Neighborhoods of Starlike and Convex Functions Associated with Parabola

Let f be a normalized analytic function defined on the unit disk and fλ(z):=(1−λ)z+λf(z) for 00, a function f∈ðÂ’®ðÂ’«(α,λ) if zf′(z)/fλ(z) lies in the parabolic region Ω:={w:|w−α|0, the δ-neighbourhood of a function f∈ðÂ’žðÂ’«(α,λ) is shown to consist of functions in the class ðÂ’®ðÂ’«(α,λ)

Heavy fermions and two loop electroweak corrections to b→s+γb\rightarrow s+\gamma

Applying effective Lagrangian method and on-shell scheme, we analyze the electroweak corrections to the rare decay $b\rightarrow s+\gamma$ from some special two loop diagrams in which a closed heavy fermion loop is attached to the virtual charged gauge bosons or Higgs. At the decoupling limit where the virtual fermions in inner loop are much heavier than the electroweak scale, we verify the final results satisfying the decoupling theorem explicitly when the interactions among Higgs and heavy fermions do not contain the nondecoupling couplings. Adopting the universal assumptions on the relevant couplings and mass spectrum of new physics, we find that the relative corrections from those two loop diagrams to the SM theoretical prediction on the branching ratio of $B\rightarrow X_{_s}\gamma$ can reach 5% as the energy scale of new physics $\Lambda_{_{\rm NP}}=200$ GeV.Comment: 30 pages,4 figure

Anomalous tqγtq\gamma coupling effects in exclusive radiative B-meson decays

The top-quark FCNC processes will be searched for at the CERN LHC, which are correlated with the B-meson decays. In this paper, we study the effects of top-quark anomalous interactions $tq\gamma$ in the exclusive radiative $B\to K^*\gamma$ and $B\to\rho\gamma$ decays. With the current experimental data of the branching ratios, the direct CP and the isospin asymmetries, bounds on the coupling $\kappa_{tcR}^{\gamma}$ from $B\to K^*\gamma$ and $\kappa_{tuR}^{\gamma}$ from $B\to \rho\gamma$ decays are derived, respectively. The bound on $|\kappa_{tcR}^{\gamma}|$ from ${\mathcal B}(B\to K^{*}\gamma)$ is generally compatible with that from ${\mathcal B}(B\to X_{s}\gamma)$. However, the isospin asymmetry $\Delta(K^{*}\gamma)$ further restrict the phase of $\kappa_{tcR}^{\gamma}$, and the combined bound results in the upper limit, $\mathcal B(t\to c\gamma)<0.21$, which is lower than the CDF result. For real $\kappa_{tcR}^{\gamma}$, the upper bound on $\mathcal B(t\to c\gamma)$ is about of the same order as the $5\sigma$ discovery potential of ATLAS with an integrated luminosity of $10 {\rm fb}^{-1}$. For $B\to\rho\gamma$ decays, the NP contribution is enhanced by a large CKM factor $|V_{ud}/V_{td}|$, and the constraint on $tu\gamma$ coupling is rather restrictive, $\mathcal B(t\to u\gamma)<1.44\times 10^{-5}$. With refined measurements to be available at the LHCb and the future super-B factories, we can get close correlations between $B\to V \gamma$ and the rare $t\to q\gamma$ decays, which will be studied directly at the LHC ATLAS and CMS.Comment: 25 pages, 15 figures, pdflate

The Benefits of B ---> K* l+ l- Decays at Low Recoil

Using the heavy quark effective theory framework put forward by Grinstein and Pirjol we work out predictions for B -> K* l+ l-, l = (e, mu), decays for a softly recoiling K*, i.e., for large dilepton masses sqrt{q^2} of the order of the b-quark mass m_b. We work to lowest order in Lambda/Q, where Q = (m_b, sqrt{q^2}) and include the next-to-leading order corrections from the charm quark mass m_c and the strong coupling at O(m_c^2/Q^2, alpha_s). The leading Lambda/m_b corrections are parametrically suppressed. The improved Isgur-Wise form factor relations correlate the B -> K* l+ l- transversity amplitudes, which simplifies the description of the various decay observables and provides opportunities for the extraction of the electroweak short distance couplings. We propose new angular observables which have very small hadronic uncertainties. We exploit existing data on B -> K* l+ l- distributions and show that the low recoil region provides powerful additional information to the large recoil one. We find disjoint best-fit solutions, which include the Standard Model, but also beyond-the-Standard Model ones. This ambiguity can be accessed with future precision measurements.Comment: 31 pages, 8 figures; Instability near minimal recoil from numerics removed, Fig. 1 replaced and minor shifts in short distance uncertainties in SM predictions; typos corrected and references added; main results and conclusions unchange

Comparative study on calcium, magnesium and cobalt in diabetic and non diabetic patients (males) in Punjab, Pakistan

Minerals are very important because of their important role in the maintenance of human health. Our study was aimed at assessing and comparing the levels of Ca, Mg and Co in the blood samples of diabetic and non diabetic persons (males) of five age groups between one and 75 years. For this purpose, fasting blood samples of diabetic and non diabetic males of selected age groups were collected. The blood samples were centrifuged to get serum. The mineral elements in the serum were analyzed by using atomic absorption spectrophotometer. The results depicted that the diabetic patients had higher mean concentration of Ca (141.47 ppm), Mg (18 ppm) and Co (0.057 ppm) while non diabetic persons had higher mean concentration of Ca (201.33 ppm), Mg (36.15 ppm) and Co (0.047 ppm). Statistical analysis was done by applying Student’s T-test. It can be concluded from the study that the diabetic patients of all five age groups are deficient of Ca, Mg, whereas the concentration of Co is higher in diabetic patients. In the further study physiological parameters along with other inorganic cofactors are being taken into consideration.Key words: Diabetes mellitus, blood serum, Ca, Mg, Co

Forecasting Tunisian type 2 diabetes prevalence to 2027: validation of a simple model.

