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Register a new userPhotonic Nambu-Goldstone bosons
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Added by
Miguel-Angel Garcia-March
Publication date
2017
fields
Physics
and research's language is
English
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We study numerically the spatial dynamics of light in periodic square lattices in the presence of a Kerr term, emphasizing the peculiarities stemming from the nonlinearity. We find that, under rather general circumstances, the phase pattern of the stable ground state depends on the character of the nonlinearity: the phase is spatially uniform if it is defocusing whereas in the focusing case, it presents a chess board pattern, with a difference of $pi$ between neighboring sites. We show that the lowest lying perturbative excitations can be described as perturbations of the phase and that finite-sized structures can act as tunable metawaveguides for them. The tuning is made by varying the intensity of the light that, because of the nonlinearity, affects the dynamics of the phase fluctuations. We interpret the results using methods of condensed matter physics, based on an effective description of the optical system. This interpretation sheds new light on the phenomena, facilitating the understanding of individual systems and leading to a framework for relating different problems with the same symmetry. In this context, we show that the perturbative excitations of the phase are Nambu-Goldstone bosons of a spontaneously broken $U(1)$ symmetry.
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Phenomenological implications of a minimal extension to the Standard Model are considered, in which a Nambu-Goldstone boson emerges from the spontaneous breaking of a global U(1) symmetry. This is felt only by a scalar field which is a singlet under all Standard Model symmetries, and possibly by neutrinos. Mixing between the Standard Model Higgs boson field and the new singlet field may lead to predominantly invisible Higgs boson decays. The natural region in the Higgs boson mass spectrum is determined, where this minimally extended Standard Model is a valid theory up to a high scale related with the smallness of neutrino masses. Surprisingly, this region may coincide with low visibility of all Higgs bosons at the LHC. Monte-Carlo simulation studies of this nightmare situation are performed and strategies to search for such Higgs boson to invisible (Nambu-Goldstone boson) decays are discussed. It is possible to improve the signal-to-background ratio by looking at the distribution of either the total transverse momentum of the leptons and the missing transverse momentum, or by looking at the distribution of the azimuthal angle between the missing transverse momentum and the momentum of the lepton pair for the Z- and Higgs-boson associated production. We also study variations of the model with non-Abelian symmetries and present approximate formulae for Higgs boson decay rates. Searching for Higgs bosons in such a scenario at the LHC would most likely be solely based on Higgs to invisible decays.
We develop the effective field theory of diffusive Nambu-Goldstone (NG) modes associated with spontaneous internal symmetry breaking taking place in nonequilibrium open systems. The effective Lagrangian describing semi-classical dynamics of the NG modes is derived and matching conditions for low-energy coefficients are also investigated. Due to new terms peculiar to open systems, the associated NG modes show diffusive gapless behaviors in contrast to the propagating NG mode in closed systems. We demonstrate two typical situations relevant to the condensed matter physics and high-energy physics, where diffusive type-A or type-B NG modes appear.
We discuss symmetry breaking quantum phase transitions on the oft studied Bethe lattice in the context of the ferromagnetic scalar spherical model or, equivalently, the infinite $N_f$ limit of ferromagnetic models with $O(N_f)$ symmetry. We show that the approach to quantum criticality is characterized by the vanishing of a gap to just the global modes so that {it all} local correlation functions continue to exhibit massive behavior. This behavior persists into the broken symmetry phase even as the order parameter develops an expectation value and thus there are no massless Goldstone bosons in the spectrum. We relate this feature to a spectral property of the graph Laplacian shared by the set of `expander graphs, and argue that our results apply to symmetry breaking transitions on such graphs quite generally.
Motivated by recent constructions of TeV-scale strongly-coupled dynamics, either associated with the Higgs sector itself as in pseudo-Nambu-Goldstone boson (pNGB) Higgs models or in theories of asymmetric dark matter, we show that stable solitonic Q- balls can be formed from light pion-like pNGB fields carrying a conserved global quantum number in the presence of the Higgs field. We focus on the case of thick-wall Q-balls, where solutions satisfying all constraints are shown to exist over a range of parameter values. In the limit that our approximations hold, the Q-balls are weakly bound and parametrically large, and the form of the interactions of the light physical Higgs with the Q-ball is determined by the breaking of scale symmetry.
We consider chiral perturbation theory in a finite volume and in a mixed regime of quark masses. We take N_l light quarks near the chiral limit, in the so-called epsilon-regime, while the remaining N_h quarks are heavier and in the standard p-regime. We compute in this new mixed regime the finite-size scaling of the light meson correlators in the scalar, pseudoscalar, vector and axial vector channels.Using the replica method, we easily extend our results to the partially quenched theory. With the help of our results, lattice QCD simulations with 2+1 flavors can safely investigate pion physics with very light up and down quark masses even in the region where the pions correlation length overcomes the size of the space-time lattice.
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