QCD factorization of the four-lepton decay $$B^-\rightarrow \ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$

Motivated by the first search for the rare charged-current B decay to four leptons, $$\ell \bar{\nu }_\ell \ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ν ¯ ℓ ℓ ( ′ ) ℓ ¯ ( ′ ) , we calculate the decay amplitude with factorization methods. We obtain the $$B\rightarrow \gamma ^*$$ B → γ ∗ form factors, which depend on the invariant masses of the two lepton pairs, at leading power in an expansion in $$\Lambda _\mathrm{QCD}/m_b$$ Λ QCD / m b to next-to-leading order in $$\alpha _s$$ α s , and at $$\mathcal {O}(\alpha _s^0)$$ O ( α s 0 ) at next-to-leading power. Our calculations predict branching fractions of a few times $$10^{-8}$$ 10 - 8 in the $$\ell ^{(\prime )} \bar{\ell }^{(\prime )}$$ ℓ ( ′ ) ℓ ¯ ( ′ ) mass-squared bin up to $$q^2=1~$$ q 2 = 1 GeV$$^2$$ 2 with $$n_+q>3~$$ n + q > 3 GeV. The branching fraction rapidly drops with increasing $$q^2$$ q 2 . An important further motivation for this investigation has been to explore the sensitivity of the decay rate to the inverse moment $$\lambda _B$$ λ B of the leading-twist B meson light-cone distribution amplitude. We find that in the small-$$q^2$$ q 2 bin, the sensitivity to $$\lambda _B$$ λ B is almost comparable to $$B^- \rightarrow \mathrm {\ell }^- \bar{\nu }_{\mathrm {\ell }}\gamma $$ B - → ℓ - ν ¯ ℓ γ when $$\lambda _B$$ λ B is small, but with an added uncertainty from the light-meson intermediate resonance contribution. The sensitivity degrades with larger $$q^2$$ q 2 .

Measurement of the γ*γ*→ η' transition form factor and of the e+e−→ π+π−π0π0π0 and π+π−π0π0η cross sections by BABAR

Two recent studies from the BABAR experiment at SLAC on low-energy hadronic final states in e+e− annihilations are presented. The first study provides the first-ever measurement of the γ*γ*→ η' transition factor, where γ* denotes an off-shell photon. The second study provides the first-ever measurements of the e+e−→ π+ π−π0π0π0 and π+π−π0π0η cross sections, including studies of the intermediate resonance states and the corresponding J/ψ and ψ(2S) branching fractions.

Mathematical Model of the Dynamic Action of the Controlled Vibration Exciter on the Processed Medium of Mixer with Toroidal Working Container

Vibration mixers are technological machines that are meant for mixing of different processed medium. A driving force in such machines is realizing by oscillation exciter. In this article, the constructive scheme of the vibration mixer is introduced. Such a mixer has the toroidal working container and is equipped with controlled mechanical centrifugal unbalanced exciters of oscillations with a vertically located unbalanced shaft. The work principle of one of the possible configurations in this exciter is considered and provided. One inflexible and two mobile unbalances are strengthen on its unbalanced shaft. The mobile unbalances by means of independent external action, that is caused by mechanism for managing of mobile unbalances, have an opportunity to change synchronously its positions on the unbalanced shaft directly in time of mixer’s work. The centrifugal inertia forces of inflexible and mobile unbalances make the dynamic wrench that consists of the main vector and the main moment and rotates with unbalanced shaft. It is determined that the value of the main vector and the main moment evaluate the dynamic action of this vibration exciter to the mixer’s working container. The mathematical model of the dynamic action of oscillator exciter on the processed medium of mixer with the toroidal working container is received. Depending on the value of turn angle of mobile unbalances from its starting positions exciter: a) staying in the dynamic balance state; b) is generating the translation force field; c) generates the wrench force field of this or that direction. These opportunities of controlled vibration exciter firmly provide anfractuous circulative motion of the processed medium on the volume of the mixer’s working container. Using of controlled exciter also leaves out the transfers through intermediate resonance frequencies. As its starting and stopping happen in a dynamic balance state, so it leaves out the possibility of manifestation of the “Sommerfeld’s effect” that is harmful for the driven motor, improves the constructive availability of the vibration mixer and increases its efficiency and life duration.

Study of B+ c decays to the K+K−π+ final state by using B0 s , χc0 and D0 resonances and weak annihilation nonresonant topologys

In this research the weak decay ofBc+decays to theK+K−π+final state, which is being observed by LHCb collaboration for the first time, is calculated in the quasi-two-body decays which takes theBs0, χc0andD0resonances and weak annihilation nonresonant contributions into account. In this process, theBc+meson decays first intoBs0π+, χc0π+andD0π+intermediate states, and then theBs0, χc0andD0resonances decay intoK+K−components, which undergo final state interaction. The mode of theBc+ → D0(→K−π+)K+is also associated with the calculation, in this mode the intermediate resonanceD0decays to theK−π+final mesons. The resonancesBs0, χc0andD0effects in theBc+ → Bs0(→K+K−)π+,Bc+ → χc0(→K+K−)π+andBc+ → D0(→K+K−)π+,D0(→K−π+)K+decays are described in terms of the quasi-two-body modes. There is a weak annihilation nonresonant contribution in whichBc+decays to theK+K−π+directly, so the point-like 3-body matrix element$$ \left\langle {K}^{+}{K}^{-}{\pi}^{+}\left|u\overline{d}\right|0\right\rangle $$K+K−π+ud¯0is also considered. The decay mode of the$$ {B}_c^{+}\to {\overline{K}}^{\ast 0}(892){K}^{+} $$Bc+→K¯∗0892K+is contributed to the annihilation contribution. The branching ratios of quasi-two-body decays expand in the range of (2.12 ± 0.61) × 10−6to (7.56 ± 1.71) × 10−6.