Approximate Discrete Symmetry Research Articles

Host group degeneracy in gravitational lensing time delay determination of H 0

Abstract Massive elliptical galaxies, that serve as lenses in gravitational lensing time delay measurements of the Hubble parameter H 0, often reside in a host group. We consider degeneracies in the modeling of the group halo. When the group effect on imaging can be summarized by its flexion (the next order term beyond shear in the tidal expansion), the posterior likelihood map can develop disjoint local minima, associated with an approximate discrete symmetry of a dominant flexion term. Monte-Carlo Markov Chain (MCMC) algorithms that are not designed to explore a rich posterior landscape can miss some of the minima, introducing systematic bias. We study mock data and demonstrate that the bias in H 0 can exceed 10%, and pulls the inference value of H 0 above its truth value, for a reason that can be traced to the structure of a mismodeled flexion term. MCMC algorithms that are designed to cope with a rich posterior landscape can uncover the structure. If the group is X-ray bright enough, X-ray data may also help to resolve the degeneracy, by pinpointing the group's center of mass. Finally, we show that some implementations in the literature used an inaccurate kinematical prior, mis-modeling the group velocity dispersion by as much as 20%.

Removing degeneracy and multimodality in gravitational wave source parameters

Quasicircular binary black hole mergers are described by 15 parameters, of which gravitational wave observations can typically constrain only $\sim 10$ independent combinations to varying degree. In this work, we devise coordinates that remove correlations, and disentangle well- and poorly-measured quantities. Additionally, we identify approximate discrete symmetries in the posterior as the primary cause of multimodality, and design a method to tackle this type of multimodality. The resulting posteriors have little structure and can be sampled efficiently and robustly. We provide a Python package for parameter estimation, cogwheel, that implements these methods together with other algorithms for accelerating the inference process. One of the coordinates we introduce is a spin azimuth that is measured remarkably well in several events. We suggest this might be a sensitive indicator of orbital precession, and we anticipate that it will shed light on the occurrence of spin-orbit misalignment in nature.

Transverse positron polarization in the polarized μ+ decay related with the muonium-to-antimuonium transition

The constructions of the new high-intensity muon beamlines are progressing in facilities around the world, and new physics searches related to the muons are expected. The facilities can observe the transverse positron polarization of the polarized ${\ensuremath{\mu}}^{+}$ decay to test the standard model. The transition of muonium into antimuonium (Mu-to-$\overline{\mathrm{Mu}}$ transition), which is one of the interesting possibilities in the models beyond the standard model, can be also tested. An observation of the transition in the near future would have a great impact since it would indicate that there is an approximate discrete symmetry in the lepton sector. If the Mu-to-$\overline{\mathrm{Mu}}$ transition operator is generated, a new muon decay operator can exist, and it may interfere with the standard model muon decay operator to induce the corrections to the transverse positron polarization in the ${\ensuremath{\mu}}^{+}$ decay. We examine the possibility that the Mu-to-$\overline{\mathrm{Mu}}$ transition and the correction to the transverse positron polarization are related, and we show that the two are related in the model of a neutral flavor gauge boson. We also investigate the models to generate the Mu-to-$\overline{\mathrm{Mu}}$ transition, such as an inert $SU(2{)}_{L}$ doublet, an $SU(2{)}_{L}$ triplet for the type-II seesaw model, a dilepton gauge boson, and a left-right model. The nonzero value of the transverse polarization for one of the two directions, ${P}_{{\mathrm{T}}_{2}}$, violates the time-reversal invariance, and the experimental constraint of the electron electric dipole moment can provide a severe constraint on ${P}_{{\mathrm{T}}_{2}}$, depending on the model.

\u03b8 and the \u03b7\u2032 in large N supersymmetric QCD

We study the large N θ dependence and the η′ potential in supersymmetric QCD with small soft SUSY-breaking terms. Known exact results in SUSY QCD are found to reflect a variety of expectations from large N perturbation theory, including the presence of branches and the behavior of theories with matter (both with Nf ≪ N and Nf ∼ N ). However, there are also striking departures from ordinary QCD and the conventional large N description: instanton effects, when under control, are not exponentially suppressed at large N , and branched structure in supersymmetric QCD is always associated with approximate discrete symmetries. We suggest that these differences motivate further study of large N QCD on the lattice.

Large field excursions and approximate discrete symmetries from a clockwork axion

We present a renormalizable theory of scalars in which the low energy effective theory contains a pseudo-Goldstone Boson with a compact field space of 2{\pi} F and an approximate discrete shift symmetry Z_Q with Q>>1, yet the number of fields in the theory goes as log(Q). Such a model can serve as a UV completion to models of relaxions and is a new source of exponential scale separation in field theory. While the model is local in `theory space', it appears to not have a continuum generalization (i.e., it cannot be a deconstructed extra dimension). Our framework shows that super-Planckian field excursions can be mimicked while sticking to renormalizable four-dimensional quantum field theory. We show that a supersymmetric extension is straightforwardly obtained and we illustrate possible UV completions based on a compact extra-dimension, where all global symmetries arise accidentally as a consequence of gauge invariance and 5D locality.

