Three body radiative decay Bs→ϕKˉ0γB_s\to \phi \bar K^0 \gamma in the PQCD approach

We study the three body radiative decay $B_s\to \phi \bar K^0 \gamma$ by introducing the $\phi K$ pair distribution amplitudes (DAs) in the perturbative QCD approach. This nonperturbative inputs, the two meson DAs, is very important to simplify the calculations. Besides the dominant electromagnetic penguin operator $O_{7\gamma}$, the subleading contributions from chromomagnetic penguin operator $O_{8g}$, quark-loop corrections and annihilation type amplitudes are also considered. We find that the branching ratio for the decay $B_s\to \phi \bar K^0 \gamma$ is about $(9.26^{+1.79+3.12+0.64}_{-1.61-3.86-0.49})\times10^{-8}$, which is much smaller compared with that for the decay $B^0\to \phi K^0\gamma$. It is mainly because that the former decay induces by $b\to d\gamma$ with small CKM matrix element being proportional to $\lambda^3$. The prediction for the direct CP asymmetry is $A^{dir}_{CP}(B_s\to \phi \bar K^0 \gamma)=(-4.1^{+0.4+1.7+0.2}_{-0.6-1.2-0.1})\%$, which is well consistent with the result from the U-spin symmetry approach. we also predict the $B_s \to\phi \bar K^0\gamma$ decay spectrum, which exhibits a maximu at the $\phi K$ invariant masss around 1.95 GeV.Comment: 17 pages,6 figures, Accepted for publication in EPJ

Effects of Exchangeable Soil Calcium, Magnesium and Calcium/Magnesium Ratios on Plant Nutrition and Growth of Lettuce on an Ultisol

Two greenhouse pot experiments were conducted to study the effects of exchangeable soil calcium, magnesium and calcium/magnesium ratios on nutrition and growth of lettuce (Lactuca sativa L.) on an Ultisol (Manana soil series) with low pH (4.35), Ca (0.57 cmolc kg-1) and Mg (0.60 cmoh kg-1) in Hawaii to obtain calibration data for Ca and Mg in Hawaii soils and test the current sufficiency recommendations for Ca and Mg for making fertilizer recommendations. The objectives of this study were; to identify the sufficiency levels of exchangeable soil Ca and Mg for growth of lettuce; to investigate the validity of an ideal Ca/Mg ratio for growth of lettuce and to determine the effects of soil Ca and Mg levels as well as Ca/Mg ratios on soil nutrients and the nutrition and growth of lettuce. Lettuce yield increased as soil Ca increased and also as plant Ca level increased. The Cate- Nelson method was applied to determine the critical levels of Ca, Mg and the Ca/Mg ratio in the soil and plant. A critical soil Ca level for lettuce was determined to be 1.9 cmolc kg-1 and is more reasonable and lower than the value of 5 cmok kg-1 that is currently recommended in Hawaii. Lettuce in the zero Ca treatment with 0.57 cmoh kg-1 soil Ca exhibited Ca deficiency symptoms in the Ca experiment. A critical plant Ca concentration for lettuce at maturity was also determined to be 4 g kg-1. Exchangeable soil cations interact with each other and application of a large amount of liming material can cause cation imbalance. In the Ca experiment, soil Mg, K and Na decreased as soil Ca increased. Application of Ca increased the soil Ca level, increased Ca uptake by the plant and reduced the uptake of Mg and Na but had no effect on the uptake of P. Soil Ca restricted K uptake at low Ca levels due to decreased ion selectivity and leakiness of membranes membranes when Ca was deficient. Lettuce growth was normal with all soil Mg levels in the Mg experiment. Lettuce yield also was not related to plant Mg level. A critical soil Mg level for lettuce could not be established, however, the soil Mg level of the zero Mg treatment, 0.67 cmoU kg’\ was apparently adequate for normal lettuce growth. Therefore, the sufficiency range for soil Mg recommended in Hawaii (2.5 to 3.3 cmok kg'^) appears too high. Lettuce in the zero Mg treatment did not show any Mg deficiency symptoms. A critical plant Mg concentration for lettuce at maturity also could not be determined, however, the plant Mg concentration of the zero Mg treatment, 4 g k g '\ was apparently sufficient for normal growth of lettuce. Interactions between soil cations also occurred in the Mg experiment where soil Ca, K, and Na decreased as soil Mg increased. Increased levels of soil Mg increased the uptake of Mg by the plant, and reduced the uptake of Ca and Na, but had no effect on the uptake of K and P. In the soil Ca/Mg ratios ranged from 0.11 to 7.70, lettuce growth was limited by a Ca/Mg ratio of around 0.11 and no yield reduction was observed in the Ca/Mg ratio range from 0.50 to 7.70, which is within the optimal range. This study provides evidence for the conclusion that plants can grow normally within a broad range of Ca/Mg ratios. Lettuce yield was related to both soil Ca/Mg ratio and plant Ca/Mg ratio. The lower critical level of the soil Ca/Mg ratio for lettuce was determined to be 0.5. However, caution should be used in interpreting yield response to the soil Ca/Mg ratio because soil Ca or Mg levels can also affect plant growth. The critical plant Ca/Mg concentration ratio for lettuce at maturity was also determined to be 0.5. Plant Ca/Mg ratios in lettuce were significantly related to soil Ca/Mg ratios

