A Cosmological Signature of the Standard Model Higgs Vacuum Instability: Primordial Black Holes as Dark Matter

For the current central values of the Higgs and top masses, the Standard Model Higgs potential develops an instability at a scale of the order of $10^{11}$ GeV. We show that a cosmological signature of such instability could be dark matter in the form of primordial black holes seeded by Higgs fluctuations during inflation. The existence of dark matter might not require physics beyond the Standard Model.Comment: 6+1 pages, 3 figures; v2: updated to the published PRL version, and added an Appendix about Non-Gaussian effect

The Lightest Higgs Boson Mass in the Minimal Supersymmetric Standard Model

We compute the upper bound on the mass of the lightest Higgs boson in the Minimal Supersymmetric Standard Model in a model-independent way, including leading (one-loop) and next-to-leading order (two-loop) radiative corrections. We find that (contrary to some recent claims) the two-loop corrections are negative with respect to the one-loop result and relatively small (\simlt 3\%). After defining physical (pole) top quark mass $M_t$, by including QCD self-energies, and physical Higgs mass $M_H$, by including the electroweak self-energies $\Pi\left(M_H^2\right)-\Pi(0)$, we obtain the upper limit on $M_H$ as a function of supersymmetric parameters. We include as supersymmetric parameters the scale of supersymmetry breaking $M_S$, the value of $\tan \beta$ and the mixing between stops $X_t= A_t + \mu \cot\beta$ (which is responsible for the threshold correction on the Higgs quartic coupling). Our results do not depend on further details of the supersymmetric model. In particular, for $M_S\leq 1$ TeV, maximal threshold effect $X_t^2=6M_S^2$ and any value of $\tan\beta$, we find $M_H\leq 140$ GeV for $M_t\leq 190$ GeV. In the particular scenario where the top is in its infrared fixed point we find $M_H\leq 86$ GeV for $M_t = 170$ GeV.Comment: 24 pages + 15 figures in one compressed uuencoded tarred postscript file (The figures can be obtained by e-mail from [email protected]; also, the whole postscript file of the text including the figures can be obtained by ANONYMOUS FTP from ROCA.CSIC.ES (161.111.20.20) at the directory HEP the file being HIGGS.PS: just type GET HEP/HIGGS.PS), Latex, CERN-TH.7334/9

Theoretical Constraints on the Vacuum Oscillation Solution to the Solar Neutrino Problem

The vacuum oscillation (VO) solution to the solar anomaly requires an extremely small neutrino mass splitting, Delta m^2_{sol}\leq 10^{-10} eV^2. We study under which circumstances this small splitting (whatever its origin) is or is not spoiled by radiative corrections. The results depend dramatically on the type of neutrino spectrum. If m_1^2 \sim m_2^2 \geq m_3^2, radiative corrections always induce too large mass splittings. Moreover, if m_1 and m_2 have equal signs, the solar mixing angle is driven by the renormalization group evolution to very small values, incompatible with the VO scenario (however, the results could be consistent with the small-angle MSW scenario). If m_1 and m_2 have opposite signs, the results are analogous, except for some small (though interesting) windows in which the VO solution may be natural with moderate fine-tuning. Finally, for a hierarchical spectrum of neutrinos, m_1^2 << m_2^2 << m_3^2, radiative corrections are not dangerous, and therefore this scenario is the only plausible one for the VO solution.Comment: 13 pages, LaTeX, 3 ps figures (psfig.sty

Implications for New Physics from Fine-Tuning Arguments: II. Little Higgs Models

We examine the fine-tuning associated to electroweak breaking in Little Higgs scenarios and find it to be always substantial and, generically, much higher than suggested by the rough estimates usually made. This is due to implicit tunings between parameters that can be overlooked at first glance but show up in a more systematic analysis. Focusing on four popular and representative Little Higgs scenarios, we find that the fine-tuning is essentially comparable to that of the Little Hierarchy problem of the Standard Model (which these scenarios attempt to solve) and higher than in supersymmetric models. This does not demonstrate that all Little Higgs models are fine-tuned, but stresses the need of a careful analysis of this issue in model-building before claiming that a particular model is not fine-tuned. In this respect we identify the main sources of potential fine-tuning that should be watched out for, in order to construct a successful Little Higgs model, which seems to be a non-trivial goal.Comment: 39 pages, 26 ps figures, JHEP forma