Volume renormalization and the Higgs

¹ Institute of Natural Sciences, Shanghai Key Lab for Particle Physics and Cosmology, and Center for Astrophysics and Astronomy, Department of Physics and Astronomy, Shanghai Jiao Tong University - Shanghai 200240, China
² HEPCOS, Department of Physics, SUNY at Buffalo - Buffalo, NY 14260-1500, USA

Received: 8 September 2013
Accepted: 2 January 2014

Abstract

Traditionally, Quantum Field Theory (QFT) treats particle excitations as point-like objects, which is the source of ubiquitous divergences. We demonstrate that a minimal modification of QFT with finite-volume particles may cure QFT of divergences and illuminate the physics behind the mathematical construct of our theories. The method allows for a non-perturbative treatment of the free field and self-interacting theories (though extensions to all interacting field theories might be possible). In particular, non-perturbatively defined mass is finite. When applied to the standard model Higgs mechanism, the method implies that a finite range of parameters allows for creation of a well-defined Higgs particle, whose Compton wavelength is larger than its physical size, in the broken symmetry phase (as small oscillations around the vacuum). This has profound consequences for Higgs production at the LHC. The parameter range in which the Higgs excitation with the mass of 125 GeV behaves as a proper particle is very restricted.