B-decay anomalies in Pati-Salam SU(4)

Attempts to incorporate in a coherent picture the $B$-decay anomalies presumably observed in $b\rightarrow c$ and $b\rightarrow s$ semi-leptonic decays have to face the absence of signals in other related experiments, both at low and at high energies. By extending and making more precise the content of Ref. [1], we describe one such attempt based on the Pati-Salam SU(4) group, that unifies colour and the $B$-$L$ charge, in the context of a new strongly interacting sector, equally responsible for producing a pseudo-Goldstone Higgs boson.Comment: 24 pages, 3 figure

Cosmological Production of Dark Nuclei

We study the formation of Dark Matter nuclei in scenarios where DM particles are baryons of a new confining gauge force. The dark nucleosynthesis is analogous to the formation of light elements in the SM and requires as a first step the formation of dark deuterium. We compute this process from first principles, using the formalism of pion-less effective theory for nucleon-nucleon interactions. This controlled effective field theory expansion allows us to systematically compute the cross sections for generic SM representations under the assumption of shallow bound states. In the context of vector-like confinement models we find that, for nucleon masses in the TeV range, baryonic DM made of electro-weak constituents can form a significant fraction of dark deuterium and a much smaller fraction of dark tritium. Formation of dark nuclei can also lead to monochromatic photon lines in indirect detection. Models with singlets do not undergo nucleosynthesis unless a dark photon is added to the theory.Comment: 26 pages, 4 figures. v2) improved discussion on indirect detection, refs adde

On the Tuning and the Mass of the Composite Higgs

We analyze quantitatively the tuning of composite Higgs models with partial compositeness and its interplay with the predicted Higgs mass. In this respect we identify three classes of models, characterized by different quantum numbers of the fermionic colored resonances associated with the top quark, the so-called top partners. The main result of this classification is that in all models with moderate tuning a light Higgs, of 125 GeV mass, requires the presence of light top partners, around 1 TeV. The minimal tuning is comparable to the one of the most attractive supersymmetric models in particular the ones realizing Natural SUSY. This gives further support to an extensive program of top partners searches at the LHC that can already probe the natural region of composite Higgs models.Comment: 32 pages, 14 figures; v2: version published in JHE

Baryogenesis at a Lepton-Number-Breaking Phase Transition

We study a scenario in which the baryon asymmetry of the universe arises from a cosmological phase transition where lepton-number is spontaneously broken. If the phase transition is first order, a lepton-number asymmetry can arise at the bubble wall, through dynamics similar to electroweak baryogenesis, but involving right-handed neutrinos. In addition to the usual neutrinoless double beta decay in nuclear experiments, the model may be probed through a variety of "baryogenesis by-products," which include a stochastic background of gravitational waves created by the colliding bubbles. Depending on the model, other aspects may include a network of topological defects that produce their own gravitational waves, additional contribution to dark radiation, and a light pseudo-Goldstone boson (majoron) as dark matter candidate.Comment: 21 pages + 10 appendices & references, 3 figure

Fundamental partial compositeness

We construct renormalizable Standard Model extensions, valid up to the Planck scale, that give a composite Higgs from a new fundamental strong force acting on fermions and scalars. Yukawa interactions of these particles with Standard Model fermions realize the partial compositeness scenario. Under certain assumptions on the dynamics of the scalars, successful models exist because gauge quantum numbers of Standard Model fermions admit a minimal enough 'square root'. Furthermore, right-handed SM fermions have an SU(2)$_R$-like structure, yielding a custodially-protected composite Higgs. Baryon and lepton numbers arise accidentally. Standard Model fermions acquire mass at tree level, while the Higgs potential and flavor violations are generated by quantum corrections. We further discuss accidental symmetries and other dynamical features stemming from the new strongly interacting scalars. If the same phenomenology can be obtained from models without our elementary scalars, they would reappear as composite states.Comment: 36 pages, 3 figures, 5 tables. v2: final published version, expanded discussion about neutrino masses, dark matter and flavou

Well-posedness of a mathematical model for Alzheimer's disease

We consider the existence and uniqueness of solutions of an initial-boundary value problem for a coupled system of PDE's arising in a model for Alzheimer's disease. Apart from reaction diffusion equations, the system contains a transport equation in a bounded interval for a probability measure which is related to the malfunctioning of neurons. The main ingredients to prove existence are: the method of characteristics for the transport equation, a priori estimates for solutions of the reaction diffusion equations, a variant of the classical contraction theorem, and the Wasserstein metric for the part concerning the probability measure. We stress that all hypotheses on the data are not suggested by mathematical artefacts, but are naturally imposed by modelling considerations. In particular the use of a probability measure is natural from a modelling point of view. The nontrivial part of the analysis is the suitable combination of the various mathematical tools, which is not quite routine and requires various technical adjustments