119104621
Flavour physics from an approximate U(2)3 symmetry
A bstractThe quark sector of the Standard Model exhibits an approximate U(2)3 flavour symmetry. This symmetry, broken in specific directions dictated by minimality, can explain the success of the Cabibbo-Kobayashi-Maskawa picture of flavour mixing and CP violation, confirmed by the data so far, while allowing for observable deviations from it, as expected in most models of ElectroWeak Symmetry Breaking. Building on previous work in the specific context of supersymmetry, we analyze the expected effects and we quantify the current bounds in a general Effective Field Theory framework. As a further relevant example we then show how the U(2)3 symmetry and its breaking can be implemented in a generic composite Higgs model and we make a first analysis of its peculiar consequences. We also discuss how some partial extension of U(2)3 to the lepton sector can arise, both in general and in composite Higgs models. An optimistic though conceivable interpretation of the considerations developed in this paper gives reasons to think that new physics searches in the flavour sector may be about to explore an interesting realm of phenomena.
119219385
A 125 GeV composite Higgs boson versus flavour and electroweak precision tests
A bstractA composite Higgs boson of 125 GeV mass, only mildly fine-tuned, requires top partners with a semi-perturbative coupling and a mass not greater than about a TeV. We analyze the strong constraints on such picture arising from flavour and electroweak precision tests in models of partial compositeness. We consider different representations for the composite fermions and compare the case of an anarchic flavour structure to models with a U(3)3 and U(2)3 flavour symmetry. Although non trivially, some models emerge that look capable of accommodating a 125GeV Higgs boson with top partners in an interesting mass range for discovery at the LHC as well as associated flavour signals.
118648451
Less minimal flavour violation
A bstractWe consider the approximate U(2)3 flavour symmetry exhibited by the quark sector of the Standard Model and all its possible breaking terms appearing in the quark Yukawa couplings. Taking an Effective Field Theory point of view, we determine the current bounds on these parameters, assumed to control the breaking of flavour in a generic extension of the Standard Model at a reference scale Λ. In particular, a significant bound from ϵ′/ϵ is derived, which is relevant to Minimal Flavour Violation as well. In the up- quark sector, the recently observed CP violation in D → π+π−, K+K− decays might be accounted for in this generic framework, consistently with any other constraint.
119181209
Exploring the Higgs sector of a most natural NMSSM
The Next to Minimal Supersymmetric Standard Model (NMSSM) with a Higgs-singlet coupling {\lambda} close to unity, moderate tan {\beta} and stop masses below 1 TeV minimizes the fine tuning of the electroweak scale, making possible that the lightest new particles, except perhaps for the LSP, be part of the extended Higgs system. We show how the measurements of the couplings of the 126 GeV Higgs boson constrain the region of the physical parameters of a generic NMSSM most relevant to this context. In the same region of parameter space we determine the cross section for the production of a heavier CP-even scalar together with its total width and its most relevant branching ratios. For comparison we show the same analysis for the MSSM. We also comment on how a coupling {\lambda} ~ 1 can be compatible with gauge coupling unification.
119112600
Flavour physics and flavour symmetries after the first LHC phase
A bstractBased on flavour symmetries only, there are two ways to give rise to an effective description of flavour physics in the quark sector close to the CKM picture: one is based on U(3)q × U(3)u × U(3)d (or equivalent) and the other on U(2)q × U(2)u × U(2)d (or equivalent). In this context we analyze the current status of flavour physics measurements and we compare their impact, in the specific case of supersymmetry, with the direct searches of new particles at the LHC, present or foreseen.
54021743
Investigating the near-criticality of the Higgs boson
A bstractWe extract from data the parameters of the Higgs potential, the top Yukawa coupling and the electroweak gauge couplings with full 2-loop NNLO precision, and we extrapolate the SM parameters up to large energies with full 3-loop NNLO RGE precision. Then we study the phase diagram of the Standard Model in terms of high-energy parameters, finding that the measured Higgs mass roughly corresponds to the minimum values of the Higgs quartic and top Yukawa and the maximum value of the gauge couplings allowed by vacuum metastability. We discuss various theoretical interpretations of the near-criticality of the Higgs mass.
115175198
Representations of the Heisenberg algebra and moduli spaces of framed sheaves
We give a `geometrical' construction of an action of a Heisenberg algebra on the homology of the moduli spaces of torsion free sheaves on a complex smooth connected projective surface, framed along a smooth connected genus zero curve. This result generalizes Nakajima's construction for the Hilbert schemes of points.
119676782
Framed sheaves on projective stacks
Given a normal projective irreducible stack $\mathscr X$ over an algebraically closed field of characteristic zero we consider framed sheaves on $\mathscr X$, i.e., pairs $(\mathcal E,\phi_{\mathcal E})$, where $\mathcal E$ is a coherent sheaf on $\mathscr X$ and $\phi_{\mathcal E}$ is a morphism from $\mathcal E$ to a fixed coherent sheaf $\mathcal F$. After introducing a suitable notion of (semi)stability, we construct a projective scheme, which is a moduli space for semistable framed sheaves with fixed Hilbert polynomial, and an open subset of it, which is a fine moduli space for stable framed sheaves. If $\mathscr X$ is a projective irreducible orbifold of dimension two and $\mathcal F$ a locally free sheaf on a smooth divisor $\mathscr D\subset \mathscr X$ satisfying certain conditions, we consider $(\mathscr{D}, \mathcal{F})$-framed sheaves, i.e., framed sheaves $(\mathcal E,\phi_{\mathcal E})$ with $\mathcal E$ a torsion-free sheaf which is locally free in a neighborhood of $\mathscr D$, and ${\phi_{\mathcal{E}}}_{| \mathscr{D}}$ an isomorphism. These pairs are $\mu$-stable for a suitable choice of a parameter entering the (semi)stability condition, and of the polarization of $\mathscr X$. This implies the existence of a fine moduli space parameterizing isomorphism classes of $(\mathscr{D}, \mathcal{F})$-framed sheaves on $\mathscr{X}$ with fixed Hilbert polynomial, which is a quasi-projective scheme. In an appendix we develop the example of stacky Hirzebruch surfaces. This is the first paper of a project aimed to provide an algebro-geometric approach to the study of gauge theories on a wide class of 4-dimensional Riemannian manifolds by means of framed sheaves on "stacky" compactifications of them. In particular, in a subsequent paper we will use these results to study gauge theories on ALE spaces of type $A_k$.