A New Look at Higgs Constraints on Stops

We present a simple new way to visualize the constraints of Higgs coupling measurements on light stops in natural SUSY scenarios beyond the MSSM, which works directly in the plane of stop mass eigenvalues (with no need to make assumptions about mixing angles). For given stop mass eigenvalues, the smallest value of $X_t$ that can bring the correction to the $h \to gg$ and $h\to \gamma\gamma$ couplings into agreement with data is computed. Requiring that this $X_t$ is consistent--i.e. that the chosen mass eigenvalues can be the outcome of diagonalizing a matrix with a given off-diagonal term--rules out the possibility that both stops have a mass below $\approx$ 400 GeV. Requiring that $X_t$ is not fine-tuned for agreement with the data shows that neither stop can be lighter than $\approx$ 100 GeV. These constraints are interesting because, unlike direct searches, they apply no matter how stops decay, and suggest a minimum electroweak fine-tuning of between a factor of 5 and 10. We show that a multi-parameter fit can slightly weaken this conclusion by allowing a large Higgs coupling to $b$-quarks, but only if a second Higgs boson is within reach of experiment. Certain models, like $R$-symmetric models with Dirac gauginos, are much more strongly constrained because they predict negligible $X_t$. We illustrate how the constraints will evolve given precise measurements at future colliders (HL-LHC, ILC, and TLEP), and comment on the more difficult case of Folded Supersymmetry.Comment: v2: references added, accepted by JHE

Heavy Gravitino and Split SUSY in the Light of BICEP2

High-scale supersymmetry (SUSY) with a split spectrum has become increasingly interesting given the current experimental results. A SUSY scale above the weak scale could be naturally associated with a heavy unstable gravitino, whose decays populate the dark matter (DM) particles. In the mini-split scenario with gravitino at about the PeV scale and the lightest TeV scale neutralino being (a component of) DM, the requirement that the DM relic abundance resulting from gravitino decays does not overclose the Universe and satisfies the indirect detection constraints demand the reheating temperature to be below 10^9 - 10^{10} GeV. On the other hand, the BICEP2 result prefers a heavy inflaton with mass at around 10^{13} GeV and a reheating temperature at or above 10^9 GeV with some general assumptions. The mild tension could be alleviated if SUSY scale is even higher with the gravitino mass above the PeV scale. Intriguingly, in no-scale supergravity, gravitinos could be very heavy at about 10^{13} GeV, the inflaton mass scale, while gauginos could still be light at the TeV scale.Comment: 20 pages, 2 figures, references added, to appear in JHE

Clockwork Axions in Cosmology: Is Chromonatural Inflation Chrononatural?

Many cosmological models rely on large couplings of axions to gauge fields. Examples include theories of magnetogenesis, inflation on a steep potential, chiral gravitational waves, and chromonatural inflation. Such theories require a mismatch between the axion field range and the mass scale appearing in the $a F \widetilde{F}$ coupling. This mismatch suggests an underlying monodromy, with the axion winding around its fundamental period a large number of times. We investigate the extent to which this integer can be explained as a product of smaller integers in a UV completion: in the parlance of our times, can the theory be "clockworked"? We argue that a clockwork construction producing a potential $\mu^4 \cos(\frac{a}{j F_a})$ for an axion of fundamental period $F_a$ will obey the constraint $\mu < F_a$. For some applications, including chromonatural inflation with sub-Planckian field range, this constraint obstructs a clockwork UV completion. Alternative routes to a large coupling include fields of large charge (an approach limited by strong coupling) or kinetic mixing (requiring a lighter axion). Our results suggest that completions of axion cosmologies that explain the large parameter in the theory potentially alter the phenomenological predictions of the model