 Award ID(s):
 1500424
 NSFPAR ID:
 10156295
 Date Published:
 Journal Name:
 International Mathematics Research Notices
 Volume:
 2019
 Issue:
 21
 ISSN:
 10737928
 Page Range / eLocation ID:
 6797 to 6817
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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A bstract Searches for CP violation in the twobody decays $$ {D}_{(s)}^{+}\to {h}^{+}{\pi}^0 $$ D s + → h + π 0 and $$ {D}_{(s)}^{+}\to {h}^{+}\eta $$ D s + → h + η (where h + denotes a π + or K + meson) are performed using pp collision data collected by the LHCb experiment corresponding to either 9 fb − 1 or 6 fb − 1 of integrated luminosity. The π 0 and η mesons are reconstructed using the e + e − γ final state, which can proceed as threebody decays π 0 → e + e − γ and η → e + e − γ , or via the twobody decays π 0 → γγ and η → γγ followed by a photon conversion. The measurements are made relative to the control modes $$ {D}_{(s)}^{+}\to {K}_{\mathrm{S}}^0{h}^{+} $$ D s + → K S 0 h + to cancel the production and detection asymmetries. The CP asymmetries are measured to be $$ {\displaystyle \begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}{\pi}^0\right)=\left(1.3\pm 0.9\pm 0.6\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}{\pi}^0\right)=\left(3.2\pm 4.7\pm 2.1\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}^{+}\to {\pi}^{+}\eta \right)=\left(0.2\pm 0.8\pm 0.4\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}^{+}\to {K}^{+}\eta \right)=\left(6\pm 10\pm 4\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}{\pi}^0\right)=\left(0.8\pm 3.9\pm 1.2\right)\%,\\ {}\begin{array}{c}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {\pi}^{+}\eta \right)=\left(0.8\pm 0.7\pm 0.5\right)\%,\\ {}{\mathcal{A}}_{CP}\left({D}_s^{+}\to {K}^{+}\eta \right)=\left(0.9\pm 3.7\pm 1.1\right)\%,\end{array}\end{array}\end{array}\end{array}} $$ A CP D + → π + π 0 = − 1.3 ± 0.9 ± 0.6 % , A CP D + → K + π 0 = − 3.2 ± 4.7 ± 2.1 % , A CP D + → π + η = − 0.2 ± 0.8 ± 0.4 % , A CP D + → K + η = − 6 ± 10 ± 4 % , A CP D s + → K + π 0 = − 0.8 ± 3.9 ± 1.2 % , A CP D s + → π + η = 0.8 ± 0.7 ± 0.5 % , A CP D s + → K + η = 0.9 ± 3.7 ± 1.1 % , where the first uncertainties are statistical and the second systematic. These results are consistent with no CP violation and mostly constitute the most precise measurements of $$ {\mathcal{A}}_{CP} $$ A CP in these decay modes to date.more » « less

Abstract We consider the focusing energycritical quintic nonlinear wave equation in 3D Euclidean space. It is known that this equation admits a oneparameter family of radial stationary solutions, called solitons, which can be viewed as a curve in $ \dot H^s_x({{\mathbb{R}}}^3) \times H^{s1}_x({{\mathbb{R}}}^3)$, for any $s> 1/2$. By randomizing radial initial data in $ \dot H^s_x({{\mathbb{R}}}^3) \times H^{s1}_x({{\mathbb{R}}}^3)$ for $s> 5/6$, which also satisfy a certain weighted Sobolev condition, we produce with high probability a family of radial perturbations of the soliton that give rise to global forwardintime solutions of the focusing nonlinear wave equation that scatter after subtracting a dynamically modulated soliton. Our proof relies on a new randomization procedure using distorted Fourier projections associated to the linearized operator around a fixed soliton. To our knowledge, this is the 1st longtime random data existence result for a focusing wave or dispersive equation on Euclidean space outside the small data regime.

