Casimir effect due to a single boundary as a manifestation of the Weyl problem

The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases the divergences can be eliminated by methods such as zeta-function regularization or through physical arguments (ultraviolet transparency of the boundary would provide a cutoff). Using the example of a massless scalar field theory with a single Dirichlet boundary we explore the relationship between such approaches, with the goal of better understanding the origin of the divergences. We are guided by the insight due to Dowker and Kennedy (1978) and Deutsch and Candelas (1979), that the divergences represent measurable effects that can be interpreted with the aid of the theory of the asymptotic distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having geometrical origin, and an "intrinsic" term that is independent of the cutoff. The Weyl terms make a measurable contribution to the physical situation even when regularization methods succeed in isolating the intrinsic part. Regularization methods fail when the Weyl terms and intrinsic parts of the Casimir effect cannot be clearly separated. Specifically, we demonstrate that the Casimir self-energy of a smooth boundary in two dimensions is a sum of two Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a geometrical term that is independent of cutoff, and a non-geometrical intrinsic term. As by-products we resolve the puzzle of the divergent Casimir force on a ring and correct the sign of the coefficient of linear tension of the Dirichlet line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references added, version to be published in J. Phys.

Vortices, Instantons and Branes

The purpose of this paper is to describe a relationship between the moduli space of vortices and the moduli space of instantons. We study charge k vortices in U(N) Yang-Mills-Higgs theories and show that the moduli space is isomorphic to a special Lagrangian submanifold of the moduli space of k instantons in non-commutative U(N) Yang-Mills theories. This submanifold is the fixed point set of a U(1) action on the instanton moduli space which rotates the instantons in a plane. To derive this relationship, we present a D-brane construction in which the dynamics of vortices is described by the Higgs branch of a U(k) gauge theory with 4 supercharges which is a truncation of the familiar ADHM gauge theory. We further describe a moduli space construction for semi-local vortices, lumps in the CP(N) and Grassmannian sigma-models, and vortices on the non-commutative plane. We argue that this relationship between vortices and instantons underlies many of the quantitative similarities shared by quantum field theories in two and four dimensions.Comment: 32 Pages, 4 Figure

The Spin Structure of the Nucleon

We present an overview of recent experimental and theoretical advances in our understanding of the spin structure of protons and neutrons.Comment: 84 pages, 29 figure

Observations of bedforms on a dissipative macrotidal beach

NERC NE/H004262/1 and NE/H02543X/1 DRIB

Hadronic Mass Moments in Inclusive Semileptonic B Meson Decays

We have measured the first and second moments of the hadronic mass-squared distribution in B -> X_c l nu, for P(lepton) > 1.5 GeV/c. We find <M_X^2 - M_D[Bar]^2> = 0.251 +- 0.066 GeV^2, )^2 > = 0.576 +- 0.170 GeV^4, where M_D[Bar] is the spin-averaged D meson mass. From that first moment and the first moment of the photon energy spectrum in b -> s gamma, we find the HQET parameter lambda_1 (MS[Bar], to order 1/M^3 and beta_0 alpha_s^2) to be -0.24 +- 0.11 GeV^2. Using these first moments and the B semileptonic width, and assuming parton-hadron duality, we obtain |V_cb| = 0.0404 +- 0.0013.Comment: 11 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, submitted to PR

Observation of the Ωc0\Omega_{c}^{0} Charmed Baryon at CLEO

The CLEO experiment at the CESR collider has used 13.7 fb$^{-1}$ of data to search for the production of the $\Omega_c^0$ (css-ground state) in $e^{+}e^{-}$ collisions at $\sqrt{s} \simeq 10.6$ {\rm GeV}. The modes used to study the $\Omega_c^0$ are $\Omega^- \pi^+$, $\Omega^- \pi^+ \pi^0$, $\Xi^- K^- pi^+ \pi^+$, $\Xi^0 K^- pi^+$, and $\Omega^- \pi^+ \pi^- \pi^+$. We observe a signal of 40.4$\pm$9.0(stat) events at a mass of 2694.6$\pm$2.6(stat)$\pm$1.9(syst) {\rm MeV/$c^2$}, for all modes combined.Comment: 10 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Observation of B→ϕKB\to \phi K and B→ϕK∗B\to \phi K^{*}

