The piNNN--NNN problem. Connectedness, transition amplitudes and quasi-particle approximation

In this paper we review the present status of the piNNN--NNN problem. In particular, we re-consider the chain-labelled approach recently proposed by us, and identify a class of graphs, previously overlooked, which prevents the kernel of the corresponding piNNN--NNN equations from being connected. We propose some pproximate schemes, yielding connected-kernel equations. A generalization of the residue method allows to relate the transition amplitudes for the coupled piNNN--NNN system to the chain-labelled formalism. The quasi-particle approach is extended to the present situation, where emission/absorption of particles is allowed. The open problems for the piNNN--NNN system in the light of the present and of previous approaches are finally discussed

Three-nucleon portrait with pion

We report on recent results obtained by the above collaboration on the collision processes involving three nucleons, where we pay particular attention on the dynamical role of the pion. After discussing the case at intermediate energies, where real pions can be produced and detected, we have considered the case at lower energies, where the pions being exchanged are virtual. The study has revealed the presence of some new pion-exchange mechanisms, which leads to a new three-nucleon force of tensor structure. Recently, the effect of this tensor three-nucleon force to the spin observables for neutron-deuteron scattering at low energy has been analyzed, and will be briefly reviewed

Future Constraints on Angle-Dependent Non-Gaussianity from Large Radio Surveys

We investigate how well future large-scale radio surveys could measure different shapes of primordial non-Gaussianity; in particular we focus on angle-dependent non-Gaussianity arising from primordial anisotropic sources, whose bispectrum has an angle dependence between the three wavevectors that is characterized by Legendre polynomials $\mathcal{P}_L$ and expansion coefficients $c_L$. We provide forecasts for measurements of galaxy power spectrum, finding that Large-Scale Structure (LSS) data could allow measurements of primordial non-Gaussianity competitive or improving upon current constraints set by CMB experiments, for all the shapes considered. We argue that the best constraints will come from the possibility to assign redshift information to radio galaxy surveys, and investigate a few possible scenarios for the EMU and SKA surveys. A realistic (futuristic) modeling could provide constraints of $f_{\rm NL}^{\rm loc} \approx 1 (0.5)$ for the local shape, $f_{\rm NL}$ of $\mathcal{O}(10) (\mathcal{O}(1))$ for the orthogonal, equilateral and folded shapes, and $c_{L=1} \approx 80 (2)$, $c_{L=2} \approx 400 (10)$ for angle-dependent non-Gaussianity. The more futuristic forecasts show the potential of LSS analyses to considerably improve current constraints on non-Gaussianity, and so on models of the primordial Universe. Finally, we find the minimum requirements that would be needed to reach $\sigma(c_{L=1})=10$, which can be considered as a typical (lower) value predicted by some (inflationary) models

Two-loop low-energy effective action in Abelian supersymmetric Chern–Simons matter models

We compute two-loop low-energy effective actions in Abelian Chern–Simons matter models with =2 and =3 supersymmetry up to four-derivative order. Calculations are performed with a slowly-varying gauge superfield background. Though the gauge superfield propagator depends on the gauge fixing parameter, it is shown that the obtained results are independent of this parameter. In the massless case the considered models are superconformal. We demonstrate that the superconformal symmetry strongly restricts the form of two-loop quantum corrections to the effective actions such that the obtained terms have simpler structure than the analogous ones in the effective action of three-dimensional supersymmetric electrodynamics (SQED) with vanishing topological mass

Superconformal structures on the three-sphere

With the motivation to develop superconformal field theory on S 3 we introduce a 2 n -extended supersphere S 3|4 n with n =1 2 . . . as a homogeneous space of the three-dimensional Euclidean superconformal group OSp (2 n |2 2) such that its bosonic body is S 3 . Supertwistor and bi-supertwistor realizations of S 3|4 n are derived. We study in detail the n =1 case, which is unique in the sense that the R -symmetry subgroup SO * (2 n ) of the superconformal group is compact only for n =1. In particular, we show that the OSp (2|2 2) transformations preserve the chiral subspace of S 3|4 . Several supercoset realizations of S 3|4 n are presented. Harmonic/projective extensions of the supersphere by auxiliary bosonic fibre directions are sketched

