Revisiting $$B_s \rightarrow \mu ^+\mu ^-$$ B s → μ + μ - in the two-Higgs doublet models with $$Z_2$$ Z 2 symmetry

Abstract

We revisit the rare leptonic decay B s → μ + μ − in the two-Higgs doublet models (2HDMs) with a softly broken Z 2 symmetry, namely type-I, type-II, type-X and type-Y 2HDMs. We have derived the relevant full one-loop Wilson coefficients of the four 2HDMs from the recent calculation in the aligned 2HDM by Li, Lu and Pich, which could be mapped to all the four 2HDMs for both large and small tan β. It is found that a new term associated with the soft Z 2 symmetry breaking parameter M can be enhanced by tan 2 β in the type-II 2HDM, which has not been considered in the literature. Imposing both theoretical and experimental constraints, we have renewed the bounds on the parameter spaces of the four 2HDMs. Different from our previous paper, however, we find that all the four 2HDMs give sizable and similar contributions to B(B s → μ + μ − ) within the stringently restricted parameter spaces, but very tiny as regards the mass-eigenstate rate asymmetry A ; this makes it unfeasible to discriminate the four types of 2HDM with the correlations between the observables in B s → μ + μ − decay.

$$B^*_{s,d} \rightarrow \mu ^+ \mu ^-$$ B s , d ∗ → μ + μ - and its impact on $$B_{s,d} \rightarrow \mu ^+ \mu ^-$$ B s , d → μ + μ -

“…Furthermore, the branching fractions of the leptonic decays of scalar meson go through an additional helicity suppression factor by m 2 μ /M 2 S , where a e-mail: nophy0@gmail.com m μ and M S denote the masses of the muon lepton and the scalar meson, respectively. The suppression can be removed in several NP models, such as the two-Higgs-doublet models [3], the minimal supersymmetric standard model [4], the next minimal supersymmetric standard model [5], the dark matter [6], the universal extra dimensional model [7], the lepton universality violation model [8], the fourth generation of fermions [9], and so on [10]. The branching fractions of B s,d → μ + μ − measured by the CMS and LHCb Collaborations [2], and predicted within the SM [1] with NNLO QCD [11] and NLO EW [12] corrections are presented in Table 1.…”

CFD‐PBE‐PBE simulation of an airlift loop crystallizer

“…This can be attributed partly to the neglect of the aggregation process due to the limitation of the SMM. The aggregation increases the mean particle size as pointed out by Cheng et al who simulated the precipitation of BaSO 4 . The uncertainty of secondary nucleation rate can also lead to this inaccuracy as well.…”

“…The depletion rate of OH ‐ decreases with the increase of the initial concentration of Ca(OH) 2 . This trend is in agreement with the experimental results of Gómez‐Díaz et al The particle diameter slightly decreases with the increase of Ca(OH) 2 initial concentration, which corresponds well with results of other authors . The CSD becomes narrower and shifts towards the left when the Ca(OH) 2 initial concentration increases.…”

“…The effective diffusion coefficient is computed as the turbulent viscosity divided by the turbulent Schmidt number Sc t , i.e. , with Sc t equal to 0.7 . The source term S g is the specific crystal growth rate calculated by: where the volume shape factor k v is taken as 1.0 according to Kotaki and Tsuge .…”

“…Crystallization is an important separation and purification unit operation, which is widely used in the production of pharmaceuticals, catalysts, pigments, and other fine or bulk chemicals . Most industrial crystallizers are designed with impellers and pumping devices to achieve mixing and suspension of crystals, resulting in strong mechanical interaction between crystals and mechanical parts, and consequently an enhanced level of crystal attrition .…”