The breaking of the SU(2)L×U(1)YSU(2)_L\times U(1)_Y symmetry: The 750 GeV resonance at the LHC and perturbative unitarity

If the di-photon excess at 750 GeV hinted by the 2015 data at the LHC is explained in terms of a scalar resonance participating in the breaking of the electro-weak symmetry, this resonance must be accompanied by other scalar states for perturbative unitarity in vector boson scattering to be preserved. The simplest set-up consistent with perturbative unitarity and with the data of the di-photon excess is the Georgi-Machacek model.Comment: 9 pages, 5 figures. v2: Minor changes, bibliography updated. v3: Minor change

Natural minimal dark matter

We show how the Higgs boson mass is protected from the potentially large corrections due to the introduction of minimal dark matter if the new physics sector is made supersymmetric. The fermionic dark matter candidate (a 5-plet of $SU(2)_L$) is accompanied by a scalar state. The weak gauge sector is made supersymmetric and the Higgs boson is embedded in a supersymmetric multiplet. The remaining standard model states are non-supersymmetric. Non vanishing corrections to the Higgs boson mass only appear at three-loop level and the model is natural for dark matter masses up to 15 TeV--a value larger than the one required by the cosmological relic density. The construction presented stands as an example of a general approach to naturalness that solves the little hierarchy problem which arises when new physics is added beyond the standard model at an energy scale around 10 TeV.Comment: 6 pages, 4 figures. v2: Discussion on the mass splitting extended and improved. References adde

Finite-time blowup and existence of global positive solutions of a semi-linear SPDE

We consider stochastic equations of the prototype $du(t,x) =(\Delta u(t,x)+u(t,x)^{1+\beta})dt+\kappa u(t,x) dW_{t}$ on a smooth domain $D\subset \mathord{\rm I\mkern-3.6mu R\:}^d$, with Dirichlet boundary condition, where $\beta$, $\kappa$ are positive constants and $\{W_t$, $t\ge0\}$ is a one-dimensional standard Wiener process. We estimate the probability of finite time blowup of positive solutions, as well as the probability of existence of non-trivial positive global solutions

Antiproton constraints on the GeV gamma-ray excess: a comprehensive analysis

A GeV gamma-ray excess has possibly been individuated in Fermi-LAT data from the Galactic Center and interpreted in terms of Dark Matter (DM) annihilations, either in hadronic (essentially $b\bar{b}$) or leptonic channels. In order to test this tantalizing interpretation, we address two issues: (i) we improve the computation of secondary emission from DM (Inverse Compton and Bremsstrahlung) with respect to previous works, confirming it to be very relevant for determining the DM spectrum in the leptonic channels, so that any conclusion on the DM nature of the signal critically depends on this contribution; (ii) we consider the constraints from antiprotons on the DM hadronic channel, finding that the uncertainties on the propagation model, and in particular on the halo height, play a major role. Moreover, we discuss the role of solar modulation, taking into account possible charge dependent effects whose importance is estimated exploiting detailed numerical tools. The limits that we obtain severely constrain the DM interpretation of the excess in the hadronic channel, for standard assumptions on the Galactic propagation parameters and solar modulation. However, they considerably relax if more conservative choices are adopted.Comment: 22 pages, 6 figures, 2 table

Mixing-induced Spontaneous Supersymmetry Breaking

It is conjectured that flavor mixing furnishes a universal mechanism for the spontaneous breaking of supersymmetry. The conjecture is proved explicitly for the mixing of two Wess--Zumino $\mathcal{N}=1$ supermultiplets and arguments for its general validity are given. The mechanism relies on the fact that, despite mixing treats fermions and bosons symmetrically, both the fermionic and the bosonic zero point energies are shifted by a positive amount and this kind of shift does not respect supersymmetry.Comment: 5 pages, 1 figure, Eq(12) of V1 corrected to Eq(22), explicit off-shell formulation included, one reference adde