Rough Sets Determined by Quasiorders

In this paper, the ordered set of rough sets determined by a quasiorder relation $R$ is investigated. We prove that this ordered set is a complete, completely distributive lattice. We show that on this lattice can be defined three different kinds of complementation operations, and we describe its completely join-irreducible elements. We also characterize the case in which this lattice is a Stone lattice. Our results generalize some results of J. Pomykala and J. A. Pomykala (1988) and M. Gehrke and E. Walker (1992) in case $R$ is an equivalence.Comment: 18 pages, major revisio

A Measurement of Rb using a Double Tagging Method

The fraction of Z to bbbar events in hadronic Z decays has been measured by the OPAL experiment using the data collected at LEP between 1992 and 1995. The Z to bbbar decays were tagged using displaced secondary vertices, and high momentum electrons and muons. Systematic uncertainties were reduced by measuring the b-tagging efficiency using a double tagging technique. Efficiency correlations between opposite hemispheres of an event are small, and are well understood through comparisons between real and simulated data samples. A value of Rb = 0.2178 +- 0.0011 +- 0.0013 was obtained, where the first error is statistical and the second systematic. The uncertainty on Rc, the fraction of Z to ccbar events in hadronic Z decays, is not included in the errors. The dependence on Rc is Delta(Rb)/Rb = -0.056*Delta(Rc)/Rc where Delta(Rc) is the deviation of Rc from the value 0.172 predicted by the Standard Model. The result for Rb agrees with the value of 0.2155 +- 0.0003 predicted by the Standard Model.Comment: 42 pages, LaTeX, 14 eps figures included, submitted to European Physical Journal

Reflectivity, Reflexivity, Reflexivism: IR's 'Reflexive Turn' - and Beyond

The notion of ‘reflexivity’ has been so intimately tied to the critique of positivism and empiricism in International Relations (IR) that the emergence of post-positivism has naturally produced the anticipation of a ‘reflexive turn’ in IR theory. Three decades after the launch of the post-positivist critique, however, reflexive IR has failed to impose itself as either a clear or serious contender to mainstream scholarship. Reasons for this failure include: the proliferation of different understandings of ‘reflexivity’ in IR theory that entail significantly different projects and concerns for IR scholarship; the equation of ‘reflexive theory’ with ‘critical’ and ‘emancipatory theory’ and the consequent confusion of ethical/normative issues with strictly epistemic/theoretical ones; and the refusal to consider reflexive IR as a ‘research programme’ concerned with empirical knowledge, not just meta-explanation. The development of reflexivity in IR theory as a sustainable cognitive and praxeological effort is nonetheless possible — and still needed. This article suggests what taking the ‘reflexive turn’ would really entail for IR.</jats:p

Measurement of the B+ and B-0 lifetimes and search for CP(T) violation using reconstructed secondary vertices

The lifetimes of the B+ and B-0 mesons, and their ratio, have been measured in the OPAL experiment using 2.4 million hadronic Z(0) decays recorded at LEP. Z(0) --> b (b) over bar decays were tagged using displaced secondary vertices and high momentum electrons and muons. The lifetimes were then measured using well-reconstructed charged and neutral secondary vertices selected in this tagged data sample. The results aretau(B+) = 1.643 +/- 0.037 +/- 0.025 pstau(Bo) = 1.523 +/- 0.057 +/- 0.053 pstau(B+)/tau(Bo) = 1.079 +/- 0.064 +/- 0.041,where in each case the first error is statistical and the second systematic.A larger data sample of 3.1 million hadronic Z(o) decays has been used to search for CP and CPT violating effects by comparison of inclusive b and (b) over bar hadron decays, No evidence fur such effects is seen. The CP violation parameter Re(epsilon(B)) is measured to be Re(epsilon(B)) = 0.001 +/- 0.014 +/- 0.003and the fractional difference between b and (b) over bar hadron lifetimes is measured to(Delta tau/tau)(b) = tau(b hadron) - tau((b) over bar hadron)/tau(average) = -0.001 +/- 0.012 +/- 0.008

Measurement of the Forward-Backward Asymmetry in the B -> K(*) mu+ mu- Decay and First Observation of the Bs -> phi mu+ mu- Decay

