[Paper Review] Soft mass generation

Jiří Hošek|arXiv (Cornell University)|Sep 3, 2009

Particle physics theoretical and experimental studies2 references3 citations

TL;DR

This paper proposes a novel mechanism for soft mass generation in the Standard Model by replacing the Higgs sector with a strong, non-abelian $SU(3)_F$ horizontal flavor gauge dynamics. The model generates masses for fermions, $W$ and $Z$ bosons, and the eight flavor gluons via spontaneous symmetry breaking and non-perturbative solutions to Schwinger-Dyson equations, yielding a single-parameter framework that explains the hierarchy of fermion masses and electroweak symmetry breaking without a fundamental Higgs boson.

ABSTRACT

We replace the Higgs sector of the Standard electroweak gauge model of three fermion families by a horizontal non-vector-like gauge SU(3) quantum flavor dynamics with one parameter. With plausible physical assumptions we suggest that the new dynamics generates spontaneously the masses of its eight flavor gluons, of leptons and quarks, and of the intermediate W and Z bosons. Absence of axial anomalies requires neutrino right-handed electroweak singlets and the dynamics then suggests the existence of massive Majorana neutrinos.

Motivation & Objective

• To replace the Standard Model's Higgs sector with a minimal, strongly-coupled $SU(3)_F$ flavor gauge dynamics to explain mass generation without introducing a fundamental Higgs boson.
• To demonstrate that fermion and gauge boson masses arise dynamically through spontaneous breaking of global $SU(3)_F$ symmetry via non-perturbative solutions to Schwinger-Dyson equations.
• To show that the $W$ and $Z$ boson masses emerge as a consequence of dynamically generated fermion self-energies, avoiding the need for a separate Higgs sector.
• To derive a mass formula for fermions that reproduces the observed hierarchy of masses using a single coupling constant and a heavy flavor gluon scale.
• To ensure anomaly freedom by introducing right-handed sterile neutrinos, linking the model to Majorana neutrino masses and potential astrophysical signatures.

Proposed method

• Introduce a strong, non-vector-like $SU(3)_F$ gauge theory with one coupling constant $h$, where the eight gauge bosons (flavor gluons) interact with all chiral fermions.
• Use nonlinear Schwinger-Dyson equations for fermion self-energies $\Sigma(q^2)$ to find ultraviolet-finite, symmetry-breaking solutions that generate fermion masses.
• Model the flavor gluon polarization tensor $\Pi^{\mu\nu}_{ab}(q)$ to show the emergence of massless poles corresponding to composite Nambu-Goldstone bosons from spontaneous $SU(3)_F$ breaking.
• Implement the Schwinger mechanism for electroweak symmetry breaking by showing that dynamically generated fermion self-energies trigger spontaneous breaking of $SU(2)_L \times U(1)_Y$.
• Derive mass sum rules for $W$ and $Z$ bosons in terms of fermion self-energies $\Sigma_U$, $\Sigma_D$, using Ward identities from the broken symmetry.
• Adopt a low-momentum effective ansatz for the sliding coupling, leading to an exponential mass formula $m = M \exp[-8\pi^2/h^{*2}]$ with $M \sim 10^6$ GeV.

Experimental results

Research questions

• RQ1 Can the full fermion mass spectrum of the Standard Model be generated dynamically through a single coupling constant in a strongly-coupled flavor gauge theory?
• RQ2 How do non-perturbative solutions to the Schwinger-Dyson equations for fermion self-energies lead to spontaneous mass generation without a fundamental Higgs?
• RQ3 What is the role of the flavor gluon self-energy and its polarization tensor in realizing the Schwinger mechanism for $W$ and $Z$ boson masses?
• RQ4 How does anomaly freedom in the $SU(3)_F$ model constrain the neutrino sector and lead to massive Majorana neutrinos?
• RQ5 Can the observed hierarchy of fermion masses, including the top quark and light neutrinos, be reproduced by a single effective coupling in a low-momentum approximation?

Key findings

• The model generates fermion masses via non-perturbative solutions to the Schwinger-Dyson equations, with a mass formula $m = M \exp[-8\pi^2/h^{*2}]$ where $M \sim 10^6$ GeV.
• A neutrino mass of $m_\nu \sim 10^{-9}$ GeV is obtained with $h_\nu^2/4\pi = 2\pi/(15\ln 10)$, and a top quark mass of $m_t \sim 10^2$ GeV with $h_t^2/4\pi = 2\pi/(4\ln 10)$.
• The $W$ and $Z$ boson masses are dynamically generated through sum rules involving fermion self-energies, with $m_W^2$ and $m_Z^2$ proportional to $\Sigma_U^2$ and $\Sigma_D^2$ respectively.
• The model predicts no generic Fermi scale; instead, $m_W$ and $m_Z$ masses are consequences of the large top quark mass via the sum rules.
• Anomaly freedom requires the introduction of three right-handed sterile neutrinos, suggesting a Majorana nature for neutrinos and potential experimental signatures in neutrino oscillations and astrophysics.
• The unitarization of longitudinal vector boson scattering is expected to proceed via massive composite cousins of the would-be Nambu-Goldstone bosons, though the full spectrum remains unknown.