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Several years ago, it was proposed that the usual solutions of the Yang-Baxter equation associated to Lie groups can be deduced in a systematic way from four-dimensional gauge theory. In the present paper, we extend this picture, fill in…
We report the results of a search for the decay B0 -> K*+ K*- with a sample of 454 +/- 5 million BBbar pairs collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at the Stanford Linear Accelerator Center. We…
We use a sample of 384 million BBbar events collected with the Babar detector at the PEP-II e+e- collider to study angular distributions in the rare decays B -> K* l+l-, where l+l- is either e+e- or mu+mu-. For low dilepton invariant…
Using a sample of 3.7 x 10^{6} Y(4S) --> B-anti-B events collected with the BABAR detector at the PEP-II storage ring, we search for the electroweak penguin decays B^+ --> K^+e^+e^-, B^+ --> K^+mu^+mu^-, B^0 --> K^{*0)e^+e^-, and B^0 -->…
A differential system $[A] : \; Y'=AY$, with $A\in \mathrm{Mat}(n, \bar{k})$ is said to be in reduced form if $A\in \mathfrak{g}(\bar{k})$ where $\mathfrak{g}$ is the Lie algebra of the differential Galois group $G$ of $[A]$. In this…
We construct $R$-matrices (with a multidimensional spectral parameter) that include additive as well as non-additive parameters. They satisfy the colored Yang-Baxter equation. The solutions depend on a set of commuting operators. They…
The quantum Yang-Baxter equation admits generalisations to systems of Yang-Baxter type equations called Yang-Baxter systems. Starting from algebra structures, we propose new constructions of some constant as well as the spectral-parameter…
The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with…
We present preliminary results from a search for inclusive charmless B->KX decays. These decays occur dominantly via one-loop b->s penguin transitions, and can provide useful information about these processes. Using a sample of 288.5/fb…
In this paper, we complete the classification of 4 x 4 solutions of the Yang-Baxter equation. Regular solutions were recently classified and in this paper we find the remaining non-regular solutions. We present several new solutions, then…
Within the QCD factorization approach, we calculate the branching fractions and $CP$ asymmetry parameters of 12 $B \to K_0^*(1430)K^{(*)}$ decay modes under the assumption that the scalar meson $K_0^*(1430)$ is the first excited state or…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
Two results are presented for reduced Yang-Mills integrals with different symmetry groups and dimensions: the first is a compact integral representation in terms of the relevant variables of the integral, the second is a method to…
We report a search for the rare decays B+ to D+ K0 and B+ to D+ K*0 in an event sample of approximately 465 million BBbar pairs collected with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC. We find no significant…
The CLEO Collaboration recently reported the observation of the $B^0\to D^{*-}p\bar{n}$ mode at a rate only a factor of 4--5 lower than $B^0\to D^{*-}\rho^+$ and $D^{*-}\pi^+$. We try to understand this with a factorization approach of…
In one of his papers on the weak order of Coxeter groups, Dyer formulates several conjectures. Among these, one affirms that the extended weak order forms a lattice, while another offers an algebraic-geometric description of the join of two…
The most general model-independent analysis of the rare $B$ decay, $\Bsll$, is presented. There are ten independent local four-Fermi interactions which may contribute to this process. The branching ratio, the forward-backward asymmetry, and…
Set-theoretic solutions of the Yang--Baxter equation form a meeting-ground of mathematical physics, algebra and combinatorics. Such a solution consists of a set $X$ and a function r:X x X --> X x X which satisfies the braid relation. We…
We calculate the $B_{u,d,s}\to T$ form factors within the framework of the perturbative QCD approach, where $T$ denotes a light tensor meson with $J^P=2^+$. Due to the similarities between the wave functions of a vector and a tensor meson,…
New solutions of the quantum Yang-Baxter equation, depending in general on three arbitrary parameters, are written down. They are based on the root of unity representations of the quantum orthosymplectic superalgebra \\U, which were found…