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Mixing at 1-loop in a SU(2)_L gauge theory of weak interactions

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 Added by Bruno Machet
 Publication date 2009
  fields
and research's language is English
 Authors Bruno Machet




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Flavor mixing is scrutinized at 1-loop in a SU(2)_L gauge theory of massive fermions. The main issue is to cope with kinetic-like, momentum (p^2) dependent effective interactions that arise at this order. They spoil the unitarity of the connection between flavor and mass states, which potentially alters the standard Cabibbo-Kobayashi-Maskawa (CKM) phenomenology by giving rise, in particular, to extra flavor changing neutral currents (FCNC). We explore the conservative requirement that these should be suppressed, which yields relations between the CKM angles, the fermion and $W$ masses, and a renormalization scale $mu$. For two generations, two solutions arise: either the mixing angle of the fermion pair the closer to degeneracy is close to maximal while, inversely, the mass and flavor states of the other pair are quasi-aligned, or mixing angles in both sectors are very small. For three generations, all mixing angles of neutrinos are predicted to be large (theta_{23}, close to maximal, is the largest) and the smallness of their mass differences induces mass-flavor quasi-alignment for all charged leptons. The hadronic sector differs in that the top quark is twice as heavy as the W. The situation is, there, bleaker, as all angles come out too large, but, nevertheless, encouraging, because theta_{12} decreases as the top mass increases. Whether other super-heavy fermions could drag it down to realistic values stays an open issue, together with the role of higher order corrections. The same type of counterterms that turned off the 4th order static corrections to the quark electric dipole moment are, here too, needed, in particular to stabilize quantum corrections to mixing angles.



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168 - Bruno Machet 2009
We show that 1-loop transitions between two quasi-degenerate fermions can induce a potentially large renormalization of their mixing angle, and a large renormalized Cabibbo (or PMNS) angle when the second fermion pair in the same two generations is far from degeneracy. At the resonance, the Cabibbo angle gets maximal and simply connected to masses without invoking any new physics beyond the standard model. This solution appears as the only one perturbatively stable (mixing angles are then renormalized with respect to their classical values by small amounts).
This paper includes two main parts. In the first part, we present generalized gauge models based on SU(3)_C x SU(4)_L x U(1)_X (3-4-1) gauge group with arbitrary electric charge of leptons. The mixing matrix of neutral gauge bosons is analysed, the eigenmasses and eigenstates are obtained. The anomaly free as well as matching conditions are discussed precisely. In the second part, we present new development of the original 3-4-1 model [1,2]. In difference from previous works, in this paper the neutrinos, with the help of the decuplet H, get the Dirac masses at the tree level. The VEV of the Higgs field in the decuplet H acquiring VEV responsible for neutrino Dirac mass leads to mixing in separated pairs of singly charged gauge bosons, namely the SM W boson and K - new gauge boson acting in right-handed lepton sector, and the singly charged bileptons X and Y. Due to the mixing, there occurs a right-handed current carried by the SM W bosons. From the expression of the electromagnetic coupling constant, ones get the limit of square sinus of the Weinberg angle: sin^2 theta_W < 0.25 and a constraint on electric charges of extra leptons. In the limit of lepton number conservation, the Higgs sector contains all massless Goldstone bosons for massive gauge bosons and the SM-like Higgs. Some phenomenology are pointed out.
We study the left-right asymmetric model based on SU(3)_C otimes SU(2)_L otimes SU(3)_R otimes U(1)_X gauge group, which improves the theoretical and phenomenological aspects of the known left-right symmetric model. This new gauge symmetry yields that the fermion generation number is three, and the tree-level flavor-changing neutral currents arise in both gauge and scalar sectors. Also, it can provide the observed neutrino masses as well as dark matter automatically. Further, we investigate the mass spectrum of the gauge and scalar fields. All the gauge interactions of the fermions and scalars are derived. We examine the tree-level contributions of the new neutral vector, Z_R, and new neutral scalar, H_2, to flavor-violating neutral meson mixings, say K-bar{K}, B_d-bar{B}_d, and B_s-bar{B}_s, which strongly constrain the new physics scale as well as the elements of the right-handed quark mixing matrices. The bounds for the new physics scale are in agreement with those coming from the rho-parameter as well as the mixing parameters between W, Z bosons and new gauge bosons.
We consider extension of the standard model $SU(2)_l times SU(2)_h times U(1)$ where the first two families of quarks and leptons transform according to the $SU(2)_l$ group and the third family according to the $SU(2)_h$ group. In this approach, the largeness of top-quark mass is associated with the large vacuum expectation value of the corresponding Higgs field. The model predicts almost degenerate heavy $W$ and $Z$ bosons with non-universal couplings, and extra Higgs bosons. We present in detail the symmetry breaking mechanism, and carry out the subsequent phenomenology of the gauge sector. We compare the model with electroweak precision data, and conclude that the extra gauge bosons and the Higgs bosons whose masses lie in the TeV range, can be discovered at the LHC.
A new vector dark matter (DM) scenario in the context of the gauge-Higgs unification (GHU) is proposed. The DM particle is identified with an electric-charge neutral component in an $SU(2)_L$ doublet vector field with the same quantum number as the Standard Model Higgs doublet. Since such an $SU(2)_L$ doublet vector field is incorporated in any models of the GHU scenario, it is always a primary and model-independent candidate for the DM in the scenario. The observed relic density is reproduced through a DM pair annihilations into the weak gauge bosons with a TeV-scale DM mass, which is nothing but the compactification scale of extra-dimensions. Due to the higher-dimensional gauge structure of the GHU scenario, a pair of the DM particles has no direct coupling with a single $Z$-boson/Higgs boson, so that the DM particle evades the severe constraint from the current direct DM search experiments.
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