Effective field theory of Bose-Einstein condensation of $\alpha$ clusters and Nambu-Goldstone-Higgs states in $^{12}$C

TL;DR

This paper develops an effective field theory for alpha cluster condensation in carbon-12, explaining the nature of Hoyle and cluster states through spontaneous symmetry breaking and predicting Nambu-Goldstone-Higgs states that match experimental spectra.

Contribution

It introduces a novel effective field theory framework for alpha clustering in $^{12}$C, incorporating Nambu-Goldstone-Higgs modes to explain observed energy states.

Findings

Reproduces experimental spectrum of alpha cluster states

Demonstrates existence of Nambu-Goldstone-Higgs states in $^{12}$C

Calculates gamma decay transition probabilities

Abstract

An effective field theory of $\alpha$ cluster condensation is formulated as a spontaneously broken symmetry in quantum field theory to understand the raison d'etre and nature of the Hoyle and $\alpha$ cluster states in $^{12}$C. The Nambu--Goldstone and Higgs mode operators in infinite systems are replaced with a pair of canonical operators whose Hamiltonian gives rise to discrete energy states in addition to the Bogoliubov--de Gennes excited states. The calculations reproduce well the experimental spectrum of the $\alpha$ cluster states. The existence of the Nambu--Goldstone--Higgs states is demonstrated and crucial. The $\gamma$ decay transitions are also obtained.