We reconstruct the rare decays $B^+ \to K^+\mu^+\mu^-$, $B^0 \to K^{*}(892)^0\mu^+\mu^-$, and $B^0_s \to \phi(1020)\mu^+\mu^-$ in a data sample corresponding to $4.4 {\rm fb^{-1}}$ collected in $p\bar{p}$ collisions at $\sqrt{s}=1.96 {\rm TeV}$ by the CDF II detector at the Fermilab Tevatron Collider. Using $121 \pm 16$ $B^+ \to K^+\mu^+\mu^-$ and $101 \pm 12$ $B^0 \to K^{*0}\mu^+\mu^-$ decays we report the branching ratios. In addition, we report the measurement of the differential branching ratio and the muon forward-backward asymmetry in the $B^+$ and $B^0$ decay modes, and the $K^{*0}$ longitudinal polarization in the $B^0$ decay mode with respect to the squared dimuon mass. These are consistent with the theoretical prediction from the standard model, and most recent determinations from other experiments and of comparable accuracy. We also report the first observation of the $B^0_s \to \phi\mu^+\mu^- decay and measure its branching ratio${\mathcal{B}}(B^0_s \to \phi\mu^+\mu^-) = [1.44 \pm 0.33 \pm 0.46] \times 10^{-6}$using$27 \pm 6$signal events. This is currently the most rare$B^0_s$ decay observed.Comment: 7 pages, 2 figures, 3 tables. Submitted to Phys. Rev. Let

Search for a New Heavy Gauge Boson Wprime with Electron + missing ET Event Signature in ppbar collisions at sqrt(s)=1.96 TeV

We present a search for a new heavy charged vector boson $W^\prime$ decaying to an electron-neutrino pair in $p\bar{p}$ collisions at a center-of-mass energy of 1.96\unit{TeV}. The data were collected with the CDF II detector and correspond to an integrated luminosity of 5.3\unit{fb}^{-1}. No significant excess above the standard model expectation is observed and we set upper limits on $\sigma\cdot{\cal B}(W^\prime\to e\nu)$. Assuming standard model couplings to fermions and the neutrino from the $W^\prime$ boson decay to be light, we exclude a $W^\prime$ boson with mass less than 1.12\unit{TeV/}c^2 at the 95\unit{%} confidence level.Comment: 7 pages, 2 figures Submitted to PR

Measurements of the properties of Lambda_c(2595), Lambda_c(2625), Sigma_c(2455), and Sigma_c(2520) baryons

We report measurements of the resonance properties of Lambda_c(2595)+ and Lambda_c(2625)+ baryons in their decays to Lambda_c+ pi+ pi- as well as Sigma_c(2455)++,0 and Sigma_c(2520)++,0 baryons in their decays to Lambda_c+ pi+/- final states. These measurements are performed using data corresponding to 5.2/fb of integrated luminosity from ppbar collisions at sqrt(s) = 1.96 TeV, collected with the CDF II detector at the Fermilab Tevatron. Exploiting the largest available charmed baryon sample, we measure masses and decay widths with uncertainties comparable to the world averages for Sigma_c states, and significantly smaller uncertainties than the world averages for excited Lambda_c+ states.Comment: added one reference and one table, changed order of figures, 17 pages, 15 figure

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

Performance of CMS muon reconstruction in pp collision events at sqrt(s) = 7 TeV

The performance of muon reconstruction, identification, and triggering in CMS has been studied using 40 inverse picobarns of data collected in pp collisions at sqrt(s) = 7 TeV at the LHC in 2010. A few benchmark sets of selection criteria covering a wide range of physics analysis needs have been examined. For all considered selections, the efficiency to reconstruct and identify a muon with a transverse momentum pT larger than a few GeV is above 95% over the whole region of pseudorapidity covered by the CMS muon system, abs(eta) < 2.4, while the probability to misidentify a hadron as a muon is well below 1%. The efficiency to trigger on single muons with pT above a few GeV is higher than 90% over the full eta range, and typically substantially better. The overall momentum scale is measured to a precision of 0.2% with muons from Z decays. The transverse momentum resolution varies from 1% to 6% depending on pseudorapidity for muons with pT below 100 GeV and, using cosmic rays, it is shown to be better than 10% in the central region up to pT = 1 TeV. Observed distributions of all quantities are well reproduced by the Monte Carlo simulation.Comment: Replaced with published version. Added journal reference and DO

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