Chiral ring in the 4-D W(3) string
I summarize some recent results obtained in collaboration with P.~Bouwknegt and K.~Pilch on the spectrum of physical states in $\cW_3$ gravity coupled to $c=2$ matter. In particular, it is shown that the algebra of operators corresponding to physical states -- defined as a semi-infinite (or BRST) cohomology of the $\cW_3$ algebra -- carries the structure of a G-algebra. This G-algebra has a quotient which is isomorphic to the G-algebra of polyvector fields on the base affine space of $SL(3,\CC)$. Details have appeared elsewhere. To appear (with title change) in the proceedings of the ``H.S. Green and A. Hurst Festschrift: Confronting the Infinite'' Adelaide, March 1994.

title: Minimal models on Riemann surfaces
abstract: We extend the Coulomb gas representation of minimal model correlation functions to higher genius Riemann surfaces. Specifically, we incorporate the “BRS” structure of this representation into the operator formalism. This allows traces over the spectrum of a minimal model to be computed from traces over Fock spaces of a free scalar field. This our results are obtained by standard sewing techniques. The formulation is general, but we present here in particular the two-loop characters of the Ising model.

title: Free Field Approach to 2-Dimensional Conformal Field Theories

title: BV Structure of the Cohomology of Nilpotent Subalgebras and the Geometry of(W) Strings
abstract: AbstractGiven a simple, simply laced, complex Lie algebra 
$$\mathfrak{g}$$
corresponding to the Lie group G, let 
$$\mathfrak{n}_ + $$
 be thesubalgebra generated by the positive roots. In this Letter we construct aBV algebra 
$${\text{BV}}[\mathfrak{g}]$$
 whose underlying graded commutative algebra is given by the cohomology, with respect to 
$$\mathfrak{n}_ + $$
, of the algebra of regular functions on G with values in 
$$ \wedge (\mathfrak{n}_ + \backslash \mathfrak{g})$$
. We conjecture that 
$${\text{BV}}[\mathfrak{g}]$$
 describes the algebra of allphysical (i.e., BRST invariant) operators of the noncritical 
$$\mathcal{W}[\mathfrak{g}]$$
string. The conjecture is verified in the two explicitly known cases,
$$\mathfrak{g} = \mathfrak{s}\mathfrak{l}$$
2 (the Virasoro string) and 
$$\mathfrak{g} = \mathfrak{s}\mathfrak{l}$$
3 (the 
$$\mathcal{W}_3 $$
 string).

title: Fusing the coordinates of quantum superspace
abstract: We introduce the notion of a fused quantum superplane by allowing for terms θθ ∼ x in the defining relations. We develop the differential calculus for a large class of fused quantum superplanes related to particular solutions of the Yang-Baxter equation.

title: Covariant field theory of the compactified closed bosonic string
abstract: We covariantly first-quantize, via the BRST approach, the closed bosonic string compactified on a torus — in particular the 18-dimensional theory with E8 × E8 gauge bosons. Further, we give the corresponding free field theory. Thus the model is ready for the introduction of string interactions, and may be very useful for the study of gauge interactions in string theories.

title: x and ξ scaling of the nuclear structure function at large x
abstract: Inclusive electron scattering data are presented for ^2H, C, Fe, and Au targets at an incident electron energy of 4.045 GeV for a range of momentum transfers from Q^2=1 to 7 (GeV/c)^2. Data were taken at Jefferson Laboratory for low values of energy loss, corresponding to values of Bjorken x ≳ 1. The structure functions do not show scaling in x in this range, where inelastic scattering is not expected to dominate the cross section. The data do show scaling, however, in the Nachtmann variable ξ. This scaling appears to be the result of Bloom- Gilman duality in the nucleon structure function combined with the Fermi motion of the nucleons in the nucleus. The resulting extension of scaling to larger values of ξ opens up the possibility of accessing nuclear structure functions in the high-x region at lower values of Q^2 than previously believed.

