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We highlight the important role that canonical normalisation of kinetic terms in flavour models based on family symmetries can play in determining the Yukawa matrices. Even though the kinetic terms may be correctly canonically normalised to begin with, they will inevitably be driven into a non-canonical form by a similar operator expansion to that which determines the Yukawa operators. Therefore in models based on family symmetry canonical re-normalisation is mandatory before the physical Yukawa matrices can be extracted. In nearly all examples in the literature this is not done. As an example we perform an explicit calculation of such mixing associated with canonical normalisation of the Kahler metric in a supersymmetric model based on SU(3) family symmetry, where we show that such effects can significantly change the form of the Yukawa matrix. In principle quark mixing could originate entirely from canonical normalisation, with only diagonal Yukawa couplings before canonical normalisation.
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We present empirical relations that connect the dimensionless ratios of fermion masses for the charged lepton, up-type quark and down-type quark sectors. Explaining these relations from first principles imposes strong constraints on the search for the theory of flavor. We present a simple set of normalized Yukawa matrices, with only two real parameters and one complex phase, which accounts with precision for these mass relations and for the CKM matrix elements and also suggests a simpler parametrization of the CKM matrix. The proposed Yukawa matrices accommodate the measured CP-violation, giving a particular relation between standard model CP-violating phases, beta=Arg(2 - exp^{-i*gamma}). According to this relation, the measured value of beta is close to the maximum value that can be reached. Finally, the particular mass relations with the charged lepton sector find their simplest explanation in the context of grand unified models through the use of the Georgi-Jarlskog factor.
Sets of zero-dimensional ideals in the polynomial ring $k[x,y]$ that share the same leading term ideal with respect to a given term ordering are known to be affine spaces called Grobner cells. Conca-Valla and Constantinescu parametrize such Grobner cells in terms of certain canonical Hilbert-Burch matrices for the lexicographical and degree-lexicographical term orderings, respectively. In this paper, we give a parametrization of $(x,y)$-primary ideals in Grobner cells which is compatible with the local structure of such ideals. More precisely, we extend previous results to the local setting by defining a notion of canonical Hilbert-Burch matrices of zero-dimensional ideals in the power series ring $k[[x,y]]$ with a given leading term ideal with respect to a local term ordering.
We analyze the quantum transport equations for supersymmetric electroweak baryogenesis including previously neglected bottom and tau Yukawa interactions and show that they imply the presence of a previously unrecognized dependence of the cosmic baryon asymmetry on the spectrum of third generation quark and lepton superpartners. For fixed values of the CP-violating phases in the supersymmetric theory, the baryon asymmetry can vary in both magnitude and sign as a result of the squark and slepton mass dependence. For light, right-handed top and bottom quark superpartners, the baryon number creation can be driven primarily by interactions involving third generation leptons and their superpartners.
We explore a scenario in the Standard Model in which dimension four Yukawa couplings are either forbidden by a symmetry, or happen to be very tiny, and the Yukawa interactions are dominated by effective dimension six interactions. In this case, the Higgs interactions to the fermions are enhanced in a large way, whereas its interaction with the gauge bosons remains the same as in the Standard Model. In hadron colliders, Higgs boson production via gluon gluon fusion increases by a factor of nine. Higgs decay widths to fermion anti-fermion pairs also increase by the same factor, whereas the decay widths to photon photon and gamma Z are reduced. Current Tevatron exclusion range for the Higgs mass increases to ~ 142-200 GeV in our scenario, and new physics must appear at a scale below a TeV.
We consider models which are natural extensions of those where supersymmetry is broken at low energy scales and transmitted to visible matter by gauge interactions. We investigate the situation where the quark and lepton superfields of the MSSM are localized to a brane in a higher dimensional space while the messenger fields and the sector which breaks supersymmetry dynamically are localized to another brane in the same space. The MSSM gauge and Higgs fields are assumed to propagate in the bulk. If some of the messenger fields and the Higgs fields have the same quantum numbers, this allows the possibility of mixing between these fields so that the physical Higgs and messenger fields are admixtures of the brane and bulk fields. This manifests itself in direct couplings of the quark and lepton fields to the physical messengers that are proportional to the MSSM Yukawa couplings and hence preserve the flavor structure of the CKM matrix. The result is new contributions to the soft supersymmetry breaking parameters that are related to the Yukawa couplings and which therefore naturally satisfy the constraints from FCNCs. For messenger scales greater then 1000 TeV these new contributions are parametrically of the same order of magnitude as gauge mediation. This scenario naturally avoids the cosmological problems associated with stable messengers and admits a simple and natural solution to the $mu$ problem based on the NMSSM.
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