731 research outputs found
Scalar--flat K\"ahler metrics with conformal Bianchi V symmetry
We provide an affirmative answer to a question posed by Tod \cite{Tod:1995b},
and construct all four-dimensional Kahler metrics with vanishing scalar
curvature which are invariant under the conformal action of Bianchi V group.
The construction is based on the combination of twistor theory and the
isomonodromic problem with two double poles. The resulting metrics are
non-diagonal in the left-invariant basis and are explicitly given in terms of
Bessel functions and their integrals. We also make a connection with the LeBrun
ansatz, and characterise the associated solutions of the SU(\infty) Toda
equation by the existence a non-abelian two-dimensional group of point
symmetries.Comment: Dedicated to Maciej Przanowski on the occasion of his 65th birthday.
Minor corrections. To appear in CQ
Strominger--Yau--Zaslow geometry, Affine Spheres and Painlev\'e III
We give a gauge invariant characterisation of the elliptic affine sphere
equation and the closely related Tzitz\'eica equation as reductions of real
forms of SL(3, \C) anti--self--dual Yang--Mills equations by two
translations, or equivalently as a special case of the Hitchin equation.
We use the Loftin--Yau--Zaslow construction to give an explicit expression
for a six--real dimensional semi--flat Calabi--Yau metric in terms of a
solution to the affine-sphere equation and show how a subclass of such metrics
arises from 3rd Painlev\'e transcendents.Comment: 38 pages. Final version. To appear in Communications in Mathematical
Physic
Observation of vortex dynamics in arrays of nanomagnets
Vortex dynamics within arrays of square ferromagnetic nanoelements have been studied by time-resolved
scanningKerr microscopy (TRSKM),while x-ray photoemission electronmicroscopy has been used to investigate
the equilibrium magnetic state of the arrays. An alternating field demagnetization process was found to initialize
a distribution of equilibrium states within the individual elements of the array, including quasiuniform states
and vortex states of different chirality and core polarization. Repeated initialization revealed some evidence of
stochastic behavior during the formation of the equilibrium state. TRSKM with a spatial resolution of ∼300 nm
was used to detect vortex gyration within arrays of square nanoelements of 250-nm lateral size. Two arrays were
studied consisting of a 9 × 9 and 5 × 5 arrangement of nanoelements with 50- and 500-nm element edge-to-edge
separation to encourage strong and negligible dipolar interactions, respectively. In the 5 × 5 element array,
TRSKM images, acquired at a fixed phase of the driving microwave magnetic field, revealed differences in the
gyrotropic phase within individual elements. While some phase variation is attributed to the dispersion in the
size and shape of elements, the vortex chirality and core polarization are also shown to influence the phase. In
the 9 × 9 array, strong magneto-optical response due to vortex gyration was observed across regions with length
equal to either one or two elements. Micromagnetic simulations performed for 2 × 2 arrays of elements suggest
that particular combinations of vortex chirality and polarization in neighboring elements are required to generate
the observed magneto-optical contrast.Engineering and Physical Sciences Research Council (EPSRC
Long and short paths in uniform random recursive dags
In a uniform random recursive k-dag, there is a root, 0, and each node in
turn, from 1 to n, chooses k uniform random parents from among the nodes of
smaller index. If S_n is the shortest path distance from node n to the root,
then we determine the constant \sigma such that S_n/log(n) tends to \sigma in
probability as n tends to infinity. We also show that max_{1 \le i \le n}
S_i/log(n) tends to \sigma in probability.Comment: 16 page
Measurement of the Branching Fraction of the Decay in Fully Reconstructed Events at Belle
We present an analysis of the exclusive
decay, where represents an
electron or a muon, with the assumption of charge-conjugation symmetry and
lepton universality. The analysis uses the full data sample
collected by the Belle detector, corresponding to 711 fb of integrated
luminosity. We select the events by fully reconstructing one meson in
hadronic decay modes, subsequently determining the properties of the other
meson. We extract the signal yields using a binned maximum-likelihood fit to
the missing-mass squared distribution in bins of the invariant mass of the two
pions or the momentum transfer squared. We measure a total branching fraction
of , where the
uncertainties are statistical and systematic, respectively. This result is the
first reported measurement of this decay.Comment: 23 pages, 19 figure
Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach
We report a measurement of violating asymmetries in decays with a time-dependent Dalitz approach. This analysis