A bstract Measurements of the production crosssections of the Standard Model (SM) Higgs boson ( H ) decaying into a pair of τ leptons are presented. The measurements use data collected with the ATLAS detector from pp collisions produced at the Large Hadron Collider at a centreofmass energy of $$ \sqrt{s} $$ s = 13 TeV, corresponding to an integrated luminosity of 139 fb − 1 . Leptonic ( τ → ℓν ℓ ν τ ) and hadronic ( τ → hadrons ν τ ) decays of the τ lepton are considered. All measurements account for the branching ratio of H → ττ and are performed with a requirement y H  < 2 . 5, where y H is the true Higgs boson rapidity. The crosssection of the pp → H → ττ process is measured to be 2 . 94 ± $$ 0.21{\left(\mathrm{stat}\right)}_{0.32}^{+0.37} $$ 0.21 stat − 0.32 + 0.37 (syst) pb, in agreement with the SM prediction of 3 . 17 ± 0 . 09 pb. Inclusive crosssections are determined separately for the four dominant production modes: 2 . 65 ± $$ 0.41{\left(\mathrm{stat}\right)}_{0.67}^{+0.91} $$ 0.41 stat − 0.67 + 0.91 (syst) pb for gluongluon fusion, 0 . 197 ± $$ 0.028{\left(\mathrm{stat}\right)}_{0.026}^{+0.032} $$ 0.028 stat − 0.026 + 0.032 (syst) pb for vectorboson fusion, 0 . 115 ± $$ 0.058{\left(\mathrm{stat}\right)}_{0.040}^{+0.042} $$ 0.058 stat − 0.040 + 0.042 (syst) pb for vectorboson associated production, and 0 . 033 ± $$ 0.031{\left(\mathrm{stat}\right)}_{0.017}^{+0.022} $$ 0.031 stat − 0.017 + 0.022 (syst) pb for topquark pair associated production. Measurements in exclusive regions of the phase space, using the simplified template crosssection framework, are also performed. All results are in agreement with the SM predictions.more » « less

Abstract Twinning, on par with dislocations, is critically required in plastic deformation of hexagonal closepacked crystals at low temperatures. In contrast to that in cubicstructured crystals, twinning in hexagonal closepacked crystals requires atomic shuffles in addition to shear. Though the twinning shear that is carried by twinning dislocations has been captured for decades, direct experimental observation of the atomic shuffles, especially when the shuffling mode is not unique and does not confine to the plane of shear, remains a formidable challenge to date. Here, by using insitu transmission electron microscopy, we directly capture the atomic mechanism of the
twinning in hexagonal close packed rhenium nanocrystals. Results show that the$$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$ twinning is dominated by the ($$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$b _{1/2}, h_{1/2}) twinning disconnections. In contrast to conventional expectations, the atomic shuffles accompanying the twinning disconnections proceed on alternative basal planes along 1/6 , which may be attributed to the free surface in nanocrystal samples, leading to a lack of mirror symmetry across the$$\left\langle 1\bar{1}00\right\rangle$$ $\left(1\overline{1}00\right)$ twin boundary.$$\left\{11\bar{2}1\right\}$$ $\left(11\overline{2}1\right)$ 
Abstract Given a suitable solution
V (t ,x ) to the Korteweg–de Vries equation on the real line, we prove global wellposedness for initial data . Our conditions on$$u(0,x) \in V(0,x) + H^{1}(\mathbb {R})$$ $u(0,x)\in V(0,x)+{H}^{1}\left(R\right)$V do include regularity but do not impose any assumptions on spatial asymptotics. We show that periodic profiles satisfy our hypotheses. In particular, we can treat localized perturbations of the muchstudied periodic traveling wave solutions (cnoidal waves) of KdV. In the companion paper Laurens (Nonlinearity. 35(1):343–387, 2022.$$V(0,x)\in H^5(\mathbb {R}/\mathbb {Z})$$ $V(0,x)\in {H}^{5}(R/Z)$https://doi.org/10.1088/13616544/ac37f5 ) we show that smooth steplike initial data also satisfy our hypotheses. We employ the method of commuting flows introduced in Killip and Vişan (Ann. Math. (2) 190(1):249–305, 2019.https://doi.org/10.4007/annals.2019.190.1.4 ) where . In that setting, it is known that$$V\equiv 0$$ $V\equiv 0$ is sharp in the class of$$H^{1}(\mathbb {R})$$ ${H}^{1}\left(R\right)$ spaces.$$H^s(\mathbb {R})$$ ${H}^{s}\left(R\right)$