A road towards a beyond the Standard Model model

In this talk we describe examples of renormalizable strongly interacting field theories where chiral symmetry, broken at the UV cutoff by the presence of some irrelevant d > 4 operators in the fundamental Lagrangian, is recovered at low energy owing to the tuning of certain Lagrangian parameters. The interference of UV effects with IR features coming from the spontaneous breaking of the recovered chiral symmetry yields non perturbatively generated elementary fermion masses parametrically expressed by formulae of the kind mq ~ Cq(α)ΛRGI with α the gauge coupling constant and ΛRGI the RGI scale of the theory. Upon introducing EW interactions, this mechanism can be extended to give mass to EW bosons and leptons and can thus be used as an alternative to the Higgs scenario. In order to give the top quark and the weak gauge bosons a mass of the phenomenologically correct order of magnitude, the model must necessarily include (yet unobserved) super-strongly interacting massive fermions endowed, besides ordinary Standard Model interactions, with super-strong interactions with a RGI scale, ΛT ΛQCD in the few TeV range. Though limited in its scope (here we ignore hypercharge and leptons and discuss only the case of one family neglecting weak isospin splitting), the model opens the way to a solution of the naturalness problem and an understanding of the fermion mass hierarchy.

Dilaton chiral perturbation theory and applications

We review dilaton chiral perturbation theory (dChPT), the effective low-energy theory for the light sector of near-conformal, confining theories. dChPT provides a systematic expansion in both the fermion mass and the distance to the conformal window. It accounts for the pions and the light scalar, the approximate Nambu–Goldstone bosons for chiral and scale symmetry, respectively. A unique feature of dChPT is the existence of a large-mass regime in which the theory exhibits approximate hyperscaling, while the expansion nevertheless remains systematic. We discuss applications to lattice data, presenting successes as well as directions for future work.

A translational flavor symmetry in the mass terms of Dirac and Majorana fermions

Requiring the effective mass term for a category of fundamental Dirac or Majorana fermions of the same electric charge to be invariant under the translational transformations $\psi^{}_{\alpha \rm L (R)} \to \psi^{}_{\alpha \rm L (R)} + n^{}_{\alpha} z^{}_{\psi \rm L(R)}$ in the flavor space, where $n^{}_\alpha$ and $z^{}_{\psi \rm L(R)}$ stand respectively for the flavor-dependent complex numbers and a constant spinor field anticommuting with the fermion fields, we show that $n^{}_\alpha$ can be identified as the elements $U^{}_{\alpha i}$ in the $i$-th column of the unitary matrix $U$ used to diagonalize the corresponding Hermitian or symmetric fermion mass matrix $M^{}_\psi$, and $m^{}_i = 0$ holds accordingly. We find that the reverse is also true. Now that the mass spectra of charged leptons, up- and down-type quarks are all strongly hierarchical and current experimental data allow the lightest neutrino to be massless, we argue that the zero mass limit for the first-family fermions and the translational flavor symmetry behind it should be a natural starting point for building viable fermion mass models.

Precision test of the muon-Higgs coupling at a high-energy muon collider

We explore the sensitivity of directly testing the muon-Higgs coupling at a high-energy muon collider. This is strongly motivated if there exists new physics that is not aligned with the Standard Model Yukawa interactions which are responsible for the fermion mass generation. We illustrate a few such examples for physics beyond the Standard Model. With the accidentally small value of the muon Yukawa coupling and its subtle role in the high-energy production of multiple (vector and Higgs) bosons, we show that it is possible to measure the muon-Higgs coupling to an accuracy of ten percent for a 10 TeV muon collider and a few percent for a 30 TeV machine by utilizing the three boson production, potentially sensitive to a new physics scale about Λ ∼ 30 − 100 TeV.

