A Measurement of the Branching Ratio of the pi0 Dalitz Decay using K(L) ---> 3 pi0 Decays from KTeV

The authors present a measurement of B({pi}{sup 0} {yields} e{sup +}e{sup -}{gamma})/B({pi}{sup 0} {yields} {gamma}{gamma}) using data taken in 1999 by the E832 KTeV experiment at Fermilab. The {pi}{sup 0}s were produced by K{sub L} decays in flight that are fully reconstructed. They find 63,693 K{sub L} {yields} 3{pi}{sup 0} {yields} {gamma}{gamma} {gamma}{gamma} e{sup +}e{sup -}{gamma} decays in KTeV data (an increase of a factor of {approx} 20 in event statistics over previous experiments), and normalize to K{sub L} {yields} 3{pi}{sup 0} {yields} 6{gamma}, to extract B({pi}{sup 0} {yields} e{sup +}e{sup -}{gamma}, m{sub e{sup +}e{sup -}} > 15 MeV/c{sup 2})/B({pi}{sup 0} {yields} {gamma}{gamma}) = (3.920 {+-} 0.016 {+-} 0.036) x 10{sup -3}, where the first error is statistical and the second is systematic. Using the Mikaelian and Smith prediction for the e{sup +}e{sup -} mass spectrum as implemented in the KTeV Monte Carlo to correct to the full e{sup +}e{sup -} mass range yields B({pi}{sup 0} {yields} e{sup +}e{sup -}{gamma})/B({pi}{sup 0} {yields} {gamma}{gamma}) = (1.1559 {+-} 0.0046 {+-} 0.0107)%. This result is consistent with previous measurements and with theoretical predictions, and the uncertainty is a factor of three smaller than any previous measurement

Wall-crossing structures in Donaldson-Thomas invariants, integrable systems and Mirror Symmetry

We introduce the notion of Wall-Crossing Structure and discuss it in several examples including complex integrable systems, Donaldson-Thomas invariants and Mirror Symmetry. For a big class of non-compact Calabi-Yau 3-folds we construct complex integrable systems of Hitchin type with the base given by the moduli space of deformations of those 3-folds. Then Donaldson-Thomas invariants of the Fukaya category of such a Calabi-Yau 3-fold can be (conjecturally) described in two more ways: in terms of the attractor flow on the base of the corresponding complex integrable system and in terms of the skeleton of the mirror dual to the total space of the integrable system. The paper also contains a discussion of some material related to the main subject, e.g. Betti model of Hitchin systems with irregular singularities, WKB asymptotics of connections depending on a small parameter, attractor points in the moduli space of complex structures of a compact Calabi-Yau 3-fold, relation to cluster varieties, etc.Comment: 111 pages, accepted for Proceedings of the Cetraro Conference "Mirror Symmetry and Tropical Geometry" (Lecture Notes in Mathematics

SYZ mirror symmetry for hypertoric varieties

We construct a Lagrangian torus fibration on a smooth hypertoric variety and a corresponding SYZ mirror variety using $T$-duality and generating functions of open Gromov-Witten invariants. The variety is singular in general. We construct a resolution using the wall and chamber structure of the SYZ base.Comment: v_2: 31 pages, 5 figures, minor revision. To appear in Communications in Mathematical Physic

Dynamic critical behavior of the worm algorithm for the Ising model

We study the dynamic critical behavior of the worm algorithm for the two- and three-dimensional Ising models, by Monte Carlo simulation. The autocorrelation functions exhibit an unusual three-time-scale behavior. As a practical matter, the worm algorithm is slightly more efficient than Swendsen-Wang for simulating the two-point function of the three-dimensional Ising model

