Slavnov-Taylor identities in Coulomb gauge Yang-Mills theory

The Slavnov-Taylor identities of Coulomb gauge Yang-Mills theory are derived from the (standard, second order) functional formalism. It is shown how these identities form closed sets from which one can in principle fully determine the Green's functions involving the temporal component of the gauge field without approximation, given appropriate input.Comment: 20 pages, no figure

Hypermatrix factors for string and membrane junctions

The adjoint representations of the Lie algebras of the classical groups SU(n), SO(n), and Sp(n) are, respectively, tensor, antisymmetric, and symmetric products of two vector spaces, and hence are matrix representations. We consider the analogous products of three vector spaces and study when they appear as summands in Lie algebra decompositions. The Z3-grading of the exceptional Lie algebras provide such summands and provides representations of classical groups on hypermatrices. The main natural application is a formal study of three-junctions of strings and membranes. Generalizations are also considered.Comment: 25 pages, 4 figures, presentation improved, minor correction

The ACS Virgo Cluster Survey. XII. The Luminosity Function of Globular Clusters in Early Type Galaxies

We analyze the luminosity function of the globular clusters (GCs) belonging to the early-type galaxies observed in the ACS Virgo Cluster Survey. We have obtained estimates for a Gaussian representation of the GC luminosity function (GCLF) for 89 galaxies. We have also fit the GCLFs with an "evolved Schechter function", which is meant to reflect the preferential depletion of low-mass GCs, primarily by evaporation due to two-body relaxation, from an initial Schechter mass function similar to that of young massive clusters. We find a significant trend of the GCLF dispersion with galaxy luminosity, in the sense that smaller galaxies have narrower GCLFs. We show that this narrowing of the GCLF in a Gaussian description is driven by a steepening of the GC mass function above the turnover mass, as one moves to smaller host galaxies. We argue that this behavior at the high-mass end of the GC mass function is most likely a consequence of systematic variations of the initial cluster mass function. The GCLF turnover mass M_TO is roughly constant, at ~ 2.2 x 10^5 M_sun in bright galaxies, but it decreases slightly in dwarfs with M_B >~ -18. We show that part of the variation could arise from the shorter dynamical friction timescales in smaller galaxies. We probe the variation of the GCLF to projected galactocentric radii of 20-35 kpc in the Virgo giants M49 and M87, finding that M_TO is essentially constant over these spatial scales. Our fits of evolved Schechter functions imply average dynamical mass losses (Delta) over a Hubble time that fall in the range 2 x 10^5 <~ (Delta/M_sun) < 10^6 per GC. We agree with previous suggestions that if the full GCLF is to be understood in more detail GCLF models will have to include self-consistent treatments of dynamical evolution inside time-dependent galaxy potentials. (Abridged)Comment: 46 pages, 20 figures, 6 tables. Accepted for publication in ApJS. Also available at http://www1.cadc-ccda.hia-iha.nrc-cnrc.gc.ca/community/ACSVCS/publications.htm

Reciprocity as a foundation of financial economics

This paper argues that the subsistence of the fundamental theorem of contemporary financial mathematics is the ethical concept ‘reciprocity’. The argument is based on identifying an equivalence between the contemporary, and ostensibly ‘value neutral’, Fundamental Theory of Asset Pricing with theories of mathematical probability that emerged in the seventeenth century in the context of the ethical assessment of commercial contracts in a framework of Aristotelian ethics. This observation, the main claim of the paper, is justified on the basis of results from the Ultimatum Game and is analysed within a framework of Pragmatic philosophy. The analysis leads to the explanatory hypothesis that markets are centres of communicative action with reciprocity as a rule of discourse. The purpose of the paper is to reorientate financial economics to emphasise the objectives of cooperation and social cohesion and to this end, we offer specific policy advice

