[Paper Review] Higgs-field Portal into Hidden Sectors

Brian Patt, Frank Wilczek|ArXiv.org|May 16, 2006

Particle physics theoretical and experimental studiesPhysics and Astronomy287 citations

TL;DR

This paper proposes a renormalizable Higgs portal mechanism that allows Standard Model (SM) singlet fields—forming a 'phantom' hidden sector—to couple to the SM exclusively through the Higgs mass term, which is uniquely superrenormalizable. This coupling enables new decay channels for the Higgs boson, potentially spreading its resonance into multiple lighter states or rendering it invisible, while preserving naturalness and offering a dynamical explanation for the weak scale without fine-tuning.

ABSTRACT

The Higgs field mass term, being superrenomalizable, has a unique status within the standard model. Through the opening it affords, $SU(3) imes SU(2) imes U(1)$ singlet fields can have renormalizable couplings to standard model fields. We present examples that are neither grotesque nor unnatural. A possible consequence is to spread the Higgs particle resonance into several weaker ones, or to afford it additional, effectively invisible decay channels.

Motivation & Objective

• To explore the unique role of the Higgs mass term as a superrenormalizable portal for $SU(3)\times SU(2)\times U(1)$ singlet fields into hidden sectors.
• To demonstrate that such couplings can lead to natural, non-gruesome models of hidden sectors with weak-scale dynamics.
• To investigate how the Higgs portal can lead to invisible or multi-channel Higgs decays, altering Higgs phenomenology.
• To analyze cosmological constraints and dark matter implications of such hidden sectors.
• To extend the seesaw mechanism to hidden sectors via dimension-5 operators, enabling sterile neutrino-like states.

Proposed method

• Introduce a Higgs portal Lagrangian term $\mathcal{L}_{\text{link}} = \eta \phi_s^\dagger \phi_s \phi_p^\dagger \phi_p$, where $\phi_s$ is the SM Higgs and $\phi_p$ is a hidden sector scalar singlet.
• Analyze the scalar potential $V(\phi_s, \phi_p) = \mu_s^2 |\phi_s|^2 + \lambda_s |\phi_s|^4 + \mu_p^2 |\phi_p|^2 + \lambda_p |\phi_p|^4 - \eta |\phi_s|^2 |\phi_p|^2$ to study symmetry breaking and mixing.
• Classify couplings into three categories: (1) hidden sector Higgs not VEV-ed, (2) hidden sector Higgs VEV-ed with mixing, (3) direct trilinear couplings without gauge symmetry.
• Study the role of Nambu-Goldstone bosons from spontaneous chiral symmetry breaking in the hidden sector, which couple directly to the SM Higgs.
• Assess cosmological constraints, particularly from Big Bang Nucleosynthesis (BBN), to ensure hidden sectors do not overclose the universe.
• Consider extensions to supersymmetric models, focusing on neutral Higgs mixing and minimal perturbation of gauge coupling unification.

Experimental results

Research questions

• RQ1 Can the Higgs mass term serve as a natural, renormalizable portal to hidden sectors with $SU(3)\times SU(2)\times U(1)$ singlet fields?
• RQ2 What are the phenomenological consequences of Higgs decays into hidden sector states, particularly in terms of resonance width and signal dilution?
• RQ3 How do cosmological constraints—especially from BBN—limit the existence and temperature of hidden sectors coupled via the Higgs portal?
• RQ4 Can the seesaw mechanism be generalized to hidden sectors via dimension-5 operators, leading to sterile neutrino-like states?
• RQ5 What is the role of Nambu-Goldstone bosons from hidden sector chiral symmetry breaking in mediating Higgs decays?

Key findings

• The Higgs mass term $-\mu^2 \phi^\dagger \phi$ is uniquely superrenormalizable, enabling renormalizable couplings of SM singlet fields to the SM without introducing explicit mass scales.
• In models with a confining hidden sector, spontaneous chiral symmetry breaking generates an effective Higgs mass term $-\eta \kappa^2$, potentially triggering electroweak symmetry breaking naturally.
• Higgs boson decay rates can be significantly altered: the total width may be shared among multiple hidden states, or decay into invisible modes, diluting conventional signals.
• When the hidden sector Higgs acquires a vacuum expectation value, mixing between SM and hidden Higgs states occurs, leading to a mixed physical spectrum.
• Nambu-Goldstone bosons from hidden chiral symmetry breaking can couple directly to the SM Higgs and dominate its decay width if they are light.
• Cosmological constraints allow hidden sectors to be cooler than the visible sector at BBN, provided they decouple early and do not overproduce entropy or alter nucleosynthesis.