We have studied two-body charmless hadronic decays of $B$ mesons into the final states phi K and phi K^*. Using 9.7 million $B\bar{B}$ pairs collected with the CLEO II detector, we observe the decays B- -> phi K- and B0 -> phi K*0 with the following branching fractions: BR(B- -> phi K-)=(5.5 +2.1-1.8 +- 0.6) x 10^{-6} and BR(B0 -> phi K*0)=(11.5 +4.5-3.7 +1.8-1.7) x 10^{-6}. We also see evidence for the decays B0 -> phi K0 and B- -> phi K*-. However, since the statistical significance is not overwhelming for these modes we determine upper limits of <12.3 x 10^{-6} and <22.5 x 10^{-6} (90% C.L.) respectively.Comment: 9 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Evidence of New States Decaying into Ξc′π\Xi^{\prime}_{c}\pi

Using 13.7 $fb^{-1}$ of data recorded by the CLEO detector at CESR, we report evidence for two new charmed baryons: one decaying into $\Xi_c^{0 \prime}\pi^+$ with the subsequent decay $\Xi_c^{0 \prime} \to \Xi_c^0 \gamma$, and its isospin partner decaying into $\Xi_c^{+ \prime} \pi^-$ followed by $\Xi_c^{+\prime} \to \Xi_c^+\gamma$. We measure the following mass differences for the two states: $M(\Xi_c^0 \gamma \pi^+)-M(\Xi_c^0)$=318.2+-1.3+-2.9 MeV, and $M(\Xi_c^+ \gamma \pi^-)-M(\Xi_c^+)$=324.0+-1.3+-3.0 MeV. We interpret these new states as the $J^P = 1/2^- \Xi_{c1}$ particles, the charmed-strange analogs of the $\Lambda_{c1}^+(2593)$.Comment: 10 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Measurement of the Relative Branching Fraction of Υ(4S)\Upsilon(4S) to Charged and Neutral B-Meson Pairs

We analyze 9.7 x 10^6 B\bar{B}$ pairs recorded with the CLEO detector to determine the production ratio of charged to neutral B-meson pairs produced at the Y(4S) resonance. We measure the rates for B^0 -> J/psi K^{(*)0} and B^+ -> J/psi K^{(*)+} decays and use the world-average B-meson lifetime ratio to extract the relative widths f+-/f00 = Gamma(Y(4S) -> B+B-)/Gamma(Y(4S) -> B0\bar{B0}) = = 1.04 +/- 0.07(stat) +/- 0.04(syst). With the assumption that f+- + f00 = 1, we obtain f00 = 0.49 +/- 0.02(stat) +/- 0.01(syst) and f+- = 0.51 +/- 0.02(stat) +/- 0.01(syst). This production ratio and its uncertainty apply to all exclusive B-meson branching fractions measured at the Y(4S) resonance.Comment: 11 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

First Observation of B -> D(*) rho', rho' -> omega pi-

We report on the observation of B-> D(*) pi+ pi- pi- pi^o decays. The branching ratios for D*+ and D*o are (1.72+/-0.14+/-0.24)% and (1.80+/-0.24+/-0.27)%, respectively. Each final state has a D* omega pi- component, with branching ratios (0.29+/-0.03+/-0.04)% and (0.45+/-0.10+/-0.07)% for the D*+ and D*o modes, respectively. We also observe B -> D omega pi- decays. The branching ratios for D+ and Do are (0.28+/-0.05+/-0.04)% and (0.41+/-0.07+/-0.06)%, respectively. A spin parity analysis of the D omega pi- final state prefers a wide 1^- resonance. A fit to the omega pi- mass spectrum finds a central mass of (1349+/-25^{+10}_{-5}) MeV and width of (547+/-86^{+46}_{-45}) MeV. We identify this object as the rho(1450) or the \rho'.Comment: 42 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, To Appear in PR