Gravitational waves from collapsing domain walls

We study the production of gravitational waves from cosmic domain walls created during phase transition in the early universe. We investigate the process of formation and evolution of domain walls by running three dimensional lattice simulations. If we introduce an approximate discrete symmetry, walls become metastable and finally disappear. This process might occur by a pressure difference between two vacua if a quantum tunneling is neglected.We calculate the spectrum of gravitational waves produced by collapsing metastable domain walls. Extrapolating the numerical results, we find that the signal of gravitational waves produced by domain walls whose energy scale is around 1010-1012GeV will be observable in the next generation gravitational wave interferometers.

Patterns of symmetry breaking in QCD at high baryon density

We study the structure of QCD at very large baryon density for an arbitrary number of flavors N f . We provide evidence that for any number of flavors larger than N f =2 chiral symmetry remains broken at asymptotically large chemical potential. For N c = N f =3, chiral symmetry breaking follows the standard pattern SU(3) L × SU(3) R → SU(3), but for N f >3 unusual patterns emerge. We study the case N f =3 in more detail and calculate the magnitude of the chiral order parameters 〈 ψ ̄ ψ〉 and 〈( ψ ̄ ψ) 2〉 in perturbative QCD. We show that, asymptotically, 〈 ψ ̄ ψ〉 1/3 is much smaller than 〈( ψ ̄ ψ) 2〉 1/6 . The result can be understood in terms of an approximate discrete symmetry.

Gravitational Waves from Collapsing Vacuum Domains

Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA(DART-HEP-98/03 February 5, 2008)The breaking of an approximate discrete symmetry, thefinal stages of a first order phase transition, or a post-inflationary biased probability distribution for scalar fields arepossible cosmological scenarios characterized by the presenceof unstable domain wall networks. Combining analytical andnumerical techniques, we show that the non-spherical collapseof these domains can be a powerful source of gravitationalwaves. We compute their contribution to the stochastic back-ground of gravitational radiation and explore their observabil-ity by present and future gravitational wave detectors.04.30.Db, 98.80.Cq

Supersymmetric resolution of solar and atmospheric neutrino puzzles

Renormalizable lepton number violating interactions that break R parity can induce a Majorana mass for neutrinos. Based on this, we show that it is possible to obtain a phenomenologically viable neutrino mass matrix that can accommodate atmospheric neutrino data via {nu}{sub {mu}}-{nu}{sub {tau}} mixing and the solar neutrino data via either the large or small angle MSW effect. We argue that such a mass matrix could result from an approximate discrete symmetry of the superpotential that forbids renormalizable baryon number violating couplings. {copyright} {ital 1998} {ital The American Physical Society}

Biased discrete symmetry and domain wall problem

We reconsider the cosmological evolution of domain walls produced by the spontaneous breaking of an approximate discrete symmetry. We show that domain walls may never collapse, even if the standard bound on the vacuum energy asymmetry is satisfied. Instead of disappearing, these defects may form stable “bound states”-double wall systems. Possible stability of such a wall is a dynamical question and consequently restricts the allowed range of parameters. In particular, in the two Higgs doublet standard model with an anomalous Z 2 symmetry, the above restriction suggests the mass of the pseudoscalar Higgs (would be axion) being close to the mass of the scalar one.

Biased discrete symmetry breaking and Fermi balls

The spontaneous breading of an approximate discrete symmetry is considered, with the resulting protodomains of true and false vacuum being separated by domain walls. Given a strong, symmetric Yukawa coupling of the real scalar field to a generic fermion, the domain walls accumulate a gas of fermions, which modify the domain wall dynamics. The splitting of the degeneracy of the ground states results in the false vacuum protodomain structures eventually being fragmented into tiny false vacuum bags with a Fermi gas shell (Fermi balls), that may be cosmologically stable due to the Fermi gas pressure and wall curvature forces, acting on the domain walls. As fermions inhabiting the domain walls do not undergo number density freeze out, stable Fermi balls exist only if a fermion anti-fermion asymmetry occurs. Fermi balls formed with a new Dirac fermion that possesses no standard model gauge charges provide a novel cold dark matter candidate.

Heavy triplet neutrinos as a new dark-matter option

We propose a new scheme where dark matter is made of heavy stable neutral particles N, possibly even lighter than 1 2 m Z , but uncoupled to the Z 0. Such particles should be given an efficient way to annihilate, otherwise their fossil density would overclose the universe. In this scheme, the annihilation results from a delicate interplay between N and its heavier charged electroweak partner E ±. A closure density may be naturally reached if the mass splitting is ∼10 GeV, which suggests that the E ± may be discovered at LEP 200. The species N results from the mixing between a singlet and the neutral member of a triplet, here induced by the vacuum expectation value of a Higgs triplet. The latter is kept naturally small with respect to the electroweak scale, as a result of a new approximate discrete symmetry, the triplet-parity T p. We discuss various implications of this model for astrophysics and particle physics.

Cosmology of biased discrete symmetry breaking

The cosmological consequences of spontaneous breaking of an approximate discrete symmetry are studied. The breaking leads to formation of proto-domains of false and true vacuum separated by domain walls of thickness determined by the mass scale of the model. The cosmological evolution of the walls is extremely sensitive to the magnitude of the biasing; several scenarios are possible, depending on the interplay between the surface tension on the walls and the volume pressure from the biasing. Walls may disappear almost immediately after they form, or may live long enough to dominate the energy density of the Universe and cause power-law inflation. Limits are obtained on the biasing that characterizes each possible scenario.