Copper‐Catalyzed Enantio‐ and Diastereoselective Addition of Silicon Nucleophiles to 3,3‐Disubstituted Cyclopropenes

A highly stereocontrolled syn‐addition of silicon nucleophiles across cyclopropenes with two different geminal substituents at C3 is reported. Diastereomeric ratios are excellent throughout (d.r.≥98:2) and enantiomeric excesses usually higher than 90 %, even reaching 99 %. This copper‐catalyzed C−Si bond formation closes the gap of the direct synthesis of α‐chiral cyclopropylsilanes.TU Berlin, Open-Access-Mittel - 201

Essays on numerical solutions to forward-backward stochastic differential equations and their applications in finance

In this thesis, we provide convergent numerical solutions to non-linear forward-BSDEs (Backward Stochastic Differential Equations). Applications in mathematical finance, financial economics and financial econometrics are discussed. Numerical examples show the effectiveness of our methods

Pair production of 125 GeV Higgs boson in the SM extension with color-octet scalars at the LHC

Although the Higgs boson mass and single production rate have been determined more or less precisely, its other properties may deviate significantly from its predictions in the standard model (SM) due to the uncertainty of Higgs data. In this work we study the Higgs pair production at the LHC in the Manohar-Wise model, which extends the SM by one family of color-octet and isospin-doublet scalars. We first scanned over the parameter space of the Manohar-Wise model considering exprimental constraints and performed fits in the model to the latest Higgs data by using the ATLAS and CMS data separately. Then we calculated the Higgs pair production rate and investigated the potential of its discovery at the LHC14. We conclude that: (i) Under current constrains including Higgs data after Run I of the LHC, the cross section of Higgs pair production in the Manohar-Wise model can be enhanced up to even $10^3$ times prediction in the SM. (ii) Moreover, the sizable enhancement comes from the contributions of the CP-odd color-octet scalar $S^A_I$. For lighter scalar $S^A_I$ and larger values of $|\lambda_I|$, the cross section of Higgs pair production can be much larger. (iii) After running again of LHC at 14 TeV, most of the parameter spaces in the Manohar-Wise model can be test. For an integrated luminosity of 100 fb$^{-1}$ at the LHC14, when the normalized ratio $R=10$, the process of Higgs pair production can be detected.Comment: 13 pages, 4 figure

Explanation of the ATLAS Z-peaked excess by squark pair production in the NMSSM

The ATLAS collaboration recently reported a $3\sigma$ excess in the leptonic-$Z+jets+E_{T}^{miss}$ channel. We intend to interpret this excess by squark pair production in the Next-to-Minimal Supersymmetric Standard Model (NMSSM). The decay chain we employ is $\tilde{q} \to q \tilde{\chi}_2^0 \to q \tilde{\chi}_1^0 Z$, where $\tilde{\chi}_1^0$ and $\tilde{\chi}_2^0$ denote the lightest and the next-to-lightest neutralinos with singlino and bino as their dominant components respectively. Our simulations indicate that after considering the constraints from the ATLAS searches for $jets + E_{T}^{miss}$ signal the central value of the excess can be obtained for $m_{\tilde{q}} \lesssim 1.2 {\rm TeV}$, and if the constraint from the CMS on-$Z$ search is further considered, more than 10 signal events are still attainable for $m_{\tilde{q}} \lesssim 750 {\rm GeV}$. Compared with the interpretation by gluino pair production, the squark explanation allows for a significantly wider range of $m_{\tilde{q}}$ as well as a less compressed SUSY mass spectrum. We also show that the squark explanation will be readily tested at the initial stage of the 14 TeV LHC.Comment: 19 pages, 4 figure

Explanation of the ATLAS Z-peaked excess in the NMSSM

Recently the ATLAS collaboration reported a $3\sigma$ excess in the leptonic-$Z+jets+E_{T}^{miss}$ channel. This may be interpreted in the Next-to-Minimal Supersymmetric Standard Model (NMSSM) by gluino pair production with the decay chain $\tilde{g} \to q \bar{q} \tilde{\chi}_2^0 \to q \bar{q} Z \tilde{\chi}_1^0$, where $\tilde{\chi}_1^0$ and $\tilde{\chi}_2^0$ denote the lightest and the next-to-lightest neutralinos with singlino and bino as their dominant components respectively. After exploring the relevant parameter space of the NMSSM by considering the constraints from the ATLAS searches for $jets + E_{T}^{miss}$ signals, we conclude that the NMSSM is able to explain the excess at $1 \sigma$ level with the number of the signal events reaching its measured central value in optimal cases, and the best explanation comes from a compressed spectrum such as $m_{\tilde{g}} \simeq 650 {\rm GeV}$, $m_{\tilde{\chi}_2^0} \simeq 565 {\rm GeV}$ and $m_{\tilde{\chi}_1^0} \simeq 465 {\rm GeV}$. We also check the consistency of the ATLAS results with the null result of the CMS on-$Z$ search. We find that under the CMS limits at $95\%$ C.L., the event number of the ATLAS on-$Z$ signal can still reach 11 in our scenario, which is about $1.2 \sigma$ away from the measured central value.Comment: 18 pages, 2 figure

Interpreting The 750 GeV Diphoton Excess Within Topflavor Seesaw Model

We propose to interpret the 750 GeV diphoton excess in a typical topflavor seesaw model. The new resonance X can be identified as a CP-even scalar emerging from a certain bi-doublet Higgs field. Such a scalar can couple to charged scalars, fermions as well as heavy gauge bosons predicted by the model, and consequently all of the particles contribute to the diphoton decay mode of the X. Numerical analysis indicates that the model can predict the central value of the diphoton excess without contradicting any constraints from 8 TeV LHC, and among the constraints, the tightest one comes from the Z \gamma channel, \sigma_{8 {\rm TeV}}^{Z \gamma} \lesssim 3.6 {\rm fb}, which requires \sigma_{13 {\rm TeV}}^{\gamma \gamma} \lesssim 6 {\rm fb} in most of the favored parameter space.Comment: Major changes, 17 pages, 4 figure, typos corrected, calculation details adde