Angular analysis of $$ {B}^0\to {D}^{\ast -}{D}_s^{\ast +} $$ with $$ {D}_s^{\ast +}\to {D}_s^{+}\gamma $$ decays

The first full angular analysis of the $$ {B}^0\to {D}^{\ast -}{D}_s^{\ast +} $$ B 0 → D ∗ − D s ∗ + decay is performed using 6 fb−1 of pp collision data collected with the LHCb experiment at a centre-of-mass energy of 13 TeV. The $$ {D}_s^{\ast +}\to {D}_s^{+}\gamma $$ D s ∗ + → D s + γ and D*− → $$ {\overline{D}}^0{\pi}^{-} $$ D ¯ 0 π − vector meson decays are used with the subsequent $$ {D}_s^{+} $$ D s + → K+K−π+ and $$ {\overline{D}}^0 $$ D ¯ 0 → K+π− decays. All helicity amplitudes and phases are measured, and the longitudinal polarisation fraction is determined to be fL = 0.578 ± 0.010 ± 0.011 with world-best precision, where the first uncertainty is statistical and the second is systematic. The pattern of helicity amplitude magnitudes is found to align with expectations from quark-helicity conservation in B decays. The ratio of branching fractions [ℬ($$ {B}^0\to {D}^{\ast -}{D}_s^{\ast +} $$ B 0 → D ∗ − D s ∗ + ) × ℬ($$ {D}_s^{\ast +}\to {D}_s^{+}\gamma $$ D s ∗ + → D s + γ )]/ℬ(B0 → D*−$$ {D}_s^{+} $$ D s + ) is measured to be 2.045 ± 0.022 ± 0.071 with world-best precision. In addition, the first observation of the Cabibbo-suppressed Bs → D*−$$ {D}_s^{+} $$ D s + decay is made with a significance of seven standard deviations. The branching fraction ratio ℬ(Bs → D*−$$ {D}_s^{+} $$ D s + )/ℬ(B0 → D*−$$ {D}_s^{+} $$ D s + ) is measured to be 0.049 ± 0.006 ± 0.003 ± 0.002, where the third uncertainty is due to limited knowledge of the ratio of fragmentation fractions.

The magnetic helicity density patterns from non-axisymmetric solar dynamo

We study the helicity density patterns which can result from the emerging bipolar regions. Using the relevant dynamo model and the magnetic helicity conservation law we find that the helicity density patterns around the bipolar regions depend on the configuration of the ambient large-scale magnetic field, and in general they show a quadrupole distribution. The position of this pattern relative to the equator can depend on the tilt of the bipolar region. We compute the time–latitude diagrams of the helicity density evolution. The longitudinally averaged effect of the bipolar regions shows two bands of sign for the density distributions in each hemisphere. Similar helicity density patterns are provided by the helicity density flux from the emerging bipolar regions subjected to surface differential rotation.

Relation between the magnetic free energy and relative magnetic helicity in the MHD extreme state of solar corona

<p>Magnetic helicity is a quantity describing the twist, writhe, and torsion of magnetic field lines and magnetic configurations . The concept of magnetic helicity has successfully been applied to characterize solar coronal processes. A conjecture about one approximation relation between free magnetic free energy and relative magnetic helicity in the MHD extreme state of solar corona has been proposed by using the concept of magnetic helicity conservation and Lie-Poisson mechanical structure of MHD. We use constant α force-free filed extrapolation to check out this relation. We also apply this relation to analyze the results from the simulations and observations. Such relation may be helpful to predict the solar activity like the solar flares and CMEs</p>