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A review of charmoniumlike state studies at Belle which use amplitude analyses is presented, including the Z c (4430) + , Z c (4200) + and χ c 0 (3860).

Microwave interferometry provides a sensitive measurement of amplitudes and phases of reflections. Basically, the interferometric system can be used to measure a non-electrical quantity. This paper presents a new method to evaluate data from a microwave interferometer. The method is compared with the previously used procedure. The new method provides more accurate results and also offers the possibility of self-calibration.

A 96.4-100.8 GHz quadrature oscillator utilising transformer-coupled and magnetic tuning techniques has been implemented in 90 nm CMOS technology. Under 1 V supply operation, experimental results show that the phase and amplitude error between I and Q paths are smaller than 1.6° and 0.9 dB with power dissipation from 8.7 to 21 mW. The measured phase noise is - 110.4 dBc/Hz at 10 MHz-offset away from the downconverted 98.6 GHz carrier. This oscillator occupies a chip area of 0.357 mm^sup 2^. [PUBLICATION ABSTRACT]

Based on the polarimetric-basis transformation principle, this paper proposes a method for utilisation of the scattering mechanism vectors for land classification. The experimental results show that both the amplitude and the phase components of the vectors can be used for land classification. By implementing different linear transformation processes of the scattering matrix, a variety of areas can be extracted separately.

A passive current-sensing architecture operating based on electromotive force phenomena is presented. The proposed architecture is capable of sensing a varying current over a wide range of frequencies. Simulation and measurement results of a proof-of-concept prototype implemented in a 0.13 mm CMOS confirm the performance of the presented technique for currents with frequencies up to 8 GHz. In the presented experimental results, the high-frequency performance limit is due to the measurement setup. Furthermore, the method can be used to sense currents over a wide range of amplitudes and the amplitude detection sensitivity of the technique improves as the frequency of the current signal being measured increases. [PUBLICATION ABSTRACT]

Weak decay tree and annihilation-t-channel W-exchange amplitudes for the D} \\to K} _S \\pi registered \\pi approximately process are calculated using quasi two-body QCD factorization approach and unitarity constraints. Final state strong K pi and pi pi interactions in S, P and D waves are described through corresponding form factors including many resonances. Preliminary results compare well with the effective mass distributions of the Belle and BABAR Collaboration analyses.

A bstract The search for a theory of the S-Matrix over the past five decades has revealed surprising geometric structures underlying scattering amplitudes ranging from the string worldsheet to the amplituhedron, but these are all geometries in auxiliary spaces as opposed to the kinematical space where amplitudes actually live. Motivated by recent advances providing a reformulation of the amplituhedron and planar N = 4 SYM amplitudes directly in kinematic space, we propose a novel geometric understanding of amplitudes in more general theories. The key idea is to think of amplitudes not as functions, but rather as differential forms on kinematic space. We explore the resulting picture for a wide range of massless theories in general spacetime dimensions. For the bi-adjoint ϕ 3 scalar theory, we establish a direct connection between its “scattering form” and a classic polytope — the associahedron — known to mathematicians since the 1960’s. We find an associahedron living naturally in kinematic space, and the tree level amplitude is simply the “canonical form” associated with this “positive geometry”. Fundamental physical properties such as locality and unitarity, as well as novel “soft” limits, are fully determined by the combinatorial geometry of this polytope. Furthermore, the moduli space for the open string worldsheet has also long been recognized as an associahedron. We show that the scattering equations act as a diffeomorphism between the interior of this old “worldsheet associahedron” and the new “kinematic associahedron”, providing a geometric interpretation and simple conceptual derivation of the bi-adjoint CHY formula. We also find “scattering forms” on kinematic space for Yang-Mills theory and the Non-linear Sigma Model, which are dual to the fully color-dressed amplitudes despite having no explicit color factors. This is possible due to a remarkable fact—“Color is Kinematics”— whereby kinematic wedge products in the scattering forms satisfy the same Jacobi relations as color factors. Finally, all our scattering forms are well-defined on the projectivized kinematic space, a property which can be seen to provide a geometric origin for color-kinematics duality.

Quantum scattering amplitudes for massive matter have received new attention in connection to classical calculations relevant to gravitational-wave physics. Amplitude methods and insights are now employed for precision computations of observables needed for describing the gravitational dynamics of bound massive objects such as black holes. An important direction is the inclusion of spin effects needed to accurately describe rotating (Kerr) black holes. Higher-spin amplitudes introduced by Arkani-Hamed, Huang and Huang at three points have by now a firm connection to the effective description of Kerr black-hole physics. The corresponding Compton higher-spin amplitudes remain however an elusive open problem. Here we draw from results of the higher-spin literature and show that physical insights can be used to uniquely fix the Compton amplitudes up to spin 5/2, by imposing a constraint on a three-point higher-spin current that is a necessary condition for the existence of an underlying unitary theory. We give the unique effective Lagrangians up to spin 5/2, and show that they reproduce the previously-known amplitudes. For the multi-graviton amplitudes analogous to the Compton amplitude, no further corrections to our Lagrangians are expected, and hence such amplitudes are uniquely predicted. As an essential tool, we introduce a modified version of the massive spinor-helicity formalism which allows us to conveniently obtain higher-spin states, propagators and compact expressions for the amplitudes.

Abstract The infinite tower of positive-helicity soft gravitons in any minimally coupled, tree-level, asymptotically flat four-dimensional (4D) gravity was recently shown to generate a w 1+∞ asymptotic symmetry algebra. It is natural to ask whether this classical algebra acquires quantum corrections at loop level. We explore this in quantum self-dual gravity, whose amplitudes acquire known one-loop exact all-plus helicity quantum corrections. We show using collinear splitting formulae that, remarkably, the w 1+∞ algebra persists in quantum self-dual gravity without corrections.

A bstract The scattering equations provide a powerful framework for the study of scattering amplitudes in a variety of theories. Their derivation from ambitwistor string theory led to proposals for formulae at one loop on a torus for 10 dimensional supergravity, and we recently showed how these can be reduced to the Riemann sphere and checked in simple cases. We also proposed analogous formulae for other theories including maximal super-Yang-Mills theory and supergravity in other dimensions at one loop. We give further details of these results and extend them in two directions. Firstly, we propose new formulae for the one-loop integrands of Yang-Mills theory and gravity in the absence of supersymmetry. These follow from the identification of the states running in the loop as expressed in the ambitwistor-string correlator. Secondly, we give a systematic proof of the non-supersymmetric formulae using the worldsheet factorisation properties of the nodal Riemann sphere underlying the scattering equations at one loop. Our formulae have the same decomposition under the recently introduced Q-cuts as one-loop integrands and hence give the correct amplitudes.