Evidence for the η_b(1S) Meson in Radiative Υ(2S) Decay

We have performed a search for the η_b(1S) meson in the radiative decay of the Υ(2S) resonance using a sample of 91.6 × 10^6 Υ(2S) events recorded with the BABAR detector at the PEP-II B factory at the SLAC National Accelerator Laboratory. We observe a peak in the photon energy spectrum at E_γ = 609.3^(+4.6)_(-4.5)(stat)±1.9(syst) MeV, corresponding to an η_b(1S) mass of 9394.2^(+4.8)_(-4.9)(stat) ± 2.0(syst) MeV/c^2. The branching fraction for the decay Υ(2S) → γη_b(1S) is determined to be [3.9 ± 1.1(stat)^(+1.1)_(-0.9)(syst)] × 10^(-4). We find the ratio of branching fractions B[Υ(2S) → γη_b(1S)]/B[Υ(3S) → γη_b(1S)]= 0.82 ± 0.24(stat)^(+0.20)_(-0.19)(syst)

Measurement of B(B-->X_s {\gamma}), the B-->X_s {\gamma} photon energy spectrum, and the direct CP asymmetry in B-->X_{s+d} {\gamma} decays

The photon spectrum in B --> X_s {\gamma} decay, where X_s is any strange hadronic state, is studied using a data sample of (382.8\pm 4.2) \times 10^6 e^+ e^- --> \Upsilon(4S) --> BBbar events collected by the BABAR experiment at the PEP-II collider. The spectrum is used to measure the branching fraction B(B --> X_s \gamma) = (3.21 \pm 0.15 \pm 0.29 \pm 0.08)\times 10^{-4} and the first, second, and third moments = 2.267 \pm 0.019 \pm 0.032 \pm 0.003 GeV,, )^2> = 0.0484 \pm 0.0053 \pm 0.0077 \pm 0.0005 GeV^2, and )^3> = -0.0048 \pm 0.0011 \pm 0.0011 \pm 0.0004 GeV^3, for the range E_\gamma > 1.8 GeV, where E_{\gamma} is the photon energy in the B-meson rest frame. Results are also presented for narrower E_{\gamma} ranges. In addition, the direct CP asymmetry A_{CP}(B --> X_{s+d} \gamma) is measured to be 0.057 \pm 0.063. The spectrum itself is also unfolded to the B-meson rest frame; that is the frame in which theoretical predictions for its shape are made.Comment: 37 pages, 19 postscript figures, submitted to Phys. Rev. D. No analysis or results have changed from previous version. Some changes to improve clarity based on interactions with Phys. Rev. D referees, including one new Figure (Fig. 13), and some minor wording/punctuation/spelling mistakes fixe

Precise Measurement of the e+ e- --> pi+ pi- (gamma) Cross Section with the Initial-State Radiation Method at BABAR

A precise measurement of the cross section of the process $e^+e^-\to\pi^+\pi^-(\gamma)$ from threshold to an energy of 3GeV is obtained with the initial-state radiation (ISR) method using 232fb$^{-1}$ of data collected with the BaBar detector at $e^+e^-$ center-of-mass energies near 10.6GeV. The ISR luminosity is determined from a study of the leptonic process $e^+e^-\to\mu^+\mu^-(\gamma)\gamma_{\rm ISR}$, which is found to agree with the next-to-leading-order QED prediction to within 1.1%. The cross section for the process $e^+e^-\to\pi^+\pi^-(\gamma)$ is obtained with a systematic uncertainty of 0.5% in the dominant $\rho$ resonance region. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the measured $\pi\pi$ cross section from threshold to 1.8GeV is $(514.1 \pm 2.2({\rm stat}) \pm 3.1({\rm syst}))\times 10^{-10}$.Comment: 58 pages, 56 figures, to be submitted to Phys. Rev.

Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|

We report the results of a study of the exclusive charmless semileptonic decays, B^0 --> pi^- l^+ nu, B^+ --> pi^0 l^+ nu, B^+ --> omega l^+ nu, B^+ --> eta l^+ nu and B^+ --> eta^' l^+ nu, (l = e or mu) undertaken with approximately 462x10^6 B\bar{B} pairs collected at the Upsilon(4S) resonance with the BABAR detector. The analysis uses events in which the signal B decays are reconstructed with a loose neutrino reconstruction technique. We obtain partial branching fractions in several bins of q^2, the square of the momentum transferred to the lepton-neutrino pair, for B^0 --> pi^- l^+ nu, B^+ --> pi^0 l^+ nu, B^+ --> omega l^+ nu and B^+ --> eta l^+ nu. From these distributions, we extract the form-factor shapes f_+(q^2) and the total branching fractions BF(B^0 --> pi^- l^+ nu) = (1.45 +/- 0.04_{stat} +/- 0.06_{syst})x10^-4 (combined pi^- and pi^0 decay channels assuming isospin symmetry), BF(B^+ --> omega l^+ nu) = (1.19 +/- 0.16_{stat} +/- 0.09_{syst})x10^-4 and BF(B^+ --> eta l^+ nu) = (0.38 +/- 0.05_{stat} +/- 0.05_{syst})x10^-4. We also measure BF(B^+ --> eta^' l^+ nu) = (0.24 +/- 0.08_{stat} +/- 0.03_{syst})x10^-4. We obtain values for the magnitude of the CKM matrix element V_{ub} by direct comparison with three different QCD calculations in restricted q^2 ranges of B --> pi l^+ nu decays. From a simultaneous fit to the experimental data over the full q^2 range and the FNAL/MILC lattice QCD predictions, we obtain |V_{ub}| = (3.25 +/- 0.31)x10^-3, where the error is the combined experimental and theoretical uncertainty.Comment: 35 pages, 14 figures, submitted to PR

Observation of time-reversal violation in the B0 meson system

The individually named authors work collectively as The BABAR Collaboration. Copyright @ 2012 American Physical Society.Although CP violation in the B meson system has been well established by the B factories, there has been no direct observation of time-reversal violation. The decays of entangled neutral B mesons into definite flavor states (B0 or B¯¯¯0), and J/ψK0L or cc¯K0S final states (referred to as B+ or B−), allow comparisons between the probabilities of four pairs of T-conjugated transitions, for example, B¯¯¯0→B− and B−→B¯¯¯0, as a function of the time difference between the two B decays. Using 468×106 BB¯¯¯ pairs produced in Υ(4S) decays collected by the BABAR detector at SLAC, we measure T-violating parameters in the time evolution of neutral B mesons, yielding ΔS+T=−1.37±0.14(stat)±0.06(syst) and ΔS−T=1.17±0.18(stat)±0.11(syst). These nonzero results represent the first direct observation of T violation through the exchange of initial and final states in transitions that can only be connected by a T-symmetry transformation.DOE and NSF (USA), NSERC (Canada), CEA and CNRS-IN2P3 (France), BMBF and DFG(Germany), INFN (Italy), FOM (The Netherlands), NFR (Norway), MES (Russia), MINECO (Spain), STFC (United Kingdom). Individuals have received support from the Marie Curie EIF (European Union), the A. P. Sloan Foundation (USA) and the Binational Science Foundation (USA-Israel)

Improved Limits on B0B^{0} decays to invisible (+γ)(+\gamma) final states

We establish improved upper limits on branching fractions for B0 decays to final States 10 where the decay products are purely invisible (i.e., no observable final state particles) and for final states where the only visible product is a photon. Within the Standard Model, these decays have branching fractions that are below the current experimental sensitivity, but various models of physics beyond the Standard Model predict significant contributions for these channels. Using 471 million BB pairs collected at the Y(4S) resonance by the BABAR experiment at the PEP-II e+e- storage ring at the SLAC National Accelerator Laboratory, we establish upper limits at the 90% confidence level of 2.4x10^-5 for the branching fraction of B0-->Invisible and 1.7x10^-5 for the branching fraction of B0-->Invisible+gammaComment: 8 pages, 3 postscript figures, submitted to Phys. Rev. D (Rapid Communications