IR/UV mixing from local similarity maps of scalar non-Hermitian field theories

Chernodub, Maxim N.; Millington, Peter

Abstract

We propose to "gauge"the group of similarity transformations that acts on a space of non-Hermitian scalar theories. We introduce the "similarity gauge field,"which acts as a gauge connection on the space of non-Hermitian theories characterized by (and equivalent to a Hermitian) real-valued mass spectrum. This extension leads to new effects: if the mass matrix is not the same in distant regions of space, but its eigenvalues coincide pairwise in both regions, the particle masses stay constant in the whole spacetime, making the model indistinguishable from a standard, low-energy, and scalar Hermitian one. However, contrary to the Hermitian case, the high-energy scalar particles become unstable at a particular wavelength determined by the strength of the emergent similarity gauge field. This instability corresponds to momentum-dependent exceptional points, whose locations cannot be identified from an analysis of the eigenvalues of the coordinate-dependent squared-mass matrix in isolation, as one might naively have expected. For a doublet of scalar particles with masses of the order of 1 MeV and a similarity gauge rotation of order unity at distances of 1 meter, the corrections to the masses are about 10-7 eV, which makes no experimentally detectable imprint on the low-energy spectrum. However, the instability occurs at 1018 eV, suggestively in the energy range of detectable ultra-high-energy cosmic rays, thereby making this truly non-Hermitian effect and its generalizations of phenomenological interest for high-energy particle physics.

Citation

Chernodub, M. N., & Millington, P. (2022). IR/UV mixing from local similarity maps of scalar non-Hermitian field theories. Physical Review D, 105(7), Article 076020. https://doi.org/10.1103/physrevd.105.076020

• Journal Article Type: Article
• Acceptance Date: Mar 4, 2022
• Online Publication Date: Apr 28, 2022
• Publication Date: Apr 1, 2022
• Deposit Date: May 24, 2022
• Publicly Available Date: May 24, 2022
• Journal: Physical Review D
• Print ISSN: 2470-0010
• Electronic ISSN: 2470-0029
• Publisher: American Physical Society
• Peer Reviewed: Peer Reviewed
• Volume: 105
• Issue: 7
• Article Number: 076020
• DOI: https://doi.org/10.1103/physrevd.105.076020
• Public URL: https://nottingham-repository.worktribe.com/output/8219930
• Publisher URL: https://journals.aps.org/prd/abstract/10.1103/PhysRevD.105.076020