Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle
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Regular Article - Theoretical Physics
Phenomenology of the Pauli exclusion principle violations due to the non-perturbative generalized uncertainty principle Andrea Addazi1,2 , Pierluigi Belli2,3 , Rita Bernabei2,3 , Antonino Marcianò4,5 , Homa Shababi1,a 1
Center for Theoretical Physics, College of Physical Science and Technology, Sichuan University, Chengdu 610065, People’s Republic of China INFN sezione Roma Tor Vergata, 00133 Rome, Italy 3 Dipartimento di Fisica, Universitá di Roma Tor Vergata, 00133 Rome, Italy 4 Department of Physics and Center for Field Theory and Particle Physics, Fudan University, Shanghai 200433, China 5 Laboratori Nazionali di Frascati INFN, Frascati, Rome, Italy
2
Received: 19 May 2020 / Accepted: 25 August 2020 / Published online: 31 August 2020 © The Author(s) 2020
Abstract New phenomenological implications of the Generalized Uncertainty Principle (GUP), a modification of the Heisenberg Uncertainty Principle (HUP) are explored in light of constraints arising from underground experiments. An intimate link intertwines the symplectic structure of a theory, which is at the very base of the formulation of the HUP and thus a pillar of quantum mechanics, with the symmetries of space-time and the spin-statistics. Within this wide framework, a large class of non-perturbative GUPs inevitably lead to energy-dependent violations of the total angular momentum conservation rules, and imply hence tiny Pauli Exclusion Principle (PEP) violating transitions. Exotic PEP violating nuclear transitions can be tested, for example, through extremely high precision data provided by the DAMA/LIBRA experiment. We show that several GUP violations are already ruled out up to the quantum gravity Planck scale.
1 Introduction The Heisenberg uncertainty principle immediately implies that identical particles cannot be distinguished anymore in scattering amplitudes. Indeed, in elastic electron-electron scatterings, we loose predictive power in determining specifically the scattered electron detected by the experiment. Instead, we have to account for two possible interfering amplitudes, with electron pair exchanges. If the interference of the amplitudes is destructive, i.e. if their permutation symmetry encodes a minus sign, the two particles are fermions that retain spin 21 (electrons in our case). On the other hand, identical particles with integer spin, namely bosons, undergo scattering amplitudes with construca e-mail:
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tive interference. This is certainly suggesting us how intimately the spin statistics is related to the Heisenberg Uncertainty Principle (HUP). Therefore, a natural question would be: what would happen if we modify the very foundations of quantum mechanics, deforming the standard HUP so to account for new physics? May this turn into a modification of the Spin Statistics and the Pauli Exclusion Principle (PEP)? Recently, we have shown how constraints on possible transitions that violate the PEP can provide strong bounds [1–3] on a large class of non-c
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