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Spontaneous breakdown of the continuous symmetry is studied in the framework of discretized light-front quantization. We consider linear sigma model in 3+1 dimensions and show that the careful treatment of zero modes together with the regularization of the theory by introducing NG boson mass leads to the correct description of Nambu-Goldstone phase on the light-front.
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This talk focuses on the role of light scalars in cosmology, both Nambu Goldstone bosons and pseudo moduli. The former include QCD axions, which might constitute the dark matter, and more general axions, which, under certain conditions, might play the role of inflatons, implementing {it natural inflation}. The latter are the actors in (generalized) hybrid inflation. They rather naturally yield large field inflation, even mimicking chaotic inflation for suitable ranges of parameters.
If the Higgs boson is a pseudo Nambu-Goldstone boson (PNGB), the $hZgamma$ contact interaction induced by the $mathcal{O}(p^4)$ invariants of the non-linear sigma model is free from its nonlinearity effects. The process $hrightarrow Zgamma$ can be used to eliminate the universal effects of heavy particles, which can fake the nonlinearity effects of the PNGB Higgs boson in the process $hrightarrow V^*V$ ($V=W^pm$, $Z$). We demonstrate that the ratio of the signal strength of $hrightarrow Zgamma$ and $hrightarrow V^*V$ is good to distinguish the signature of the PNGB Higgs boson from Higgs coupling deviations.
The notion that the scalar listed as $f_0 (500)$ in the particle data booklet is a pseudo-Nambu-Goldstone (NG) boson of spontaneously broken scale symmetry, explicitly broken by a small departure from an infrared fixed point, is explored in nuclear dynamics. That notion which puts the scalar -- that we shall identify as a dilaton -- on the same footing as the pseudo-scalar pseudo-NG bosons, i.e., octet $pi$, while providing a simple explanation for the $Delta I=1/2$ rule for kaon decay, generalizes the standard chiral perturbation theory (S$chi$PT) to scale chiral perturbation theory, denoted $chi$PT$_sigma$, with {it one infrared mass scale for both symmetries}, with the $sigma$ figuring as a chiral singlet NG mode in non-strange sector. Applied to nuclear dynamics, it is seen to provide possible answers to various hitherto unclarified nuclear phenomena such as the success of one-boson-exchange potentials (OBEP), the large cancellation of strongly attractive scalar potential by strongly repulsive vector potential in relativistic mean field theory of nuclear systems and in-medium QCD sum rules, the interplay of the dilaton and the vector meson $omega$ in dense skyrmion matter, the BPS skyrmion structure of nuclei accounting for small binding energies of medium-heavy nuclei, and the suppression of hyperon degrees of freedom in compact-star matter.
We present a lattice calculation of $L_{10}$, one of the low energy constants in Chiral Perturbation Theory, and the charged-neutral pion squared mass splitting, using dynamical overlap fermion. Exact chiral symmetry of the overlap fermion allows us to reliably extract these quantities from the difference of the vacuum polarization functions for vector and axial-vector currents. In the context of the technicolor models, these two quantities are read as the $S$-parameter and the pseudo-Nambu-Goldstone boson mass respectively, and play an important role in discriminating the models from others. This calculation can serve as a feasibility study of the lattice techniques for more general technicolor gauge theories.
The appearance of a light composite $0^+$ scalar resonance in nearly conformal gauge-fermion theories motivates further study of the low energy structure of these theories. To this end, we present a nonperturbative lattice calculation of s-wave scattering of Goldstone bosons in the maximal-isospin channel in SU(3) gauge theory with $N_f=8$ light, degenerate flavors. The scattering phase shift is measured both for different values of the underlying fermion mass and for different values of the scattering momentum. We examine the effect of a light flavor-singlet scalar (reported in earlier studies) on Goldstone boson scattering, employing a dilaton effective field theory (EFT) at the tree level. The EFT gives a good description of the scattering data, insofar as the magnitude of deviations between EFT and lattice data are no larger than the expected size of next-to-leading order corrections in the EFT.
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