Leptogenesis and fermion mass fit in a renormalizable SO(10) model

A non-supersymmetric renormalizable SO(10) model is investigated for its viability in explaining the observed fermion masses and mixing parameters along with the baryon asymmetry produced via thermal leptogenesis. The Yukawa sector of the model consists of complex 10H and $$ {\overline{126}}_H $$ 126 ¯ H scalars with a Peccei-Quinn like symmetry and it leads to strong correlations among the Yukawa couplings of all the standard model fermions including the couplings and masses of the right-handed (RH) neutrinos. The latter implies the necessity to include the second lightest RH neutrino and flavor effects for the precision computation of leptogenesis. We use the most general density matrix equations to calculate the temperature evolution of flavoured leptonic asymmetry. A simplified analytical solution of these equations, applicable to the RH neutrino spectrum predicted in the model, is also obtained which allows one to fit the observed baryon to photon ratio along with the other fermion mass observables in a numerically efficient way. The analytical and numerical solutions are found to be in agreement within a factor of $$ \mathcal{O}(1) $$ O 1 . We find that the successful leptogenesis in this model does not prefer any particular value for leptonic Dirac and Majorana CP phases and the entire range of values of these observables is found to be consistent. The model specifically predicts (a) the lightest neutrino mass $$ {m}_{v_1} $$ m v 1 between 2–8 meV, (b) the effective mass of neutrinoless double beta decay mββ between 4–10 meV, and (c) a particular correlation between the Dirac and one of the Majorana CP phases.

CJT effective potential approach to analyze the nature of phase transition of thermal QED$$_3$$ at finite volume

Based on the Cornwall–Jackiw–Tomboulis effective potential and the truncated Dyson–Schwinger equations, the nature of phase transition of thermal QED$$_3$$ 3 at finite volume is investigated. We show that, with the rise of temperature, the system undergoes a second-order transition in the chiral limit, and remains exhibiting the second-order with small fermion mass, while it switches to a crossover when the fermion mass exceeds a critical value about $$m_{c}$$ m c , which diminishes with the increasing volume size and tends to zero in infinite volume.

Fermion mass hierarchy and g − 2 anomalies in an extended 3HDM Model

We propose an extension of the three-Higgs-doublet model (3HDM), where the Standard Model (SM) particle content is enlarged by the inclusion of two inert SU2L scalar doublets, three inert and two active electrically neutral gauge singlet scalars, charged vector like fermions and Majorana neutrinos. These additional particles are introduced to generate the SM fermion mass hierarchy from a sequential loop suppression mechanism. In our model the top and exotic fermion masses appear at tree level, whereas the remaining fermions get their masses radiatively. Specifically, bottom, charm, tau and muon masses appear at 1-loop; the masses for the light up, down and strange quarks as well as for the electron at 2-loop and masses for the light active neutrinos at 3-loop. Our model successfully accounts for SM fermion masses and mixings and accommodates the observed Dark Matter relic density, the electron and muon anomalous magnetic moments, as well the constraints arising from charged Lepton Flavor Violating (LFV) processes. The proposed model predicts charged LFV decays within the reach of forthcoming experiments.

SU(5)×U(1)′ Models with a Vector-Like Fermion Family

Motivated by experimental measurements indicating deviations from the Standard Model predictions, we discuss F-theory-inspired models, which, in addition to the three chiral generations, contain a vector-like complete fermion family. The analysis takes place in the context of $SU(5)\times U(1)'$ GUT embedded in an $E_8$ covering group, which is associated with the (highest) geometric singularity of the elliptic fibration. In this context, the $U(1)'$ is a linear combination of four abelian factors subjected to the appropriate anomaly cancellation conditions. Furthermore, we require universal $U(1)'$ charges for the three chiral families and different ones for the corresponding fields of the vector-like representations. Under the aforementioned assumptions, we find 192 models that can be classified into five distinct categories with respect to their specific GUT properties. We exhibit representative examples for each such class and construct the superpotential couplings and the fermion mass matrices. We explore the implications of the vector-like states in low-energy phenomenology, including the predictions regarding the B-meson anomalies. The rôle of R-parity violating terms appearing in some particular models of the above construction is also discussed.

A unified Yukawa interaction for the Standard Model of quarks and leptons

To address fermion mass hierarchy and flavor mixings in the quark and lepton sectors, a minimal flavor structure without any redundant parameters beyond phenomenological observables is proposed via decomposition of the Standard Model Yukawa mass matrix into a bi-unitary form. After reviewing the roles and parameterization of the factorized matrix [Formula: see text] and [Formula: see text] in fermion masses and mixings, we generalize the mechanism to up- and down-type fermions to unify them into a universal quark/lepton Yukawa interaction. In the same way, a unified form of the description of the quark and lepton Yukawa interactions is also proposed, which shows a similar picture as the unification of gauge interactions.