Talks

We derive constraints on the sign of couplings in an effective Higgs Lagrangian using prime principles such as the naturalness principle, global symmetries, and unitarity. Specifically, we study four dimension-six operators, O_H, O_y, O_g, and O_gamma, which contribute to the production and decay of the Higgs boson at the Large Hadron Collider (LHC), among other things. Assuming the Higgs is a fundamental scalar, we find: 1) the coefficient of O_H is positive except when there are triplet scalars, resulting in a reduction in the Higgs on-shell coupling from their standard model (SM) expectations if no other operators contribute, 2) the linear combination of O_H and O_y controlling the overall Higgs coupling to fermion is always reduced, 3) the sign of O_g induced by a new colored fermion is such that it interferes destructively with the SM top contribution in the gluon fusion production of the Higgs, if the new fermion cancels the top quadratic divergence in the Higgs mass, and 4) the correlation between naturalness and the sign of O_gamma is similar to that of O_g, when there is a new set of heavy electroweak gauge bosons. Next considering a composite scalar for the Higgs, we find the reduction in the on-shell Higgs couplings persists. If further assuming a collective breaking mechanism as in little Higgs theories, the coefficient of O_H remains positive even in the presence of triplet scalars. In the end, we conclude that the gluon fusion production of the Higgs boson is reduced from the SM rate in all composite Higgs models. Our study suggests a wealth of information could be revealed by precise measurements of the Higgs couplings, providing strong motivations for both improving on measurements at the LHC and building a precision machine such as the linear collider.

The fixed point structure of the renormalization flow in Einstein gravity and higher derivative gravity is investigated in terms of the background effective action. Using a covariant operator cutoff that keeps track of powerlike divergences and the transversal-traceless decomposition a construction is proposed that renders the {\it regularized} one-loop effective action gauge independent on-shell. In combination with a `Wilsonian' matching condition nontrivial strictly positive fixed points for the dimensionless Newton constant $g$ and the cosmological constant $\lambda$ can then be identified already in one loop perturbation theory. The renormalization flow is asymptotically safe with respect to the nontrivial fixed points in both cases. In Einstein gravity a residual gauge dependence of the fixed points is unavoidable while in higher derivative gravity both the fixed point and the flow equations are universal. Along this flow spectral positivity of the Hessians can be satisfied, evading the traditional positivity problems. Dependence on $O(10)$ initial data is erased to accuracy $10^{-5}$ after $O(10)$ units of the renormalization mass scale and the flow settles on a $\lambda(g)$ orbit.