QED radiative corrections to the decay pi^0 to e^+e^-

We reconsider QED radiative corrections (RC) to the $\pi^{0}\to e^{+}e^{-}$ decay width. One kind of RC investigated earlier has a renormalization group origin and can be associated with the final state interaction of electron and positron. It determines the distribution of lepton pair invariant masses in the whole kinematic region. The other type of RC has a double-logarithmic character and is related to almost on-mass-shell behavior of the lepton form factors. The total effect of RC for the $\pi^{0}\to e^{+}e^{-}$ decay is estimated to be 3.2% and for the decay $\eta \to e^{+}e^{-}$ is 4.3%.Comment: 12 pages, 3 figure

Improved KL->pi e nu Form Factor and Phase Space Integral with Reduced Model Uncertainty

Using the published KTeV sample of 2 million KL-> pi e nu decays and a new form factor expansion with a rigorous bound on higher order terms, we present a new determination of the KL->pi e nu form factor and phase space integral. Compared to the previous KTeV result, the uncertainty in the new form factor expansion is negligible and results in an overall uncertainty in the phase space integral (IKe) that is a factor of two smaller: IKe = 0.15392 +- 0.00048 \.Comment: 3 pages, 2 figures, submitted to PRD Rapid Communicatio

Measurements of the Decay KL→e+e−γK_L \to e^+e^-\gamma

The E799-II (KTeV) experiment at Fermilab has collected 83262 $K_L \to e^+e^-\gamma$ events above a background of 79 events. We measure a decay width, normalized to the $K_L \to \pi^0\pi^0\pi^0_D$ (\pi^0 \to \gamma\gamma, \pi^0 to \gamma\gamma, \pi^0_D \to e^+e^-\gamma) decay width, of $\Gamma($K_L \to e^+e^-\gamma$)/\Gamma(K_L \to \pi^0\pi^0\pi^0_D) = (1.3302 \pm 0.0046_{stat} \pm 0.0102_{syst}) \times 10^{-3}$. We also measure parameters of two $K_L \gamma^{\ast}\gamma$ form factor models. In the Bergstrom, Masso, and Singer (BMS) parametrization, we find \caks = -0.517 \pm 0.030_{stat} \pm 0.022_{syst}. We separately fit for the first parameter of the D'Ambrosio, Isidori, and Portoles (DIP) model and find \adip = -1.729 \pm 0.043_{stat} \pm 0.028_{syst}.Comment: 5 pages, 3 figures, submitted to PR

Determination of the Parity of the Neutral Pion via the Four-Electron Decay

We present a new determination of the parity of the neutral pion via the double Dalitz decay pi^0 -> e+ e- e+ e-. Our sample, which consists of 30511 candidate decays, was collected from K_L -> pi0 pi0 pi0 decays in flight at the KTeV-E799 experiment at Fermi National Accelerator Laboratory. We confirm the negative pi^0 parity, and place a limit on scalar contributions to the pi^0 -> e+ e- e+ e- decay amplitude of less than 3.3% assuming CPT conservation. The pi^0 gamma* gamma* form factor is well described by a momentum-dependent model with a slope parameter fit to the final state phase space distribution. Additionally, we have measured the branching ratio of this mode to be B(pi^0 -> e+ e- e+ e-) = (3.26 +- 0.18) x 10^(-5).Comment: 5 pages, 4 figures. Typographical error in radiative branching ratio (Eq. 6) correcte

Search for the Rare Decays KL->pi0pi0mu+mu- and KL->pi0pi0X0->pi0pi0mu+mu-

The KTeV E799 experiment has conducted a search for the rare decays KL->pi0pi0mu+mu- and KL->pi0pi0X0->pi0pi0mu+mu-, where the X0 is a possible new neutral boson that was reported by the HyperCP experiment with a mass of (214.3 pm 0.5) MeV/c^{2}. We find no evidence for either decay. We obtain upper limits of Br(KL->pi0pi0X0->pi0pi0mu+mu-) pi0pi0mu+mu-) < 9.2 x 10^{-11} at the 90% confidence level. This result rules out the pseudoscalar X0 as an explanation of the HyperCP result under the scenario that the \bar{d}sX0 coupling is completely real