TY - JOUR

T1 - Standard Model in multiscale theories and observational constraints

AU - Nardelli, Giuseppe

AU - Calcagni, Gianluca

AU - Rodríguez-Fernández, David

PY - 2016

Y1 - 2016

N2 - We 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.

AB - We 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.

KW - multiscale theories

KW - standard model

KW - multiscale theories

KW - standard model

UR - http://hdl.handle.net/10807/91462

U2 - 10.1103/PhysRevD.94.045018

DO - 10.1103/PhysRevD.94.045018

M3 - Article

VL - 2016

SP - N/A-N/A

JO - Physical Review D

JF - Physical Review D

SN - 2470-0010

ER -