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Register a new userSolving a Fine-Tuning Problem of the Standard Model through the Introduction of Vector-Like Quarks
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We emphasise that even in the extreme chiral limit where only the top and bottom quarks acquire mass, quark mixing is physically meaningful. This implies that the natural value of $|V_{13}|^2 + |V_{23}|^2$ is of order one, which is to be compared to its experimental value of order $10^{-3}$ . We show how this fine-tuning problem of the Standard Model can be solved through an extension of the Standard Model where vector-like quarks and a complex singlet are introduced, together with a flavour symmetry. The mixings of the light quarks are generated through the mixing of the vector-like quarks with the standard quarks.
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I discuss standard motivation for the new physics at the 1 TeV scale. Although the arguments for new exotic phenomena seem to be very supportive I argue that the Standard Model still might offer a good description far beyond this energy scale. I analyze three Standard Model cases with specific boundary conditions at the lowest energies. These conditions essentially eliminate the hierarchy and fine-tuning problems. In the first model where quartic scalar interactions are required to decouple, the Higgs is predicted to weigh around 39 GeV. In the second model with composite Higgs, the top Yukawa coupling is required to be one (by hand, i.e. reflecting the assumed ground state) and the Higgs mass of about 138 GeV is favored. The third model has condensation mechanism embedded in two dimensions. The top Yukawa coupling being one comes about as prediction rather then requirement, i.e. $g_t={3g_2 over 2}sqrt{1+{1over3}(g_1over g_2)^2} (1-textit{few}%)approx 1.025 (1-textit{few}%)$ where $g_2$, $g_1$ are electroweak $SU(2)times U(1)$ gauge couplings, and the SM Higgs is expected to weigh in between 114.8 and 118.6 GeV.
This work provides an overview on the current status of phenomenology and searches for heavy vector-like quarks, which are predicted in many models of new physics beyond the Standard Model. Searches at Tevatron and at the LHC, here listed and shortly described, have not found any evidence for new heavy fermionic states (either chiral or vector-like), and have therefore posed strong bounds on their masses: depending on specific assumptions on the interactions and on the observed final state, vector-like quarks with masses up to roughly 400-600 GeV have been excluded by all experiments. In order to be as simple and model-independent as possible, the chosen framework for the phenomenological analysis is an effective model with the addition of a vector-like quark representation (singlet, doublet or triplet under SU(2)) which couples through Yukawa interactions with all SM families. The relevance of different observables for the determination of bounds on mixing parameters is then discussed and a complete overview of possible two-body final states for every vector-like quark is provided, including their subsequent decay into SM particles. A list and short description of phenomenological analyses present in literature is also provided for reference purposes.
We follow the example of Cabibbo by revising the Standard Model (SM) to present a universal mass structure for fermions. A universal Higgs coupling for each species of fundamental fermions moves the SM towards a Theory of Matter, albeit without correctly describing the observed mass spectrum. It exposes a need for a complete Theory of Matter to include components from physics beyond the Standard Model (BSM). Describing the effect of these components phenomenologically provides a means to infer the nature of some of the BSM physics required. Our results also provide constraints on some BSM matrix elements. Here we apply this concept to quarks; the application to leptons will appear in a separate paper. An immediate benefit for theory is the reduction of the largest fine structure constant for the Higgs coupling to fermions by an order of magnitude, which improves the perturbative appearance of the weak interactions. The small mixing of the third generation of each fermion in the fermion families to the others is attributed to the small BSM perturbations that produce the small mass ratio of the lighter generations to the most massive one.
We discuss gauge coupling unification in models with additional 1 to 4 complete vector-like families, and derive simple rules for masses of vector-like fermions required for exact gauge coupling unification. These mass rules and the classification scheme are generalized to an arbitrary extension of the standard model. We focus on scenarios with 3 or more vector-like families in which the values of gauge couplings at the electroweak scale are highly insensitive to the grand unification scale, the unified gauge coupling, and the masses of vector-like fermions. Their observed values can be mostly understood from infrared fixed point behavior. With respect to sensitivity to fundamental parameters, the model with 3 extra vector-like families stands out. It requires vector-like fermions with masses of order 1 TeV - 100 TeV, and thus at least part of the spectrum may be within the reach of the LHC. The constraints on proton lifetime can be easily satisfied in these models since the best motivated grand unification scale is at $sim 10^{16}$ GeV. The Higgs quartic coupling remains positive all the way to the grand unification scale, and thus the electroweak minimum of the Higgs potential is stable.
These are the notes of a set of four lectures which I gave at the 2012 CERN Summer School of Particle Physics. They cover the basic ideas of gauge symmetries and the phenomenon of spontaneous symmetry breaking which are used in the construction of the Standard Model of the Electro-Weak Interactions.
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