Solving the wrong hierarchy problem

Abstract

Many theories require augmenting the Standard Model with additional scalar fields with large order one couplings. We present a new solution to the hierarchy problem for these scalar fields. We explore parity-and Z 2 -symmetric theories where the Standard Model Higgs potential has two vacua. The parity or Z 2 copy of the Higgs lives in the minimum far from the origin while our Higgs occupies the minimum near the origin of the potential. This approach results in a theory with multiple light scalar fields but with only a single hierarchy problem, since the bare mass is tied to the Higgs mass by a discrete symmetry. The new scalar does not have a new hierarchy problem associated with it because its expectation value and mass are generated by dimensional transmutation of the scalar quartic coupling. The location of the second Higgs minimum is not a free parameter, but is rather a function of the matter content of the theory. As a result, these theories are extremely predictive. We develop this idea in the context of a solution to the strong CP problem. We show this mechanism postdicts the top Yukawa to be within 1σ of the currently measured value and predicts scalar color octets with masses in the range 9-200 TeV.

UV sensitivity of the axion mass from instantons in partially broken gauge groups

“…This can be encoded in terms of an effective Lagrangian that captures the 1-(anti)instanton effects in terms of a potential for the θ angle, which in the presence of an axion will be interpreted as an effective potential/mass term for the axion itself. In a theory without massless fermions this potential is simply given by 28) where C N (ρ) contains the instanton density and the action of the Higgs scalars…”

“…Interesting models implementing the mechanism of [12] were proposed in [14][15][16][17][18], applications to models of inflation were studied in [19]. Other approaches to modify the axion mass within QCD were proposed in [20][21][22][23] while in [24][25][26][27][28][29][30] the axion mass is raised by coupling it to a new confining gauge group.…”

A collider observable QCD axion

“…2 Alternatively, if the Higgs potential has multiple minima, the symmetry could be spontaneously broken by the Higgses living in different vacua [16].…”

Theory overview of new phenomena (non-SUSY)

“…This can be achieved by imposing the Z 2 -symmetry H ↔ H. This symmetry must be extended to the rest of interactions, and this requires adding a "SM mirror" related to the SM by the Z 2 -parity. In this case, however, it can be shown that the "Higgs mirror" H gets a very heavy VEV, making the full "SM mirror" heavy and not accessible at the LHC [2].…”