Energy quantisation and time parameterisation

We show that if space is compact, then trajectories cannot be defined in the framework of the quantum Hamilton–Jacobi (HJ) equation. The starting point is the simple observation that when the energy is quantised it is not possible to make variations with respect to the energy, and the time parameterisation <math><mrow><mi>t</mi><mo>-</mo><msub><mi>t</mi><mn>0</mn></msub><mo>=</mo><msub><mi mathvariant="italic">∂</mi><mi>E</mi></msub><msub><mi mathvariant="script">S</mi><mn>0</mn></msub></mrow></math> , implied by Jacobi’s theorem, which leads to the group velocity, is ill defined. It should be stressed that this follows directly from the quantum HJ equation without any axiomatic assumption concerning the standard formulation of quantum mechanics. This provides a stringent connection between the quantum HJ equation and the Copenhagen interpretation. Together with tunnelling and the energy quantisation theorem for confining potentials, formulated in the framework of quantum HJ equation, it leads to the main features of the axioms of quantum mechanics from a unique geometrical principle. Similar to the case of the classical HJ equation, this fixes its quantum analog by requiring that there exist point transformations, rather than canonical ones, leading to the trivial hamiltonian. This is equivalent to a basic cocycle condition on the states. Such a cocycle condition can be implemented on compact spaces, so that continuous energy spectra are allowed only as a limiting case. Remarkably, a compact space would also imply that the Dirac and von Neumann formulations of quantum mechanics essentially coincide. We suggest that there is a definition of time parameterisation leading to trajectories in the context of the quantum HJ equation having the probabilistic interpretation of the Copenhagen School

Mirror Development for the Cherenkov Telescope Array

The Cherenkov Telescope Array (CTA) is a planned observatory for very-high energy gamma-ray astronomy. It will consist of several tens of telescopes of different sizes, with a total mirror area of up to 10,000 square meters. Most mirrors of current installations are either polished glass mirrors or diamond-turned aluminium mirrors, both labour intensive technologies. For CTA, several new technologies for a fast and cost-efficient production of light-weight and reliable mirror substrates have been developed and industrial pre-production has started for most of them. In addition, new or improved aluminium-based and dielectric surface coatings have been developed to increase the reflectance over the lifetime of the mirrors compared to those of current Cherenkov telescope instruments

Higher spins in hyperspace

We consider the Sp(2 n ) invariant formulation of higher spin fields on flat and curved backgrounds of constant curvature. In this formulation an infinite number of higher spin fields are packed into single scalar and spinor master fields (hyperfields) propagating on extended spaces, to be called hyperspaces, parametrized by tensorial coordinates. We show that the free field equations on flat and AdS-like hyperspaces are related to each other by a generalized conformal transformation of the scalar and spinor master fields. We compute the four-point functions on a flat hyperspace for both scalar and spinor master fields, thus extending the two- and three-point function results of hep-th/0312244. Then using the generalized conformal transformation we derive two-, three- and four-point functions on AdS-like hyperspace from the corresponding correlators on the flat hyperspace

Radiative μ and τ leptonic decays at NLO

We present the differential rates and branching ratios of the radiative decays τ → l ν ¯ ν γ $$\tau \to l\overline{\nu}\nu \gamma$$ , with l = e or μ , and μ → e ν ¯ ν γ $$\mu \to e\overline{\nu}\nu \gamma$$ in the Standard Model at next-to-leading order. Radiative corrections are computed taking into account the full depencence on the mass m l of the final charged leptons, which is necessary for the correct determination of the branching ratios. Only partial agreement is found with previous calculations performed in the m l → 0 limit. Our results agree with the measurements of the branching ratios ℬ μ → e ν ¯ ν γ $$\mathrm{\mathcal{B}}\left(\mu \to e\overline{\nu}\nu \gamma \right)$$ and ℬ τ → μ ν ¯ ν γ $$\mathrm{\mathcal{B}}\left(\tau \to \mu \overline{\nu}\nu \gamma \right)$$ for a minimum photon energy of 10 MeV in the μ and τ rest frames, respectively. B abar ’s recent precise measurement of the branching ratio ℬ τ → e ν ¯ ν γ $$\mathrm{\mathcal{B}}\left(\tau \to e\overline{\nu}\nu \gamma \right)$$ , for the same photon energy threshold, differs from our prediction by 3.5 standard deviations

On single and double soft behaviors in NLSM

In this paper, we study the single and double soft behaviors of tree level off-shell currents and on-shell amplitudes in nonlinear sigma model (NLSM). We first propose and prove the leading soft behavior of the tree level currents with a single soft particle. In the on-shell limit, this single soft emission becomes the Adler’s zero. Then we establish leading and subleading soft behaviors of tree level currents with two adjacent soft particles. With a careful analysis of the on-shell limit, we obtain the double soft behaviors of on-shell amplitudes where the two soft particles are adjacent to each other. By applying Kleiss-Kuijf (KK) relation, we further obtain the leading and subleading behaviors of amplitudes with two nonadjacent soft particles