On the Mathematics of the Law of Mass Action

In 1864,Waage and Guldberg formulated the "law of mass action." Since that time, chemists, chemical engineers, physicists and mathematicians have amassed a great deal of knowledge on the topic. In our view, sufficient understanding has been acquired to warrant a formal mathematical consolidation. A major goal of this consolidation is to solidify the mathematical foundations of mass action chemistry -- to provide precise definitions, elucidate what can now be proved, and indicate what is only conjectured. In addition, we believe that the law of mass action is of intrinsic mathematical interest and should be made available in a form that might transcend its application to chemistry alone. We present the law of mass action in the context of a dynamical theory of sets of binomials over the complex numbers.Comment: 40 pages, no figure

Precise measurement of the W-boson mass with the CDF II detector

We have measured the W-boson mass MW using data corresponding to 2.2/fb of integrated luminosity collected in proton-antiproton collisions at 1.96 TeV with the CDF II detector at the Fermilab Tevatron collider. Samples consisting of 470126 W->enu candidates and 624708 W->munu candidates yield the measurement MW = 80387 +- 12 (stat) +- 15 (syst) = 80387 +- 19 MeV. This is the most precise measurement of the W-boson mass to date and significantly exceeds the precision of all previous measurements combined

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

Measurement of VH, H → b b ¯ production as a function of the vector-boson transverse momentum in 13 TeV pp collisions with the ATLAS detector

Cross-sections of associated production of a Higgs boson decaying into bottom-quark pairs and an electroweak gauge boson, W or Z, decaying into leptons are measured as a function of the gauge boson transverse momentum. The measurements are performed in kinematic fiducial volumes defined in the `simplified template cross-section' framework. The results are obtained using 79.8 fb-1 of proton-proton collisions recorded by the ATLAS detector at the Large Hadron Collider at a centre-of-mass energy of 13 TeV. All measurements are found to be in agreement with the Standard Model predictions, and limits are set on the parameters of an effective Lagrangian sensitive to modifications of the Higgs boson couplings to the electroweak gauge bosons

Search for heavy bottom-like quarks decaying to an electron or muon and jets in ppˉp\bar{p} collisions at s=1.96\sqrt{s}=1.96 TeV

We report the most sensitive direct search for pair production of fourth-generation bottom-like chiral quarks ($b'$) each decaying promptly to $tW$. We search for an excess of events with an electron or muon, at least five jets (one indentified as due to a $b$ or $c$ quark) and an imbalance of transverse momentum using data from $p\bar{p}$ collisions collected by the CDF II detector at Fermilab with an integrated luminosity of 4.8 fb$^{-1}$. We observe events consistent with background expectation and calculate upper limits on the $b'$ pair production cross section ($\sigma_{b\bar{b'}}\lesssim 30$ fb for $m_{b'}>$375 GeV/$c^2$) and exclude $m_{b'}<372$ \gevcc at 95% confidence level.Comment: For submission to PR

Search for heavy neutral Higgs bosons produced in association with b-quarks and decaying into b-quarks at root s=13 TeV with the ATLAS detector

A search for heavy neutral Higgs bosons produced in association with one or two b -quarks and decaying to b -quark pairs is presented using 27.8  fb − 1 of √ s = 13  TeV proton-proton collision data recorded by the ATLAS detector at the Large Hadron Collider during 2015 and 2016. No evidence of a signal is found. Upper limits on the heavy neutral Higgs boson production cross section times its branching ratio to b ¯ b are set, ranging from 4.0 to 0.6 pb at 95% confidence level over a Higgs boson mass range of 450 to 1400 GeV. Results are interpreted within the two-Higgs-doublet model and the minimal supersymmetric Standard Model

Measurement of single top-quark production in association with a W boson in the single-lepton channel at \sqrt{s} = 8\,\text {TeV} with the ATLAS detector

The production cross-section of a top quark in association with a W boson is measured using proton–proton collisions at \sqrt{s} = 8\,\text {TeV}. The dataset corresponds to an integrated luminosity of 20.2\,\text {fb}^{-1}, and was collected in 2012 by the ATLAS detector at the Large Hadron Collider at CERN. The analysis is performed in the single-lepton channel. Events are selected by requiring one isolated lepton (electron or muon) and at least three jets. A neural network is trained to separate the tW signal from the dominant t{\bar{t}} background. The cross-section is extracted from a binned profile maximum-likelihood fit to a two-dimensional discriminant built from the neural-network output and the invariant mass of the hadronically decaying W boson. The measured cross-section is \sigma _{tW} = 26 \pm 7\,\text {pb}, in good agreement with the Standard Model expectation