## Standard model

Talk given at Penn State University, Dec 17, 2019

A new quantization prescription is able to endow quantum field theory with a new type of “particle”, the fakeon (fake particle), which mediates interactions, but cannot be observed. A massive fakeon of spin 2 (together with a scalar field) allows us to build a theory of quantum gravity that is both renormalizable and unitary, and to some extent unique. The theory predicts that causality is lost at sufficiently small distances, where time makes no longer sense. After presenting the general formulation of the theory, I explain its nontrivial classical limit, the modifications of the FLRW metric and the role of the cosmological constant. Finally, I discuss the possibility that the Higgs boson might be a fakeon.

Talk given at the conference “Quantum Gravity and Quantum Geometry“, Nijmegen Oct 29 – Nov 1, 2019

A new quantization prescription is able to endow quantum field theory with a new type of “particle”, the fakeon (fake particle), which mediates interactions, but cannot be observed. A massive fakeon of spin 2 (together with a scalar field) allows us to build a theory of quantum gravity that is both renormalizable and unitary, and to some extent unique. The theory predicts that causality is lost at sufficiently small distances, where time makes no longer sense. After formulating the theory, I explain its main properties. In particular: the nontrivial classical limit, the modifications of the FLRW metric and the roles of the cosmological constant and the Hubble constant.

Several particles are not observed directly, but only through their decay products. We consider the possibility that they might be fakeons, i.e. fake particles, which mediate interactions but are not asymptotic states. A crucial role to determine the true nature of a particle is played by the imaginary parts of the one-loop radiative corrections, which are affected in nontrivial ways by the presence of fakeons in the loop. The knowledge we have today is sufficient to prove that most non directly observed particles are true physical particles. However, in the case of the Higgs boson the possibility that it might be a fakeon remains open. The issue can be resolved by means of precision measurements in existing and future accelerators.

Mod. Phys. Lett. A 34 (2019) 1950123 | DOI: 10.1142/S0217732319501232

We consider renormalizable Standard-Model extensions that violate Lorentz symmetry at high energies, but preserve CPT, and do not contain elementary scalar fields. A Nambu–Jona-Lasinio mechanism gives masses to fermions and gauge bosons, and generates composite Higgs fields at low energies. We study the effective potential at the leading order of the large-$N_{c}$ expansion, prove that there exists a broken phase and study the phase space. In general, the minimum may break invariance under boosts, rotations and CPT, but we give evidence that there exists a Lorentz invariant phase. We study the spectrum of composite bosons and the low-energy theory in the Lorentz phase. Our approach predicts relations among the parameters of the low-energy theory. We find that such relations are compatible with the experimental data, within theoretical errors. We also study the mixing among generations, the emergence of the CKM matrix and neutrino oscillations.

Phys. Rev. D83 (2011) 056005 | DOI: 10.1103/PhysRevD.83.056005

If Lorentz symmetry is violated at high energies, interactions that are usually non-renormalizable can become renormalizable by weighted power counting. Recently, a CPT invariant, Lorentz violating extension of the Standard Model containing two scalar-two fermion interactions (which can explain neutrino masses) and four fermion interactions (which can explain proton decay) was proposed. In this paper we consider a variant of this model, obtained suppressing the elementary scalar fields, and argue that it can reproduce the known low energy physics. In the Nambu$-$Jona-Lasinio spirit, we show, using a large $N_c$ expansion, that a dynamical symmetry breaking takes place. The effective potential has a Lorentz invariant minimum and the Lorentz violation does not reverberate down to low energies. The mechanism generates fermion masses, gauge-boson masses and scalar bound states, to be identified with composite Higgs bosons. Our approach is not plagued by the ambiguities of approaches based on non-renormalizable vertices. The low-energy effective action is uniquely determined and predicts relations among parameters of the Standard Model.

Eur.Phys.J. C65 (2010) 523-536 | DOI: 10.1140/epjc/s10052-009-1211-z

arXiv:0904.1849 [hep-ph]

In flat space, $\gamma_5$ and the epsilon tensor break the dimensionally continued Lorentz symmetry, but propagators have fully Lorentz invariant denominators. When the Standard Model is coupled with quantum gravity $\gamma_5$ breaks the continued local Lorentz symmetry. I show how to deform the Einstein lagrangian and gauge-fix the residual local Lorentz symmetry so that the propagators of the graviton, the ghosts and the BRST auxiliary fields have fully Lorentz invariant denominators. This makes the calculation of Feynman diagrams more efficient.

Phys. Lett. B 596 (2004) 90 | DOI: 10.1016/j.physletb.2004.06.089

arXiv:hep-th/0404032