Non-Divergence of Unipotent Flows on Quotients of Rank One Semisimple Groups

Let $G$ be a semisimple Lie group of rank $1$ and $\Gamma$ be a torsion free discrete subgroup of $G$. We show that in $G/\Gamma$, given $\epsilon>0$, any trajectory of a unipotent flow remains in the set of points with injectivity radius larger than $\delta$ for $1-\epsilon$ proportion of the time for some $\delta>0$. The result also holds for any finitely generated discrete subgroup $\Gamma$ and this generalizes Dani's quantitative nondivergence theorem \cite{D} for lattices of rank one semisimple groups. Furthermore, for a fixed $\epsilon>0$ there exists an injectivity radius $\delta$ such that for any unipotent trajectory $\{u_tx\}_{t\in [0,T]}$, either it spends at least $1-\epsilon$ proportion of the time in the set with injectivity radius larger than $\delta$ for all large $T>0$ or there exists a $\{u_t\}_{t\in\mathbb{R}}$-normalized abelian subgroup $L$ of $G$ which intersects $g\Gamma g^{-1}$ in a small covolume lattice. We also extend these results when $G$ is the product of rank-$1$ semisimple groups and $\Gamma$ a discrete subgroup of $G$ whose projection onto each nontrivial factor is torsion free.Comment: 23 page

THE ROLE OF INTERDEPENDENCE IN THE MICRO-FOUNDATIONS OF ORGANIZATION DESIGN: TASK, GOAL, AND KNOWLEDGE INTERDEPENDENCE

Interdependence is a core concept in organization design, yet one that has remained consistently understudied. Current notions of interdependence remain rooted in seminal works, produced at a time when managers’ near-perfect understanding of the task at hand drove the organization design process. In this context, task interdependence was rightly assumed to be exogenously determined by characteristics of the work and the technology. We no longer live in that world, yet our view of interdependence has remained exceedingly task-centric and our treatment of interdependence overly deterministic. As organizations face increasingly unpredictable workstreams and workers co-design the organization alongside managers, our field requires a more comprehensive toolbox that incorporates aspects of agent-based interdependence. In this paper, we synthesize research in organization design, organizational behavior, and other related literatures to examine three types of interdependence that characterize organizations’ workflows: task, goal, and knowledge interdependence. We offer clear definitions for each construct, analyze how each arises endogenously in the design process, explore their interrelations, and pose questions to guide future research

Measurement of ISR-FSR interference in the processes e+ e- --> mu+ mu- gamma and e+ e- --> pi+ pi- gamma

Charge asymmetry in processes e+ e- --> mu+ mu- gamma and e+ e- --> pi+ pi- gamma is measured using 232 fb-1 of data collected with the BABAR detector at center-of-mass energies near 10.58 GeV. An observable is introduced and shown to be very robust against detector asymmetries while keeping a large sensitivity to the physical charge asymmetry that results from the interference between initial and final state radiation. The asymmetry is determined as afunction of the invariant mass of the final-state tracks from production threshold to a few GeV/c2. It is compared to the expectation from QED for e+ e- --> mu+ mu- gamma and from theoretical models for e+ e- --> pi+ pi- gamma. A clear interference pattern is observed in e+ e- --> pi+ pi- gamma, particularly in the vicinity of the f_2(1270) resonance. The inferred rate of lowest order FSR production is consistent with the QED expectation for e+ e- --> mu+ mu- gamma, and is negligibly small for e+ e- --> pi+ pi- gamma.Comment: 32 pages,29 figures, to be submitted to Phys. Rev.

Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+

We perform amplitude analyses of the decays $B^0 \to K^+K^-K^0_S$, $B^+ \rightarrow K^+K^-K^+$, and $B^+ \to K^0_S K^0_S K^+$, and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\times 10^6$ $B\bar{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For $B^+ \to K^+K^-K^+$, we find a direct CP asymmetry in $B^+ \to \phi(1020)K^+$ of $A_{CP}= (12.8\pm 4.4 \pm 1.3)$, which differs from zero by $2.8 \sigma$. For $B^0 \to K^+K^-K^0_S$, we measure the CP-violating phase $\beta_{\rm eff} (\phi(1020)K^0_S) = (21\pm 6 \pm 2)^\circ$. For $B^+ \to K^0_S K^0_S K^+$, we measure an overall direct CP asymmetry of $A_{CP} = (4 ^{+4}_{-5} \pm 2)$. We also perform an angular-moment analysis of the three channels, and determine that the $f_X(1500)$ state can be described well by the sum of the resonances $f_0(1500)$, $f_2^{\prime}(1525)$, and $f_0(1710)$.Comment: 35 pages, 68 postscript figures. v3 - minor modifications to agree with published versio

