Unification modulo a 2-sorted Equational theory for Cipher-Decipher Block Chaining

We investigate unification problems related to the Cipher Block Chaining (CBC) mode of encryption. We first model chaining in terms of a simple, convergent, rewrite system over a signature with two disjoint sorts: list and element. By interpreting a particular symbol of this signature suitably, the rewrite system can model several practical situations of interest. An inference procedure is presented for deciding the unification problem modulo this rewrite system. The procedure is modular in the following sense: any given problem is handled by a system of `list-inferences', and the set of equations thus derived between the element-terms of the problem is then handed over to any (`black-box') procedure which is complete for solving these element-equations. An example of application of this unification procedure is given, as attack detection on a Needham-Schroeder like protocol, employing the CBC encryption mode based on the associative-commutative (AC) operator XOR. The 2-sorted convergent rewrite system is then extended into one that fully captures a block chaining encryption-decryption mode at an abstract level, using no AC-symbols; and unification modulo this extended system is also shown to be decidable.Comment: 26 page

Bs→KℓνB_s \to K \ell \nu form factors from lattice QCD

We report the first lattice QCD calculation of the form factors for the standard model tree-level decay $B_s\to K \ell\nu$. In combination with future measurement, this calculation will provide an alternative exclusive semileptonic determination of $|V_{ub}|$. We compare our results with previous model calculations, make predictions for differential decay rates and branching fractions, and predict the ratio of differential branching fractions between $B_s\to K\tau\nu$ and $B_s\to K\mu\nu$. We also present standard model predictions for differential decay rate forward-backward asymmetries, polarization fractions, and calculate potentially useful ratios of $B_s\to K$ form factors with those of the fictitious $B_s\to\eta_s$ decay. Our lattice simulations utilize NRQCD $b$ and HISQ light quarks on a subset of the MILC Collaboration's $2+1$ asqtad gauge configurations, including two lattice spacings and a range of light quark masses.Comment: 24 pages, 21 figures; Ver. 2 matches published versio

Bs→DsℓνB_s \to D_s \ell \nu Form Factors and the Fragmentation Fraction Ratio fs/fdf_s/f_d

We present a lattice quantum chromodynamics determination of the scalar and vector form factors for the $B_s \rightarrow D_s \ell \nu$ decay over the full physical range of momentum transfer. In conjunction with future experimental data, our results will provide a new method to extract $|V_{cb}|$, which may elucidate the current tension between exclusive and inclusive determinations of this parameter. Combining the form factor results at non-zero recoil with recent HPQCD results for the $B \rightarrow D \ell \nu$ form factors, we determine the ratios $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_K^2) = 1.000(62)$ and $f^{B_s \rightarrow D_s}_0(M_\pi^2) / f^{B \rightarrow D}_0(M_\pi^2) = 1.006(62)$. These results give the fragmentation fraction ratios $f_s/f_d = 0.310(30)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(6)_{\mathrm{theor.}}(38)_{\mathrm{latt.}}$ and $f_s/f_d = 0.307(16)_{\mathrm{stat.}}(21)_{\mathrm{syst.}}(23)_{\mathrm{theor.}}(44)_{\mathrm{latt.}}$, respectively. The fragmentation fraction ratio is an important ingredient in experimental determinations of $B_s$ meson branching fractions at hadron colliders, in particular for the rare decay ${\cal B}(B_s \rightarrow \mu^+ \mu^-)$. In addition to the form factor results, we make the first prediction of the branching fraction ratio $R(D_s) = {\cal B}(B_s\to D_s\tau\nu)/{\cal B}(B_s\to D_s\ell\nu) = 0.301(6)$, where $\ell$ is an electron or muon. Current experimental measurements of the corresponding ratio for the semileptonic decays of $B$ mesons disagree with Standard Model expectations at the level of nearly four standard deviations. Future experimental measurements of $R(D_s)$ may help understand this discrepancy.Comment: 21 pages, 15 figure

Summary of the 2018 CKM Working Group on Semileptonic and Leptonic b-Hadron Decays

A summary of WG II of the CKM 2018 conference on semileptonic and leptonic b-hadron decays is presented. This includes discussions on the CKM matrix element magitudes |Vub| and |Vcb|, lepton universality tests such as R(D∗) and leptonic decays. As is usual for semileptonic and leptonic decays, much discussion is devoted towards the interplay between theoretical QCD calculations and the experimental measurements

Polarization shaping for control of nonlinear propagation

We study the nonlinear optical propagation of two different classes of space-varying polarized light beams -- radially symmetric vector beams and Poincar\'e beams with lemon and star topologies -- in a rubidium vapour cell. Unlike Laguerre-Gauss and other types of beams that experience modulational instabilities, we observe that their propagation is not marked by beam breakup while still exhibiting traits such as nonlinear confinement and self-focusing. Our results suggest that by tailoring the spatial structure of the polarization, the effects of nonlinear propagation can be effectively controlled. These findings provide a novel approach to transport high-power light beams in nonlinear media with controllable distortions to their spatial structure and polarization properties.Comment: 5 pages, and 4 figure

Mirizzi Syndrome Type I: A Case Presentation.

Mirizzi syndrome (MS) is a rare complication of chronic cholelithiasis. The syndrome describes gallstone obstruction of Hartmann\u27s pouch or the cystic duct that extrinsically compresses the common hepatic duct, causing obstructive jaundice. In advanced cases, the gallstones may erode into the biliary tree creating a fistula, requiring prompt diagnosis and careful surgical management. We present a case of an 82-year-old female who presented with upper abdominal pain and jaundice, later diagnosed with suspected MS type I, and managed surgically. We aim to highlight MS type I because of the potential progression and damage to the bile duct, creating complications that may affect overall patient outcome

Rare decay B -> K ll form factors from lattice QCD

We calculate, for the first time using unquenched lattice QCD, form factors for the rare decay B -> Kll in and beyond the Standard Model. Our lattice QCD calculation utilizes a nonrelativistic QCD formulation for the b valence quarks, the highly improved staggered quark formulation for the light valence quarks, and employs the MILC 2+1 asqtad ensembles. The form factor results, based on the z expansion, are valid over the full kinematic range of q^2. We construct the ratios f0/f+ and fT/f+, which are useful in constraining new physics and verifying effective theory form factor symmetry relations. We also discuss the calculation of Standard Model observables.Comment: 30 pages, 23 figures; v2 adds a reference and fixes typos, results unchanged; v3 corrects a typo, updates references, makes minor changes in title and text, and is version published in Phys.Rev.D, results unchange