is based on a data sample of pairs accumulated
at the resonance with the Belle detector at the KEKB
asymmetric-energy collider. As the result of an unbinned maximum
likelihood fit to the selected candidates, the mixing-induced and direct
violation parameters, and are obtained for
, and other decays. We find four solutions that describe the data. There are
\{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm
2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm
8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = &
(27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to
\phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The
values for the violating phase in are similar
but other properties of the Dalitz plot are quite different for the four
solutions. These four solutions have consistent values for
all three meson decay channels and none of them deviates significantly from
the values measured in decays with the currently
available statistics. In addition, we find no significant direct
violation.Comment: submitted to PR
Measurements of Branching Fractions and Time-dependent CP Violating Asymmetries in Decays
We report measurements of branching fractions and time-dependent CP
asymmetries in and decays
using a data sample that contains pairs
collected at the resonance with the Belle detector at the KEKB
asymmetric-energy collider. We determine the branching fractions to
be
and . We measure CP asymmetry parameters and in and , ,
, and in , where the first uncertainty is
statistical and the second is systematic. We exclude the conservation of CP
symmetry in both decays at equal to or greater than significance.Comment: 7 pages, 2 figure
Measurement of CP violating asymmetries in B^0 -> K^+K^- K^0_S decays with a time-dependent Dalitz approach
We report a measurement of violating asymmetries in decays with a time-dependent Dalitz approach. This analysis
is based on a data sample of pairs accumulated
at the resonance with the Belle detector at the KEKB
asymmetric-energy collider. As the result of an unbinned maximum
likelihood fit to the selected candidates, the mixing-induced and direct
violation parameters, and are obtained for
, and other decays. We find four solutions that describe the data. There are
\{eqnarray*} \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (32.2 \pm 9.0 \pm
2.6 \pm 1.4)^{\circ}; \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = & (26.2 \pm
8.8 \pm 2.7 \pm 1.2)^{\circ};\\ \phi_1^{\rm eff}(B^0\to \phi(1020) K^0_S) & = &
(27.3 \pm 8.6 \pm 2.8 \pm 1.3)^{\circ}\; {\rm and}\\ \phi_1^{\rm eff}(B^0\to
\phi(1020) K^0_S) & = & (24.3 \pm 8.0 \pm 2.9 \pm 5.2)^{\circ}.{eqnarray*}\ The
values for the violating phase in are similar
but other properties of the Dalitz plot are quite different for the four
solutions. These four solutions have consistent values for
all three meson decay channels and none of them deviates significantly from
the values measured in decays with the currently
available statistics. In addition, we find no significant direct
violation.Comment: submitted to PR
Search for Time-Dependent CPT Violation in Hadronic and Semileptonic B Decays
We report a new sensitive search for CPT violation, which includes improved
measurements of the CPT-violating parameter z and the total decay-width
difference normalized to the averaged width DeltaGamma_d/Gamma_d of the two Bd
mass eigenstates. The results are based on a data sample of 535 x 10^6 BBbar
pairs collected at the Upsilon(4S) resonance with the Belle detector at the
KEKB asymmetric-energy e^+e^- collider. We obtain Re(z) = [+1.9 +/- 3.7 (stat)
+/- 3.3 (syst)] x 10^{-2}, Im(z) = [-5.7 +/- 3.3 (stat) +/- 3.3 (syst)] x
10^{-3}, and DeltaGamma_d/Gamma_d = [-1.7 +/- 1.8 (stat) +/- 1.1 (syst)] x
10^{-2}, all of which are consistent with zero. This is the most precise single
measurement of these parameters in the neutral B-meson system to date.Comment: 7 pages, 3 figures, 2 tables, LaTeX; addition of supplemental
information, corrections of typos, results unchange
Evidence for the Suppressed Decay B- -> DK-, D -> K+pi-
The suppressed decay chain B- -> DK-, D -> K+pi-, where D indicates a anti-D0
or D0 state, provides important information on the CP-violating angle phi_3. We
measure the ratio R_{DK} of the decay rates to the favored mode B- -> DK-, D ->
K-pi+ to be R_{DK} = [1.63^{+0.44}_{-0.41}(stat)^{+0.07}_{-0.13}(syst)] x
10^{-2}, which indicates the first evidence of the signal with a significance
of 4.1sigma. We also measure the asymmetry A_{DK} between the charge-conjugate
decays to be A_{DK} = -0.39^{+0.26}_{-0.28}(stat)^{+0.04}_{-0.03}(syst). The
results are based on the full 772 x 10^6 B anti-B pair data sample collected at
the Upsilon(4S) resonance with the Belle detector.Comment: 6 pages, 2 figures, 2 tables, accepted by Physical Review Letter
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