Searches for CP violation in two-body charm decays

The LHCb experiment recorded data corresponding to an integrated luminosity of 3.0 $fb^{-1}$ during its first run of data taking. These data yield the largest samples of charmed hadrons in the world and are used to search for CP violation in the $D^0$ system. Among the many measurements performed at LHCb, a measurement of the direct CP asymmetry in $D^0 \rightarrow K_S^0 K_S^0$ decays is presented and is found to be $A_{CP}(D^0 \rightarrow K_S^0 K_S^0) = (-2.9 \pm 5.2 \pm 2.2)\, \%,$ where the first uncertainty is statistical and the second systematic. This represents a significant improvement in precision over the previous measurement of this parameter. Measurements of the parameter $A^\Gamma$, defined as the CP asymmetry of the $D^0$ effective lifetime when decaying to a CP eigenstate, are also presented. Using semi-leptonic b-hadron decays to tag the flavour of the $D^0$ meson at production with the $K^+K^-$ and $\pi^+\pi^-$ final states yields $A^\Gamma(K^+K^-) = (-0.134 \pm 0.077^{+0.026}_{-0.034})\, \%,$ $A^\Gamma(\pi^+\pi^-) = (-0.092 \pm 0.145^{+0.025}_{-0.033})\, \%.$ Thus no evidence of direct or indirect CP violation in the $D^0$ system is found, though it is tightly constrained.Comment: Proceedings for The European Physical Society Conference on High Energy Physics, 22-29 July 2015, Vienna, Austria. On behalf of the LHCb collaboratio

Charm: Mixing, CP Violation and Rare Decays at LHCb

Recent results on mixing, CP violation and rare decays in charm physics from the LHCb experiment are presented. Study of ''wrong-sign'' $D^{0} \rightarrow K^+ \pi^-$ decays provides the highest precision measurements to date of the mixing parameters $x^{\prime 2}$ and $y^{\prime}$, and of CP violation in this decay mode. Direct and indirect CP violation in the $D^0$ system are probed to a sensitivity of around $10^{-3}$ using $D^0 \rightarrow K^+K^-$ and $D^0 \rightarrow \pi^+\pi^-$ decays and found to be consistent with zero. Searches for the rare decays $D^+_{(s)} \rightarrow \pi^+\mu^+\mu^-$, $D^+_{(s)} \rightarrow \pi^-\mu^+\mu^+$ and $D^0 \rightarrow \mu^+\mu^-$ find no evidence of signal, but set the best limits on branching fractions to date. Thus, despite many excellent results in charm physics from LHCb, no evidence for physics beyond the Standard Model is found.Comment: Proceedings for PhiPsi 2013 conference. 6 pages, 3 figure

Finite energy coordinates and vector analysis on fractals

We consider (locally) energy finite coordinates associated with a strongly local regular Dirichlet form on a metric measure space. We give coordinate formulas for substitutes of tangent spaces, for gradient and divergence operators and for the infinitesimal generator. As examples we discuss Euclidean spaces, Riemannian local charts, domains on the Heisenberg group and the measurable Riemannian geometry on the Sierpinski gasket

Time is wasting: con/sequence and s/pace in the Saw series

Horror film sequels have not received as much serious critical attention as they deserve this is especially true of the Saw franchise, which has suffered a general dismissal under the derogatory banner Torture Porn. In this article I use detailed textual analysis of the Saw series to expound how film sequels employ and complicate expected temporal and spatial relations in particular, I investigate how the Saw sequels tie space and time into their narrative, methodological and moral sensibilities. Far from being a gimmick or a means of ensuring loyalty to the franchise (one has to be familiar with the events of previous episodes to ascertain what is happening), it is my contention that the Saw cycle directly requests that we examine the nature of space and time, in terms of both cinematic technique and our lived, off-screen temporal/spatial orientations

Absolutely continuous spectrum for one-dimensional Schr\"odinger operators with slowly decaying potentials: some optimal results

The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic Schr\"odinger operators is preserved under all perturbations $V(x)$ satisfying $|V(x)|\leq C(1+x)^{-\alpha}$, $\alpha >\frac{1}{2}.$ This result is optimal in the power scale. More general classes of perturbing potentials which are not necessarily power decaying are also treated. A general criterion for stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators is established. In all cases analyzed, the main term of the asymptotic behavior of the generalized eigenfunctions is shown to have WKB form for almost all energies. The proofs rely on new maximal function and norm estimates and almost everywhere convergence results for certain multilinear integral operators

Characteristic Polynomial Patterns in Difference Sets of Matrices

We show that for every subset $E$ of positive density in the set of integer square-matrices with zero traces, there exists an integer $k \geq 1$ such that the set of characteristic polynomials of matrices in $E-E$ contains the set of \emph{all} characteristic polynomials of integer matrices with zero traces and entries divisible by $k$. Our theorem is derived from results by Benoist-Quint on measure rigidity for actions on homogeneous spaces.Comment: 9 pages, 0 figures. Comments are welcome

Shifted quantum affine algebras: integral forms in type AA (with appendices by Alexander Tsymbaliuk and Alex Weekes)

We define an integral form of shifted quantum affine algebras of type $A$ and construct Poincar\'e-Birkhoff-Witt-Drinfeld bases for them. When the shift is trivial, our integral form coincides with the RTT integral form. We prove that these integral forms are closed with respect to the coproduct and shift homomorphisms. We prove that the homomorphism from our integral form to the corresponding quantized $K$-theoretic Coulomb branch of a quiver gauge theory is always surjective. In one particular case we identify this Coulomb branch with the extended quantum universal enveloping algebra of type $A$. Finally, we obtain the rational (homological) analogues of the above results (proved earlier in arXiv:1611.06775, arXiv:1806.07519 via different techniques).Comment: v1: 65 pages; comments are welcome! v2: 67 pages; a dominance condition is added in Section 2(vii), another definition is added in Appendix A(viii), the injectivity of $\mathfrak{g}\to Y$ is added in Appendix B(ii). v3: 70 pages; minor corrections, table of contents added, Section 3(vi) updated and Remark 4.33 added following a new version of arXiv:1808.0953