Confronting brane inflation with Planck and pre-Planck data

In this paper, we compare brane inflation models with the Planck data and the pre-Planck data (which combines WMAP, ACT, SPT, BAO and H0 data). The Planck data prefer a spectral index less than unity at more than 5\sigma confidence level, and a running of the spectral index at around 2\sigma confidence level. We find that the KKLMMT model can survive at the level of 2\sigma only if the parameter $\beta$ (the conformal coupling between the Hubble parameter and the inflaton) is less than $\mathcal{O}(10^{-3})$, which indicates a certain level of fine-tuning. The IR DBI model can provide a slightly larger negative running of spectral index and red tilt, but in order to be consistent with the non-Gaussianity constraints from Planck, its parameter also needs fine-tuning at some level.Comment: 10 pages, 8 figure

Study of the K1(1270)−K1(1400)K_1(1270)-K_1(1400) mixing in the decays B→J/ΨK1(1270),J/ΨK1(1400)B\to J/\Psi K_1(1270), J/\Psi K_1(1400)

We studied the B meson decays $B\to J/\Psi K_1(1270,1400)$ in the pQCD approach beyond the leading order. With the vertex corrections and the NLO Wilson coefficients included, the branching ratios of the considered decays are $Br(B^+\to J/\Psi K_1(1270)^+)=1.76^{+0.65}_{-0.69}\times10^{-3}, Br(B^+\to J/\Psi K_1(1400)^+)=7.03^{+2.70}_{-2.52}\times10^{-4}$, and $Br(B^0\to J/\Psi K_1(1270)^0)=(1.63^{+0.60}_{-0.64})\times10^{-3}$ with the mixing angle $\theta_{K_1}=33^\circ$, which can agree well with the data or the present experimental upper limit within errors. So we support the opinion that $\theta_{K_1}\sim33^\circ$ is much more favored than $58^{\circ}$. Furthermore, we also give the predictions for the polarization fractions, direct CP violations from the different polarization components, the relative phase angles for the considered decays with the mixing angle $\theta_{K_1}=33^\circ$ and $58^\circ$, respectively. The direct CP violations of the two charged decays $B^+\to J/\Psi K_1(1270,1400)^+$ are very small $(10^{-4}\sim10^{-5})$, because there is no weak phase until up to $\mathcal{O}(\lambda^4)$ with the Wolfenstein parameter $\lambda=0.22537$. These results can be tested at the running LHCb and forthcoming Super-B experiments.Comment: 14 pages,3 figures,to appear in EPJ