Anisotropic Relaxation Functions and Strength of Oriented Solids Technical Report No. 106

Anisotropic relaxation functions and strength of oriented solid

Aerodynamic properties of turbulent combustion fields

Flow fields involving turbulent flames in premixed gases under a variety of conditions are modeled by the use of a numerical technique based on the random vortex method to solve the Navier-Stokes equations and a flame propagation algorithm to trace the motion of the front and implement the Huygens principle, both due to Chorin. A successive over-relaxation hybrid method is applied to solve the Euler equation for flows in an arbitrarily shaped domain. The method of images, conformal transformation, and the integral-equation technique are also used to treat flows in special cases, according to their particular requirements. Salient features of turbulent flame propagation in premixed gases are interpreted by relating them to the aerodynamic properties of the flow field. Included among them is the well-known cellular structure of flames stabilized by bluff bodies, as well as the formation of the characteristic tulip shape of flames propagating in ducts. In its rudimentary form, the mechanism of propagation of a turbulent flame is shown to consist of: (1) rotary motion of eddies at the flame front, (2) self-advancement of the front at an appropriate normal burning speed, and (3) dynamic effects of expansion due to exothermicity of the combustion reaction. An idealized model is used to illustrate these fundamental mechanisms and to investigate basic aerodynamic features of flames in premixed gases. The case of a confined flame stabilized behind a rearward-facing step is given particular care and attention. Solutions are shown to be in satisfactory agreement with experimental results, especially with respect to global properties such as the average velocity profiles and reattachment length

Search for XYZXYZ states in Λb\Lambda_b decays at the LHCb

We consider $X(3872)$ and $Y(4140)$ as the vector tetraquark states of $X_c^0\equiv c\bar c u\bar u(d\bar d)$ and $c\bar c s\bar s$, respectively. By connecting $\Lambda_b\to X_c^0\Lambda$ to $B^-\to X_c^0 K^-$, we predict that the branching ratios of $\Lambda_b\to \Lambda(X(3872)^0\to) J/\psi \pi^+\pi^-$ and $\Lambda_b\to \Lambda(Y(4140)\to) J/\psi \phi$ are $(5.2\pm 1.8)\times 10^{-6}$ and $(4.7\pm 2.6)\times 10^{-6}$, which are accessible to the experiments at the LHCb, respectively. The measurements of these $\Lambda_b$ modes would be the first experimental evidences for the $XYZ$ states in baryonic decays.Comment: 7 pages, 1 figure

Radiative Baryonic BB Decays

We study the structure-dependent contributions to the radiative baryonic $B$ decays of $B \to {\bf B}{\bf \bar B'}\gamma$ in the standard model. We show that the decay branching ratios of $Br(B \to {\bf B}{\bf \bar B'}\gamma)$ are $O(10^{-7})$, which are larger than the estimated values of $O(10^{-9})$ induced from inner bremsstrahlung effects of the corresponding two-body modes. In particular, we find that $Br(B^- \to \Lambda \bar p \gamma)$ is around $1 \times 10^{-6}$, which is close to the pole model estimation but smaller than the experimental measurement from BELLE.Comment: 11 pages, 2 figures, Revtex4, new fitting is include

