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Standard Model in multiscale theories and observational constraints

AuthorsCalcagni, Gianluca ; Nardelli, Giuseppe; Rodriguez-Fernandez, D.
Issue Date29-Aug-2016
PublisherAmerican Physical Society
CitationPhysical Review D - Particles, Fields, Gravitation and Cosmology 94: 045018 (2016)
AbstractWe construct and analyze the Standard Model of electroweak and strong interactions in multiscale spacetimes with (i) weighted derivatives and (ii) q-derivatives. Both theories can be formulated in two different frames, called fractional and integer picture. By definition, the fractional picture is where physical predictions should be made. (i) In the theory with weighted derivatives, it is shown that gauge invariance and the requirement of having constant masses in all reference frames make the Standard Model in the integer picture indistinguishable from the ordinary one. Experiments involving only weak and strong forces are insensitive to a change of spacetime dimensionality also in the fractional picture, and only the electromagnetic and gravitational sectors can break the degeneracy. For the simplest multiscale measures with only one characteristic time, length and energy scale t∗, ℓ∗ and E∗, we compute the Lamb shift in the hydrogen atom and constrain the multiscale correction to the ordinary result, getting the absolute upper bound t∗<10-23 s. For the natural choice α0=1/2 of the fractional exponent in the measure, this bound is strengthened to t∗<10-29 s, corresponding to ℓ∗<10-20 m and E∗>28 TeV. Stronger bounds are obtained from the measurement of the fine-structure constant. (ii) In the theory with q-derivatives, considering the muon decay rate and the Lamb shift in light atoms, we obtain the independent absolute upper bounds t∗<10-13 s and E∗>35 MeV. For α0=1/2, the Lamb shift alone yields t∗<10-27 s, ℓ∗<10-19 m and E∗>450 GeV. © 2016 American Physical Society
Description26 pags., 1 tab.
Publisher version (URL)https://doi.org/10.1103/PhysRevD.94.045018
Identifiersdoi: 10.1103/PhysRevD.94.045018
issn: 1550-2368
Appears in Collections:(CFMAC-IEM) Artículos
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