abstract

We reemphasize that the ratio \(R_{s\mu } \equiv \bar {\mathcal {B}} (B_s\to \mu \bar \mu )/\Delta M_s\) is a measure of the tension of the Standard Model (SM) with the latest measurements of \(\bar {\mathcal {B}}(B_s\to \mu \bar \mu )\) that does not suffer from the persistent puzzle on the \(|V_{cb}|\) determinations from inclusive versus exclusive \(b\to c\ell \bar \nu \) decays and which affects the value of the CKM element \(|V_{ts}|\) that is crucial for the SM predictions of both \(\bar {\mathcal {B}}(B_s\to \mu \bar \mu )\) and \(\Delta M_s\), but cancels out in the ratio \(R_{s\mu }\). In our analysis, we include higher-order electroweak and QED corrections and adapt the latest hadronic input to find a tension of about \(2\sigma \) for \(R_{s\mu }\) measurements with the SM independently of \(|V_{ts}|\). We also discuss the ratio \(R_{d\mu }\) which could turn out, in particular in correlation with \(R_{s\mu }\), to be useful for the search for new physics, when data on both ratios improve. \(R_{d\mu }\) is also independent of \(|V_{cb}|\) or more precisely \(|V_{td}|\).

abstract

Using a new result on the integral involving the product of Bessel functions and associated Laguerre polynomials, published in the mathematical literature some time ago, we present an alternative method for calculating discrete–discrete transition form factors for hydrogen-like atoms. An overview of two other commonly used methods is also given in the aim of comparison.

abstract

In this work, the bound-free pair production (BFPP) cross-section calculations are done for NICA collider. In the BFPP mechanisms, after free pair production process, free electron is captured by one of the ions. This causes the decrement of the ion from the beam, and also diminish the intensity of the beam and changes the beam lifetime. The BFPP cross-section calculations are done for the \(p\)–Au and \(p\)–Bi collisions for NICA collider which are performed in the range of a few mbarns. In this work, we used the lowest-order perturbation theory and our calculations are done in the QED framework.

abstract

We study the Duffing equation and its generalizations with polynomial non-linearities. Recently, we have demonstrated that metamorphoses of the amplitude-response curves, computed by asymptotic methods in implicit form as \(F({\mit \Omega }, A) =0\), permit prediction of qualitative changes of dynamics occurring at singular points of the implicit curve \(F( {\mit \Omega }, A) =0\). In the present work, we determine a global structure of singular points of the amplitude profiles computing bifurcation sets, i.e. sets containing all points in the parameter space for which the amplitude profile has a singular point. We connect our work with independent research on tangential points on amplitude profiles, associated with jump phenomena, characteristic for the Duffing equation. We also show that our techniques can be applied to solutions of the form of \({\mit \Omega }_{\pm }=f_{\pm }(A)\), obtained within other asymptotic approaches.

abstract

Articular cartilage is a natural tribochemical device just-designed by nature. Yet, a vivid debate goes on toward the mechanisms by which its nanoscopic viscoelastic properties facilitate lubrication in terms of ultralow static and kinetic friction coefficients. In this concisely conducted conceptual discussion, we wish to point out that a nanoscale tribomechanistic description based upon certain “viscoelastic quanta”, called fractons, expressing spectral-mechanical properties of viscoelastic nets under the influence of force/pressure factor(s), may substantially contribute to the elucidation of ultralow coefficients of friction in the articular cartilage of predictable relaxational response. Our example unveils a part of a mechanically responsive viscoelastic network, such as a tied piece of hyaluronan molecule, fit in an Edwards-type tube, in which upon water-mediated interaction of lipids with the hyaluronan when subjected to loading at the nanoscale, consecutive stress-field and ion diffusion actions occur simultaneously. It results in a natural-logarithmic formula that interrelates a number of hyaluronan’s interactive residues, \(N\), with certain molecular-elastic (an exponent \(\gamma \)) and surface-to-volume (colloid) characteristics of around \(2/3\) to emerge near thermodynamic equilibrium, that is to say after a frictional loading action performed. It enables to relate uniquely a value of the exponent \(0 \lt \gamma \lt {1/2}\) with a virtual tribomicellization scenario of the nanoscale friction–lubrication event accompanied by inevitable tubular-milieu viscosity alterations at criticality when the quasi-static friction scenario shows up, preferably with \(\gamma \to {1/3}\) from above for large enough \(N\)s. A periodic vibrational super-biopolymer’s mode is exploited, leading to a change in the nanoscale friction–lubrication period from which an opportunity to involve an essential contribution to the (nanoscale) coefficient of friction arises.