Study of Λb→Λ(ϕ,η(′))\Lambda_b\to \Lambda (\phi,\eta^{(\prime)}) and Λb→ΛK+K−\Lambda_b\to \Lambda K^+K^- decays

We study the charmless two-body $\Lambda_b\to \Lambda (\phi,\eta^{(\prime)})$ and three-body $\Lambda_b\to \Lambda K^+K^-$ decays. We obtain ${\cal B}(\Lambda_b\to \Lambda\phi)=(3.53\pm 0.24)\times 10^{-6}$ to agree with the recent LHCb measurement. However, we find that ${\cal B}(\Lambda_b\to \Lambda(\phi\to)K^+ K^-)=(1.71\pm 0.12)\times 10^{-6}$ is unable to explain the LHCb observation of ${\cal B}(\Lambda_b\to\Lambda K^+ K^-)=(15.9\pm 1.2\pm 1.2\pm 2.0)\times 10^{-6}$, which implies the possibility for other contributions, such as that from the resonant $\Lambda_b\to K^- N^*,\,N^*\to\Lambda K^+$ decay with $N^*$ as a higher-wave baryon state. For $\Lambda_b\to \Lambda \eta^{(\prime)}$, we show that ${\cal B}(\Lambda_b\to \Lambda\eta,\,\Lambda\eta^\prime)= (1.47\pm 0.35,1.83\pm 0.58)\times 10^{-6}$, which are consistent with the current data of $(9.3^{+7.3}_{-5.3},<3.1)\times 10^{-6}$, respectively. Our results also support the relation of ${\cal B}(\Lambda_b\to \Lambda\eta) \simeq {\cal B}(\Lambda_b\to\Lambda\eta^\prime)$, given by the previous study.Comment: 8 pages, 1 figure, revised version accepted by EPJ

Special Lagrangian submanifolds of log Calabi-Yau manifolds

We study the existence of special Lagrangian submanifolds of log Calabi-Yau manifolds equipped with the complete Ricci-flat K\"ahler metric constructed by Tian-Yau. We prove that if $X$ is a Tian-Yau manifold, and if the compact Calabi-Yau manifold at infinty admits a single special Lagrangian, then $X$ admits infinitely many disjoint special Lagrangians. In complex dimension $2$, we prove that if $Y$ is a del Pezzo surface, or a rational elliptic surface, and $D\in |-K_{Y}|$ is a smooth divisor with $D^2=d$, then $X= Y\backslash D$ admits a special Lagrangian torus fibration, as conjectured by Strominger-Yau-Zaslow and Auroux. In fact, we show that $X$ admits twin special Lagrangian fibrations, confirming a prediction of Leung-Yau. In the special case that $Y$ is a rational elliptic surface, or $Y= \mathbb{P}^2$ we identify the singular fibers for generic data, thereby confirming two conjectures of Auroux. Finally, we prove that after a hyper-K\"ahler rotation, $X$ can be compactified to the complement of a Kodaira type $I_{d}$ fiber appearing as a singular fiber in a rational elliptic surface $\check{\pi}: \check{Y}\rightarrow \mathbb{P}^1$.Comment: 70 pages. Updates and improvements. To appear in Duke Mathematical Journa

Finite-size scaling of pseudo-critical point distributions in the random transverse-field Ising chain

We study the distribution of finite size pseudo-critical points in a one-dimensional random quantum magnet with a quantum phase transition described by an infinite randomness fixed point. Pseudo-critical points are defined in three different ways: the position of the maximum of the average entanglement entropy, the scaling behavior of the surface magnetization, and the energy of a soft mode. All three lead to a log-normal distribution of the pseudo-critical transverse fields, where the width scales as $L^{-1/\nu}$ with $\nu=2$ and the shift of the average value scales as $L^{-1/\nu_{typ}}$ with $\nu_{typ}=1$, which we related to the scaling of average and typical quantities in the critical region.Comment: 4 pages, 2 figure

Seebeck Coefficients in Nanoscale Junctions: Effects of Electron-vibration Scattering and Local Heating

We report first-principles calculations of inelastic Seebeck coefficients in an aluminum monatomic junction. We compare the elastic and inelastic Seebeck coefficients with and without local heating. In the low temperature regime, the signature of normal modes in the profiles of the inelastic Seebeck effects is salient. The inelastic Seebeck effects are enhanced by the normal modes, and further magnified by local heating. In the high temperature regime, the inelastic Seebeck effects are weakly suppressed due to the quasi-ballistic transport.Comment: 3 Figure

Non-leptonic two-body weak decays of Λc(2286)\Lambda_c(2286)

We study the non-leptonic two-body weak decays of $\Lambda_c^+(2286)\to {\bf B}_n M$ with ${\bf B}_n$ ($M$) representing as the baryon (meson) states. Based on the $SU(3)$ flavor symmetry, we can describe most of the data reexamined by the BESIII Collaboration with higher precisions. However, our result of ${\cal B}(\Lambda_c^+ \to p\pi^0)=(5.6\pm 1.5)\times 10^{-4}$ is larger than the current experimental limit of $3\times10^{-4}$ (90\% C.L.) by BESIII. In addition, we find that ${\cal B}(\Lambda_c^+ \to \Sigma^+ K^0)=(8.0\pm 1.6)\times 10^{-4}$, ${\cal B}(\Lambda_c^+ \to \Sigma^+ \eta^\prime)=(1.0^{+1.6}_{-0.8})\times 10^{-2}$, and ${\cal B}(\Lambda_c^+ \to p \eta^\prime)=(12.2^{+14.3}_{-\,\,\,8.7})\times 10^{-4}$, which are accessible to the BESIII experiments.Comment: 12 pages, 1 figure, revised version accepted by PL