BACKGROUND: Most projections of type 2 diabetes (T2D) prevalence are simply based on demographic change (i.e. ageing). We developed a model to predict future trends in T2D prevalence in Tunisia, explicitly taking into account trends in major risk factors (obesity and smoking). This could improve assessment of policy options for prevention and health service planning. METHODS: The IMPACT T2D model uses a Markov approach to integrate population, obesity and smoking trends to estimate future T2D prevalence. We developed a model for the Tunisian population from 1997 to 2027, and validated the model outputs by comparing with a subsequent T2D prevalence survey conducted in 2005. RESULTS: The model estimated that the prevalence of T2D among Tunisians aged over 25 years was 12.0% in 1997 (95% confidence intervals 9.6%-14.4%), increasing to 15.1% (12.5%-17.4%) in 2005. Between 1997 and 2005, observed prevalence in men increased from 13.5% to 16.1% and in women from 12.9% to 14.1%. The model forecast for a dramatic rise in prevalence by 2027 (26.6% overall, 28.6% in men and 24.7% in women). However, if obesity prevalence declined by 20% in the 10 years from 2013, and if smoking decreased by 20% over 10 years from 2009, a 3.3% reduction in T2D prevalence could be achieved in 2027 (2.5% in men and 4.1% in women). CONCLUSIONS: This innovative model provides a reasonably close estimate of T2D prevalence for Tunisia over the 1997-2027 period. Diabetes burden is now a significant public health challenge. Our model predicts that this burden will increase significantly in the next two decades. Tackling obesity, smoking and other T2D risk factors thus needs urgent action. Tunisian decision makers have therefore defined two strategies: obesity reduction and tobacco control. Responses will be evaluated in future population surveys

Charm-loop effect in B→K(∗)ℓ+ℓ−B \to K^{(*)} \ell^{+} \ell^{-} and B→K∗γB\to K^*\gamma

We calculate the long-distance effect generated by the four-quark operators with $c$-quarks in the $B\to K^{(*)} \ell^+\ell^-$ decays. At the lepton-pair invariant masses far below the $\bar{c}c$-threshold, $q^2\ll 4m_c^2$, we use OPE near the light-cone. The nonfactorizable soft-gluon emission from $c$-quarks is cast in the form of a nonlocal effective operator. The $B\to K^{(*)}$ matrix elements of this operator are calculated from the QCD light-cone sum rules with the $B$-meson distribution amplitudes. As a byproduct, we also predict the charm-loop contribution to $B\to K^*\gamma$ beyond the local-operator approximation. To describe the charm-loop effect at large $q^2$, we employ the hadronic dispersion relation with $\psi=J/\psi,\psi (2S), ...$ contributions, where the measured $B\to K^{(*)}\psi$ amplitudes are used as inputs. Matching this relation to the result of QCD calculation reveals a destructive interference between the $J/\psi$ and $\psi(2S)$ contributions. The resulting charm-loop effect is represented as a $q^2$-dependent correction $\Delta C_9(q^2)$ to the Wilson coefficient $C_9$. Within uncertainties of our calculation, at $q^2$ below the charmonium region the predicted ratio $\Delta C_9(q^2)/C_9$ is $\leq 5$ for $B\to K \ell^+\ell^-$, but can reach as much as 20% for $B\to K^*\ell^+\ell^-$, the difference being mainly caused by the soft-gluon contribution.Comment: A few comments added, version to appear in JHE

Second order QCD corrections to inclusive semileptonic b \to Xc l \bar \nu_l decays with massless and massive lepton

We extend previous computations of the second order QCD corrections to semileptonic b \to c inclusive transitions, to the case where the charged lepton in the final state is massive. This allows accurate description of b \to c \tau \bar \nu_\tau decays. We review techniques used in the computation of O(\alpha_s^2) corrections to inclusive semileptonic b \to c transitions and present extensive numerical studies of O(\alpha_s^2) QCD corrections to b \to c l \bar \nu_l decays, for l =e, \tau.Comment: 30 pages, 4 figures, 5 table

Supersymmetric constraints from Bs -> mu+mu- and B -> K* mu+mu- observables

We study the implications of the recent LHCb limit and results on Bs -> mu+mu- and B -> K* mu+mu- observables in the constrained SUSY scenarios. After discussing the Standard Model predictions and carefully estimating the theoretical errors, we show the constraining power of these observables in CMSSM and NUHM. The latest limit on BR(Bs -> mu+mu-), being very close to the SM prediction, constrains strongly the large tan(beta) regime and we show that the various angular observables from B -> K* mu+mu- decay can provide complementary information in particular for moderate tan(beta) values.Comment: 30 pages, 14 figure