title: Measurements of the nucleon spin structure at SLAC in end station A.

title: Measurement of the lifetime of the $B_c^+$ meson using the $B_c^+\rightarrow J/\psi\pi^+$ decay mode
abstract: The difference in total widths between the $B_c^+$ and $B^+$ mesons is measured using 3.0fb$^{-1}$ of data collected by the LHCb experiment in 7 and 8 TeV centre-of-mass energy proton-proton collisions at the LHC. Through the study of the time evolution of $B_c^+ \rightarrow J/\psi \pi^+$ and $B^+\rightarrow J/\psi K^+$ decays, the width difference is measured to be 
$$ \Delta\Gamma \equiv \Gamma_{B_c^+} - \Gamma_{B^+} = 4.46 \pm 0.14 \pm 0.07mm^{-1}c,$$ where the first uncertainty is statistical and the second systematic. The known lifetime of the $B^+$ meson is used to convert this to a precise measurement of the $B_c^+$ lifetime, 
$$\tau_{B_c^+} = 513.4 \pm 11.0 \pm 5.7fs,$$ where the first uncertainty is statistical and the second systematic.

title: Observation of Z production in proton-lead collisions at LHCb
abstract: A bstractThe first observation of Z boson production in proton-lead collisions at a centre-of-mass energy per proton-nucleon pair of sNN$$ \sqrt{s_{N\;N}} $$ = 5 TeV is presented. The data sample corresponds to an integrated luminosity of 1.6 nb−1 collected with the LHCb detector. The Z candidates are reconstructed from pairs of oppositely charged muons with pseudorapidities between 2.0 and 4.5 and transverse momenta above 20 GeV/c. The invariant dimuon mass is restricted to the range 60 − 120 GeV/c. The Z production cross-section is measured to be
σZ→μ+μ−fwd=13.5−4.0+5.4stat.±1.2syst.nb$$ {\sigma_Z}_{\to {\mu}^{+}{\mu}^{-}}\left(\mathrm{fwd}\right)={13.5}_{-4.0}^{+5.4}\left(\mathrm{stat}.\right)\pm 1.2\left(\mathrm{syst}.\right)\mathrm{nb} $$
 in the direction of the proton beam and
σZ→μ+μ−bwd=10.7−5.1+8.4stat.±1.0syst.nb$$ {\sigma}_{Z\to {\mu}^{+}{\mu}^{-}}\left(\mathrm{bwd}\right)={10.7}_{-5.1}^{+8.4}\left(\mathrm{stat}.\right)\pm 1.0\left(\mathrm{syst}.\right)\mathrm{nb} $$
 in the direction of the lead beam, where the first uncertainty is statistical and the second systematic.

title: Model-independent search for $CP$ violation in $D^{0} \to K^{-}K^{+}\pi^{-}\pi^{+}$ and $D^{0} \to \pi^{-}\pi^{+}\pi^{+}\pi^{-}$ decays
abstract: A search for CP violation in the phase-space structures of 130 and 15 decays to the final states K-K+pi(-)pi(+) and pi(-)pi(+)pi(+)pi(-) is presented. The search is carried out with a data set corresponding to an integrated luminosity of 1.0 fb(-1) collected in 2011 by the LHCb experiment in pp collisions at a centre-of-mass energy of 7 TeV. For the K-K+pi(-)pi(+) final state, the four-body phase space is divided into 32 bins, each bin with approximately 1800 decays. The p-value under the hypothesis of no CP violation is 9.1%, and in no bin is a CP asymmetry greater than 6.5% observed. The phase space of the pi(-)pi(+)pi(+)pi(-). final state is partitioned into 128 bins, each bin with approximately 2500 decays. The p-value under the hypothesis of no CP violation is 41%, and in no bin is a CP asymmetry greater than 5.5% observed. All results are consistent with the hypothesis of no CP violation at the current sensitivity.