Phenomenology of a fake Inert Doublet Model

2021

J. High Energ. Phys.

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We prove spectral optical identities in quantum field theories of physical particles (defined by the Feynman iϵ prescription) and purely virtual particles (defined by the fakeon prescription). The identities are derived by means of purely algebraic operations and hold for every (multi)threshold separately and for arbitrary frequencies. Their major significance is that they offer a deeper understanding on the problem of unitarity in quantum field theory. In particular, they apply to “skeleton” diagrams, before integrating on the space components of the loop momenta and the phase spaces. In turn, the skeleton diagrams obey a spectral optical theorem, which gives the usual optical theorem for amplitudes, once the integrals on the space components of the loop momenta and the phase spaces are restored. The fakeon prescription/projection is implemented by dropping the thresholds that involve fakeon frequencies. We give examples at one loop (bubble, triangle, box, pentagon and hexagon), two loops (triangle with “diagonal”, box with diagonal) and arbitrarily many loops. We also derive formulas for the loop integrals with fakeons and relate them to the known formulas for the loop integrals with physical particles.

Section: Thick Fakeonsmentioning

confidence: 99%

“…More generally, they can be used to solve the problem of ghosts in higher-derivatives theories. However, they can also be employed in collider physics [24] to evade common constraints and offer new ways to solve discrepancies with data, as in the problem of the muon anomalous magnetic moment [25].…”

Section: Jhep11(2021)030 1 Introductionmentioning

confidence: 99%

Diagrammar of physical and fake particles and spectral optical theorem

2021

J. High Energ. Phys.

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“…Fakeons can be used to propose models of new physics beyond the standard model. For example, the popular inert doublet model [55][56][57][58][59] has rather different phenomenological properties if the second doublet is taken to be a fakeon [4]. Since the fake doublet avoids the Z-pole constraints regardless of the chosen mass scale, there is room for new effects below the electroweak scale.…”

Section: Phenomenology Of Fake Particlesmentioning

confidence: 99%

“…Finally, the violation of microcausality is always present, while it is possible to have no peak uncertainty (42), as in the models of ref. [4], where fakeons have identically vanishing widths due to a Z 2 symmetry.…”

Section: Peak Uncertainty and Micro Acausalitymentioning

confidence: 99%

“…At the phenomenological level, fakeons evade common constraints that limit the employment of normal particles. Among the other things, they can be used to propose new physics beyond the standard model [4] and solve discrepancies with data [5]. We stress that the fakeon diagrammatics is relatively straightforward, to the extent that it can be implemented in software like FeynCalc, FormCalc, LoopTools and Package-X [6][7][8][9][10][11][12] and used to work out physical predictions.…”

Section: Introductionmentioning

confidence: 99%

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Purely Virtual Particles in Quantum Gravity, Inflationary Cosmology and Collider Physics

2022

Symmetry

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We review the concept of purely virtual particle and its uses in quantum gravity, primordial cosmology and collider physics. The fake particle, or “fakeon”, which mediates interactions without appearing among the incoming and outgoing states, can be introduced by means of a new diagrammatics. The renormalization coincides with one of the parent Euclidean diagrammatics, while unitarity follows from spectral optical identities, which can be derived by means of algebraic operations. The classical limit of a theory of physical particles and fakeons is described by an ordinary Lagrangian plus Hermitian, micro acausal and micro nonlocal self-interactions. Quantum gravity propagates the graviton, a massive scalar field (the inflaton) and a massive spin-2 fakeon, and leads to a constrained primordial cosmology, which predicts the tensor-to-scalar ratio r in the window 0.4≲1000r≲3.5. The interpretation of inflation as a cosmic RG flow allows us to calculate the perturbation spectra to high orders in the presence of the Weyl squared term. In models of new physics beyond the standard model, fakeons evade various phenomenological bounds, because they are less constrained than normal particles. The resummation of self-energies reveals that it is impossible to get too close to the fakeon peak. The related peak uncertainty, equal to the fakeon width divided by 2, is expected to be observable.

Dressed propagators, fakeon self-energy and peak uncertainty

2022

J. High Energ. Phys.

We study the resummation of self-energy diagrams into dressed propagators in the case of purely virtual particles and compare the results with those obtained for physical particles and ghosts. The three geometric series differ by infinitely many contact terms, which do not admit well-defined sums. The peak region, which is outside the convergence domain, can only be reached in the case of physical particles, thanks to analyticity. In the other cases, nonperturbative effects become important. To clarify the matter, we introduce the energy resolution ∆E around the peak and argue that a “peak uncertainty” ∆E ≳ ∆Emin ≃ Γf/2 around energies E ≃ mf expresses the impossibility to approach the fakeon too closely, mf being the fakeon mass and Γf being the fakeon width. The introduction of ∆E is also crucial to explain the observation of unstable long-lived particles, like the muon. Indeed, by the common energy-time uncertainty relation, such particles are also affected by ill-defined sums at ∆E = 0, whenever we separate their observation from the observation of their decay products. We study the regime of large Γf, which applies to collider physics (and situations like the one of the Z boson), and the regime of small Γf, which applies to quantum gravity (and situations like the one of the muon).