Pentaquarks from intrinsic charms in Λb\Lambda_b decays

We study the three-body $\Lambda_b$ decays of $\Lambda_b\to J/\psi pM$ with $M=K^-$ and $\pi^-$. The two new states ${\cal P}_{c1}\equiv {\cal P}_c(4380)^+$ and ${\cal P}_{c2}\equiv {\cal P}_c(4450)^+$ observed recently as the resonances in the $J/\psi p$ invariant mass spectrum of $\Lambda_b\to J/\psi p K^-$ can be identified to consist of five quarks, $uudc\bar c$, being consistent with the existence of the pentaquark states. We argue that, in the doubly charmful $\Lambda_b$ decays of $\Lambda_b\to J/\psi pK^-$ through $b\to c\bar c s$, apart from those through the non-resonant $\Lambda_b\to pK^-$ and resonant $\Lambda_b\to \Lambda^*\to pK^-$ transitions, the third contribution with the non-factorizable effects is not the dominant part for the resonant $\Lambda_b\to K^-{\cal P}_{c1,c2}, {\cal P}_{c1,c2}\to J/\psi p$ processes, such that we propose that the ${\cal P}_{c1,c2}$ productions are mainly from the charmless $\Lambda_b$ decays through $b\to \bar u u s$, in which the $c\bar c$ content in ${\cal P}_{c1,c2}$ arises from the intrinsic charms within the $\Lambda_b$ baryon. We hence predict the observables related to the branching ratios and the direct CP violating asymmetries to be ${\cal B}(\Lambda_b\to \pi^-({\cal P}_{c1,c2}\to) J/\psi p)/{\cal B}(\Lambda_b\to K^-({\cal P}_{c1,c2}\to) J/\psi p)=0.8\pm 0.1$, ${\cal A}_{CP}(\Lambda_b\to \pi^-({\cal P}_{c1,c2}\to)J/\psi p)=(-3.9\pm 0.2)\%$, and ${\cal A}_{CP}(\Lambda_b\to K^-({\cal P}_{c1,c2}\to)J/\psi p)=(5.8\pm 0.2)\%$, which can alleviate the inconsistency between the theoretical expectations from the three contributions in the doubly charmful $\Lambda_b$ decays and the observed data.Comment: 10 pages, 2 figures, revised version accepted by PL

Identifying Glueball at 3.02 GeV in Baryonic BB Decays

We examine the nature of the unknown enhancement around 3 GeV observed by the BABAR collaboration in the $m_{p\bar p}$ spectrum of the $\bar B^0\to p\bar p D^0$ decay. Suspecting that the peak is a resonance, which can be neither identified as a charmonium state, such as $\eta_c$ or $J/\psi$, nor classified as one of the light-flavor mesons, we conclude that it corresponds to a glueball fitted as X(3020) with $(m_X,\;\Gamma_X)=(3020\pm 8,\; 107\pm 30)\;\text{MeV}$, which could be the first glueball state above 3 GeV. This state also appears in the $m_{p\bar p}$ spectrum of the $\bar B^0\to p\bar p D^{*0}$ decay.Comment: 11 pages, 2 figure, title changed, revised version accepted by PL

Determinations of ∣Vcb∣|V_{cb}| and ∣Vub∣|V_{ub}| from baryonic Λb\Lambda_b decays

We extract the Cabibbo-Kobayashi-Maskawa matrix element $V_{cb}$ from the exclusive decays of $\Lambda_b\to \Lambda_c\ell\bar \nu_\ell$ and $\Lambda_b\to \Lambda_c M_{(c)}$ with $M=(\pi^-,K^-)$ and $M_c=(D^-,D^-_s)$, where the branching ratios of $\Lambda_b\to \Lambda M_{(c)}$ measured with high precisions have not been used in the previous studies. Explicitly, we find $|V_{cb}|=(44.0\pm 3.5)\times 10^{-3}$, which agrees with the value of $(42.11\pm 0.74)\times 10^{-3}$ from the inclusive $B\to X_c\ell\bar \nu_\ell$ decays. Furthermore, based on the most recent ratio of $|V_{ub}|/|V_{cb}|$ from the exclusive $\Lambda_b$ decays, we obtain $|V_{ub}|=(4.2\pm 0.4)\times 10^{-3}$, which is close to the value of $(4.49\pm 0.24)\times 10^{-3}$ from the inclusive $B\to X_u\ell\bar \nu_\ell$ decays. We conclude that our determinations of $|V_{cb}|$ and $|V_{ub}|$ from the exclusive $\Lambda_b$ decays favor the inclusive extractions in the $B$ decays.Comment: 8 pages, i figur