December 23rd, 2020

лошадь, диаграмма, Фейнман

Обзор перенормировок и прецизионные тесты Стандартной Модели

TASI 2020 Lectures on Precision Tests of the Standard Model:
Ayres Freitas
This write-up of lectures given at TASI 2020 provides an introduction into precision tests of the electroweak Standard Model. The lecture notes begin with a hands-on review of the (on-shell) renormalization procedure, and subsequently highlight a few subtleties that occur in the renormalization of a theory with electroweak symmetry breaking and massive gauge bosons. After that a set of typical electroweak precision observables is introduced, as well as a range of input parameter measurements that are needed for making predictions within the Standard Model. Finally, it is discussed how comparisons of the electroweak precision observables between experiment and theory can be used to stress-test the Standard Model and probe new physics.
Comments: 41 pages
лошадь, диаграмма, Фейнман

Четырехфотонная амплитуда в КЭД с продолжением

The QED four -- photon amplitudes off-shell: part 1:
Naser Ahmadiniaz, Cristhiam Lopez-Arcos, Misha A. Lopez-Lopez, Christian Schubert
The QED four-photon amplitude has been well-studied by many authors, and on-shell is treated in many textbooks. However, a calculation with all four photons off-shell is presently still lacking, despite of the fact that this amplitude appears off-shell as a subprocess in many different contexts, in vacuum as well as with some photons connecting to external fields. The present paper is the first in a series of four where we use the worldline formalism to obtain this amplitude explicitly in terms of hypergeometric functions, and derivatives thereof, for both scalar and spinor QED. The formalism allows us to unify the scalar and spinor loop calculations, to avoid the usual breaking up of the amplitude into three inequivalent Feynman diagrams, and to achieve manifest transversality as well as UV finiteness at the integrand level by an optimized version of the integration-by-parts procedure originally introduced by Bern and Kosower for gluon amplitudes. The full permutation symmetry is maintained throughout, and the amplitudes get projected naturally into the basis of five tensors introduced by Costantini et al. in 1971. Since in many applications of the "four-photon box" some of the photons can be taken in the low-energy limit, and the formalism makes it easy to integrate out any such leg, apart from the case of general kinematics (part 4) we also treat the special cases of one (part 3) or two (part 2) photons taken at low energy. In this first part of the series, we summarize the application of the worldline formalism to the N-photon amplitudes and its relation to Feynman diagrams, derive the optimized tensor-decomposed integrands of the four-photon amplitudes in scalar and spinor QED, and outline the computational strategy to be followed in parts 2 to 4.
Comments: 38 pages, 14 figures
лошадь, диаграмма, Фейнман

Моделирование траекторий релятивистских частиц и динамики спина

Обстоятельная работа с теорией и алгоритмом.

Explicit volume-preserving numerical schemes for relativistic trajectories and spin dynamics:
R. Cabrera, A. G. Campos, D. I. Bondar, S. MacLean, F. Fillion-Gourdeau
A class of explicit numerical schemes is developed to solve for the relativistic dynamics and spin of particles in electromagnetic fields, using the Lorentz-BMT equation formulated in the Clifford algebra representation of Baylis. It is demonstrated that these numerical methods, reminiscent of the leapfrog and Verlet methods, share a number of important properties: they are energy-conserving, volume-conserving and second order convergent. These properties are analysed empirically by benchmarking against known analytical solutions in constant uniform electrodynamic fields. It is demonstrated that the numerical error in a constant magnetic field remains bounded for long time simulations in contrast to the Boris pusher, whose angular error increases linearly with time. Finally, the intricate spin dynamics of a particle is investigated in a plane wave field configuration.
Comments: 15 pages, 9 figures

И сегодня же - очередная статья Барышевского о динамике спина:

Pseudoscalar corrections to spin motion equation, search for electric dipole moment and muon magnetic (g-2) factor:
V. G. Baryshevsky, P. I. Porshnev
The spin dynamics in constant electromagnetic fields is described by the Bargmann-Michel-Telegdi equation which can be upgraded with anomalous magnetic and electric dipole moments. The upgraded equation remains self-consistent, Lorentz-covariant and gauge-invariant. It and its different forms have been confirmed in numerous experiments to high degree of accuracy. We have recently derived the spin motion equation within the Wentzel-Kramers-Brillouin weak-field approximation which adds a pseudoscalar correction to the BMT equation. The upgraded equation is again self-consistent, Lorentz-covariant, gauge-invariant, and free of unwanted artifacts. The pseudoscalar correction is expected to be small, and might become important in hypersensitive experiments, like the measurements of electric dipole moments which are themselves related to pseudoscalar quantities. It also becomes possible to explain why EDMs are so difficult to measure, since this correction term might lead to the effective screening of electric dipole moments. Within the same model, it is possible to explain the discrepancy between experimental and theoretical values of muon magnetic anomaly under assumption that the pseudoscalar correction is the dominant source of this discrepancy.
Comments: 27 pages