A Search for Dark Higgs Bosons

Recent astrophysical and terrestrial experiments have motivated the proposal of a dark sector with GeV-scale gauge boson force carriers and new Higgs bosons. We present a search for a dark Higgs boson using 516 fb-1 of data collected with the BABAR detector. We do not observe a significant signal and we set 90% confidence level upper limits on the product of the Standard Model-dark sector mixing angle and the dark sector coupling constant.Comment: 7 pages, 5 postscript figures, published version with improved plots for b/w printin

Evidence for the h_b(1P) meson in the decay Upsilon(3S) --> pi0 h_b(1P)

Using a sample of 122 million Upsilon(3S) events recorded with the BaBar detector at the PEP-II asymmetric-energy e+e- collider at SLAC, we search for the $h_b(1P)$ spin-singlet partner of the P-wave chi_{bJ}(1P) states in the sequential decay Upsilon(3S) --> pi0 h_b(1P), h_b(1P) --> gamma eta_b(1S). We observe an excess of events above background in the distribution of the recoil mass against the pi0 at mass 9902 +/- 4(stat.) +/- 2(syst.) MeV/c^2. The width of the observed signal is consistent with experimental resolution, and its significance is 3.1sigma, including systematic uncertainties. We obtain the value (4.3 +/- 1.1(stat.) +/- 0.9(syst.)) x 10^{-4} for the product branching fraction BF(Upsilon(3S)-->pi0 h_b) x BF(h_b-->gamma eta_b).Comment: 8 pages, 4 postscript figures, submitted to Phys. Rev. D (Rapid Communications

Bottomonium spectroscopy and radiative transitions involving the chi(bJ)(1P, 2P) states at BABAR

We use (121 +/- 1) million Upsilon(3S) and (98 +/- 1) million Upsilon(2S) mesons recorded by the BABAR detector at the PEP-II e(+)e(-) collider at SLAC to perform a study of radiative transitions involving the chi(bJ)(1P, 2P) states in exclusive decays with mu(+)mu(-)gamma gamma final states. We reconstruct twelve channels in four cascades using two complementary methods. In the first we identify both signal photon candidates in the electromagnetic calorimeter (EMC), employ a calorimeter timing-based technique to reduce backgrounds, and determine branching-ratio products and fine mass splittings. These results include the best observational significance yet for the chi(b0)(2P) -> gamma Upsilon(2S) and chi(b0)(1P) -> gamma Upsilon(1S) transitions. In the second method, we identify one photon candidate in the EMC and one which has converted into an e(+)e(-) pair due to interaction with detector material, and we measure absolute product branching fractions. This method is particularly useful for measuring Upsilon(3S) -> gamma chi(b1,2)(1P) decays. Additionally, we provide the most up-to-date derived branching fractions, matrix elements and mass splittings for chi(b) transitions in the bottomonium system. Using a new technique, we also measure the two lowest-order spin-dependent coefficients in the nonrelativistic QCD Hamiltonian

Player migration and opportunity: examining the efficacy of the UEFA home-grown rule in six European football leagues.

The introduction of UEFAs home-grown rule occurred for the start of the 2006–2007 season with the full quota in place from the 2008–2009 season, which imposed quotas on European clubs. From 2008, clubs are required to have at least 8 players classified as home-grown in the 25-player squad, up from 4 in 2006–2007 and 6 in 2007–2008. This study examines the efficacy of this rule across the six major European leagues (England, France, Germany, Holland, Italy and Spain) in relation to playing opportunities (minutes played and appearances) between 1999 and 2015. This was also examined in relation to age. Since the home-grown rule was introduced for the six nations hosting the major leagues, the rule had different impacts by nationality. Only Germany saw significant increases in the proportion of minutes played by their players when comparing the periods before and after the home-grown rules were imposed. Holland, albeit seeing a slight decrease overall, saw significant increases for playing time for under 21s and 22- to 25-year olds. England and Italy were the two nations where statistically significant decreases in indigenous playing opportunities were recorded since the home-grown rules were introduced

Search for Invisible Decays of a Dark Photon Produced in e(+)e(-) Collisions at BABAR

We search for single-photon events in 53 fb^-1 of e+e- collision data collected with the BaBar detector at the PEP-II B-factory. We look for events with a single high-energy photon and a large missing momentum and energy, consistent with production of a spin-1 particle A' through the process e+e->gamma A', A'->invisible. Such particles, referred to as "dark photons", are motivated by theories applying a U(1) gauge symmetry to dark matter. We find no evidence for such processes and set 90% confidence level upper limits on the coupling strength of A' to e+e- in the mass range m_A'<=8 GeV. In particular, our limits exclude the values of the A' coupling suggested by the dark-photon interpretation of the muon (g-2) anomaly, as well as a broad range of parameters for the dark-sector models.Comment: 9 pages, 13 figures; v2 is the version published in Physical Review Letter