Weak equivalence principle violation for mixed scalar particles

Massimo Blasone; Petr Jizba; Gaetano Lambiase; Luciano Petruzziello

doi:10.1140/epjc/s10052-023-12291-3

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 1130
https://doi.org/10.1140/epjc/s10052-023-12291-3

Regular Article - Theoretical Physics

Weak equivalence principle violation for mixed scalar particles

Massimo Blasone¹^,2, Petr Jizba³^,4, Gaetano Lambiase¹^,2 and Luciano Petruzziello²^,5^,6^d

¹ Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
² INFN, Sezione di Napoli, Gruppo collegato di Salerno, Salerno, Italy
³ FNSPE, Czech Technical University in Prague, Břehová 7, 115 19, Prague, Czech Republic
⁴ ITP, Freie Universität Berlin, Arnimallee 14, 14195, Berlin, Germany
⁵ Dipartimento di Ingegneria Industriale, Università di Salerno, Via Giovanni Paolo II, 132, 84084, Fisciano, SA, Italy
⁶ Institut für Theoretische Physik, Universität Ulm, Albert-Einstein-Allee 11, 89069, Ulm, Germany

^d lupetruzziello@unisa.it

Received: 14 June 2023
Accepted: 27 November 2023
Published online: 14 December 2023

Abstract

We investigate the non-relativistic limit of the Klein–Gordon equation for mixed scalar particles and show that, in this regime, one unavoidably arrives at redefining the particle’s inertial mass. This happens because, in contrast to the case when mixing is absent, the antiparticle sector contribution cannot be neglected for particles with definite flavor. To clearly demonstrate this feature, we adopt the Feshbach–Villars formalism for Klein–Gordon particles. Furthermore, within the same framework, we also demonstrate that, in the presence of a weak gravitational field, the mass parameter that couples to gravity (gravitational mass) does not match the effective inertial mass. This, in turn, implies a violation of the weak equivalence principle. Finally, we prove that the Bargmann’s superselection rule, which prohibits oscillating particles on the basis of the Galilean transformation, is incompatible with the non-relativistic limit of the Lorentz transformation and hence does not collide with the results obtained.

© The Author(s) 2023

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