Toward Three-Loop Feynman Massive Diagram Calculations

There are many methods of searching for traces of the so-called new physics in particle physics. One of them, and the main focus of this paper, is athe study of the Z-boson decay in e+e− collisions. An improvement in the precision of calculations of the Standard Model (SM) electroweak pseudo-observables, such as scattering asymmetries, effective weak mixing angles, and decay widths, related to the Z-boson will meet severe experimental requirements at the planned e+e− colliders and will increase the chance to detect non-standard effects in experimental analysis. To reach this goal, one has to calculate the next order of perturbative SM theory, namely three-loop Feynman integrals. We discuss the complexity of the problem, as well as the methods crucial for completing three-loop calculations. We show several numerical solutions for some three-loop Feynman integrals using sector decomposition, Mellin–Barnes (MB), and differential equation methods.

Topological weak mixing and diffusion at all times for a class of Hamiltonian systems

We present examples of nearly integrable analytic Hamiltonian systems with several strong diffusion properties: topological weak mixing and diffusion at all times. These examples are obtained by AbC constructions with several frequencies.

The physics potential of a reactor neutrino experiment with Skipper CCDs: measuring the weak mixing angle

We analyze in detail the physics potential of an experiment like the one recently proposed by the vIOLETA collaboration: a kilogram-scale Skipper CCD detector deployed 12 meters away from a commercial nuclear reactor core. This experiment would be able to detect coherent elastic neutrino nucleus scattering from reactor neutrinos, capitalizing on the exceptionally low ionization energy threshold of Skipper CCDs. To estimate the physics reach, we elect the measurement of the weak mixing angle as a case study. We choose a realistic benchmark experimental setup and perform variations on this benchmark to understand the role of quenching factor and its systematic uncertainties, background rate and spectral shape, total exposure, and reactor antineutrino flux uncertainty. We take full advantage of the reactor flux measurement of the Daya Bay collaboration to perform a data driven analysis which is, up to a certain extent, independent of the theoretical un- certainties on the reactor antineutrino flux. We show that, under reasonable assumptions, this experimental setup may provide a competitive measurement of the weak mixing angle at few MeV scale with neutrino-nucleus scattering.

Ergodic cocycles of IDPFT systems and non-singular Gaussian actions

It is proved that each Gaussian cocycle over a mildly mixing Gaussian transformation is either a Gaussian coboundary or sharply weak mixing. The class of non-singular infinite direct products T of transformations $T_n$ , $n\in \mathbb N$ , of finite type is studied. It is shown that if $T_n$ is mildly mixing, $n\in \mathbb N$ , the sequence of Radon–Nikodym derivatives of $T_n$ is asymptotically translation quasi-invariant and T is conservative then the Maharam extension of T is sharply weak mixing. This technique provides a new approach to the non-singular Gaussian transformations studied recently by Arano, Isono and Marrakchi.

Rigidity, weak mixing, and recurrence in abelian groups

<p style='text-indent:20px;'>The focus of this paper is the phenomenon of rigidity for measure-preserving actions of countable discrete abelian groups and its interactions with weak mixing and recurrence. We prove that results about <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{Z} $\end{document}</tex-math></inline-formula>-actions extend to this setting:</p><p style='text-indent:20px;'>1. If <inline-formula><tex-math id="M2">\begin{document}$ (a_n) $\end{document}</tex-math></inline-formula> is a rigidity sequence for an ergodic measure-preserving system, then it is a rigidity sequence for some weakly mixing system.</p><p style='text-indent:20px;'>2. There exists a sequence <inline-formula><tex-math id="M3">\begin{document}$ (r_n) $\end{document}</tex-math></inline-formula> such that every translate is both a rigidity sequence and a set of recurrence.</p><p style='text-indent:20px;'>The first of these results was shown for <inline-formula><tex-math id="M4">\begin{document}$ \mathbb{Z} $\end{document}</tex-math></inline-formula>-actions by Adams [<xref ref-type="bibr" rid="b1">1</xref>], Fayad and Thouvenot [<xref ref-type="bibr" rid="b20">20</xref>], and Badea and Grivaux [<xref ref-type="bibr" rid="b2">2</xref>]. The latter was established in <inline-formula><tex-math id="M5">\begin{document}$ \mathbb{Z} $\end{document}</tex-math></inline-formula> by Griesmer [<xref ref-type="bibr" rid="b23">23</xref>]. While techniques for handling <inline-formula><tex-math id="M6">\begin{document}$ \mathbb{Z} $\end{document}</tex-math></inline-formula>-actions play a key role in our proofs, additional ideas must be introduced for dealing with groups with multiple generators.</p><p style='text-indent:20px;'>As an application of our results, we give several new constructions of rigidity sequences in torsion groups. Some of these are parallel to examples of rigidity sequences in <inline-formula><tex-math id="M7">\begin{document}$ \mathbb{Z} $\end{document}</tex-math></inline-formula>, while others exhibit new phenomena.</p>

Measurement of the weak mixing phase ϕs through time-dependent CP-violation in Bs0 → J/ψϕ decays in the ATLAS detector

A measurement of [Formula: see text] decay parameters using data collected by the ATLAS detector in [Formula: see text] collisions at 13 TeV in 2015–2017 is performed. Integrated luminosity of this sample is 80.5 fb[Formula: see text]. The measurement of physical parameters are statistically combined with results obtained from Run 1 data at 7 and 8 TeV. The measured value of CP-violating phase [Formula: see text] is obtained, which has significantly better precision in comparison with Run 1 result. Precision of other physical parameters is also improved, including the decay width difference [Formula: see text]. Further improvement is expected from the use of full Run 2 statistics, as well as from modifications in the analysis.