The mass scales of the Higgs field

Abstract

In the first version of the theory, with a classical scalar potential, the sector inducing SSB was distinct from the Higgs field interactions induced through its gauge and Yukawa couplings. We have adopted a similar perspective but, following most recent lattice simulations, described SSB in $\lambda {\Phi }^4$ theory as a weak first-order phase transition. In this case, the resulting effective potential has two mass scales: i) a lower mass $m_h$, defined by its quadratic shape at the minima, ~and~ ii) a larger mass $M_h$, defined by the zero-point energy. These refer to different momentum scales in the propagator and are related by $M_h^2\sim m_h^2\ln ({\Lambda }_s/M_h)$, where ${\Lambda }_s$ is the ultraviolet cutoff of the scalar sector. We have checked this two-scale structure with lattice simulations of the propagator and of the susceptibility in the 4D Ising limit of the theory. These indicate that, in a cutoff theory where both $m_h$ and $M_h$ are finite, by increasing the energy, there could be a transition from a relatively low value, e.g. $m_h$=125 GeV, to a much larger $M_h$. The same lattice data give a final estimate $M_h=720\pm 30$ GeV which induces to re-consider the experimental situation at LHC. In particular an independent analysis of the ATLAS + CMS data indicating an excess in the 4-lepton channel as if there were a new scalar resonance around 700 GeV. Finally, the presence of two vastly different mass scales, requiring an interpolating form for the Higgs field propagator also in loop corrections, could reduce the discrepancy with those precise measurements which still favor large values of the Higgs particle mass.

26 pages, 7 figures, 3 tables; accepted for publication in the International Journal of Modern Physics A (IJMPA)

References in corpus (7)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Search for new phenomena in high-mass diphoton final states using 37 fb${}^{-1}$ of proton-proton collisions collected at $\sqrt{s}=13$ TeV with the ATLAS detector
• Search for high-mass diphoton resonances in proton-proton collisions at 13 TeV and combination with 8 TeV search
• Critical behaviour of the Ising model on the 4-dimensional lattice
• Non-vanishing boundary effects and quasi-first order phase transitions in high dimensional Ising models
• An alternative heavy Higgs mass limit

Cited by in corpus (6)

• Phase transition of four-dimensional lattice ${\varphi }^4$ theory with tensor renormalization group
• Experimental signals for a second resonance of the Higgs field
• Revising the universality class of the four-dimensional Ising model
• Higgs boson origin from a gauge symmetric theory of massive composite particles and massless $W^{\pm }$ and $Z^0$ bosons at the TeV scale
• The 690 GeV scalar resonance
• Second resonance of the Higgs field: motivations, experimental signals, unitarity constraints