{\rm CKM} = (-1 \pm 6) \times 10^{-4}\) provides strong constraints on all four operators, corresponding to an effective scale \({\mit \Lambda } \gt 11\) TeV (90% C.L.). Depending on the operator, this constraint is at the same level or better than that generated by the \(Z\) pole observables.

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The total \(\tau \) hadronic width can be accurately calculated using analyticity and the operator product expansion. The result turns out to be very sensitive to the value of \(\alpha _{\rm s}(m_\tau ^2)\), providing a precise determination of the strong coupling constant. The theoretical description of this observable is updated, including the recently computed \(\cal {O}(\alpha _{\rm s}^4)\) contributions. The experimental determination of \(\alpha _{\rm s}(m_\tau ^2)\) and its actual uncertainties are discussed.

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Recent theoretical and experimental improvements in the determination of charm- and bottom-quark masses are discussed. The final results, \(m_c(3\,\text {GeV})=986(13)\,\)MeV and \(m_b(m_b)=4163(16)\,\)MeV represent the presently most precise determinations of these two fundamental Standard Model parameters.

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In this contribution three-loop corrections to the quark and gluon form factor are discussed in massless QCD. They constitute building blocks to the third-order corrections of a number for physical processes. Furthermore, we discuss the Higgs–boson–gluon vertex to three-loop order including finite top-quark mass effects.

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Inclusion of down to zero-momentum gluons and their \(k_t\) resummation is shown to quench the too fast rise of the mini jet cross-section and thereby obtain realistic total cross-sections.

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I present a new determination of \(|V_{cs}|\) and \(|V_{cd}|\), using the latest CLEO data on semileptonic \(D\) decays and the \(D\to \pi \) and \(D \to K\) form factors obtained from QCD light-cone sum rules. This result emphasizes the universality of the method used before to calculate the \(B\to \pi \) form factor and determine \(|V_{ub}|\) from \(B\to \pi l \nu \) decay.

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We report on recent progress on \(V_{ub}\) determination from exclusive and inclusive semileptonic \(B\) decays.

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Determination of \(V_{cb}\) in exclusive semileptonic decays is crucial consistency check against the \(V_{cb}\) determined inclusively. Anticipated precision of \(V_{cb}\) at the Super Flavor factory is \(\sim 1\%\), with most of the theoretical error due to hadronic form factor uncertainties, but at this level of precision treating electromagnetic effects becomes inevitable. In addition to virtual photon corrections there are also emissions of real photons which are soft enough to avoid detection. The bremsstrahlung part is completely universal and is accounted for in the experimental analyses. However, the so-called structure dependent contribution, which probes the hadronic content of the process and is infrared finite, has been neglected so far. To this end, we estimated fraction of radiative events which are seen as ordinary semileptonic by experiment.

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In the two-Higgs-doublet model the alignment of the Yukawa flavour matrices of the two scalar doublets guarantees the absence of tree-level flavour-changing neutral couplings. The resulting fermion-scalar interactions are parameterized in terms of three complex parameters \(\zeta _f\), leading to a generic Yukawa structure which contains as particular cases all known specific implementations of the model based on \(\mathcal Z_2\) symmetries. These three complex parameters are potential new sources of CP violation.

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The data on high-precision flavour observables reveal certain puzzles when compared to Standard Model expectations based on a global fit of the CKM unitarity triangle and general theoretical estimates. The discussion of these tensions in the channels \(B\to J/\psi K\), \(B\to \phi K\), and \(B\to \pi K\), and the deduced constraints for New Physics operators of the class \(b\to s\bar {q}q\) form the content of this talk.

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The discrepancies found in the \(\bar {B}\to \pi \bar {K}\) decays between theory and experiment suggest the presence of new physics in the electroweak penguin sector of the theory. We show that this hypothesis can be tested more efficiently including in the analysis the non-leptonic decays \(\bar {B}_{\rm s}\to \phi \pi ,\phi \rho \).

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For large values of \(\tan \beta \) interesting effects arise in the MSSM due to the enhancement of down-quark self-energies. These effects are well-studied within the decoupling limit, i.e. in the limit of supersymmetric masses far above the electroweak scale. In this article I discuss those issues which emerge from a treatment of these effects that goes beyond the decoupling limit.

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In the presence of a low scale seesaw of type I + III, flavor violating effects in the leptonic sector are expected. Their presence in the charged sector is due to the mixing of the fermionic vector-like weak triplets with the chiral doublets, which cause non-universality of the tree-level \(Z\) coupling. We investigate the bounds on the Yukawa couplings which are responsible for the mixing and present the results for two minimal cases, a fermionic triplet with a singlet or two fermionic triplets. Different channels for these processes are considered and their current and future potential to probe these couplings is discussed.