Understanding Gauge Theories of Fundamental Interactions and their applications to Beyond Standard Model Physics

Who: Sofie Gregersen (CP3-Origins)
When: Friday, June 10, 2016

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This master thesis investigates the behaviour at different energy scales of gauge, Yukawa and scalar quartic couplings of the Standard Model and an extended model known as the Elementary Goldstone Higgs model. The main difference between the two models is the enlarged scalar sector of the Elementary Goldstone Higgs model, where we find 12 scalar degrees of freedom which couple through 18 different couplings at one-loop order, and not just one complex scalar doublet as in the Standard Model.
The behaviour of the couplings at different energy scales is described by the beta function. Thus the beta function depends on the the different couplings of the theory, which again are functions of the renormalization scale, μ.
The three one-loop gauge beta functions are nearly identical in the two theories and the Yukawa beta functions are identical. One of the Elementary Goldstone Higgs model scalar beta functions, \(\beta_{\Lambda_1}\), includes the Standard Model scalar beta function and a contribution from the enlarged scalar sector.
It is found that the two models lead to nearly identical running couplings for the gauge, Yukawa and scalar Higgs/\(\Lambda_1\) couplings, when the five of them are fitted to experimental data and all other scalar couplings are set to zero at \(M_Z\). All but three of the extra scalar couplings have trivial runnings and stay zero for all μ, the three non-zero ones stay small but slightly increasing. Letting some of the other scalar couplings take non-zero values at \(M_Z\) will only effect the scalar beta functions. The changes do not effect the running of the \(\Lambda_1\) coupling much, since the dominant contributions to its beta function comes from Yukawa and gauge couplings. The system does quickly develop IR divergences if more couplings get non-trivial runnings.
When including gravitational constraints at the Planck scale we find that the top Yukawa coupling, yt, must be lowered to 0.9 at Mt to get the correct Higgs mass at \(M_Z\). We here have a discrepancy since the experimental value is \(y_t(M_Z)\simeq 1\).