Chiral Corrections to the Hyperon Vector Form Factors

We present the complete calculation of the SU(3)-breaking corrections to the hyperon vector form factors up to O(p^4) in the Heavy Baryon Chiral Perturbation Theory. Because of the Ademollo-Gatto theorem, at this order the results do not depend on unknown low energy constants and allow to test the convergence of the chiral expansion. We complete and correct previous calculations and find that O(p^3) and O(1/M_0) corrections are important. We also study the inclusion of the decuplet degrees of freedom, showing that in this case the perturbative expansion is jeopardized. These results raise doubts on the reliability of the chiral expansion for hyperons.Comment: 20 pages, 4 figures, v2: published versio

Organic Liquid TPCs for Neutrino Physics

We present a new concept for anti-neutrino detection, an organic liquid TPC with a volume of the order of m$^3$ and an energy resolution of the order of 1% at 3 MeV and a sub-cm spatial resolution.Comment: 11 pages, 3 figure

Skew convolution semigroups and affine Markov processes

A general affine Markov semigroup is formulated as the convolution of a homogeneous one with a skew convolution semigroup. We provide some sufficient conditions for the regularities of the homogeneous affine semigroup and the skew convolution semigroup. The corresponding affine Markov process is constructed as the strong solution of a system of stochastic equations with non-Lipschitz coefficients and Poisson-type integrals over some random sets. Based on this characterization, it is proved that the affine process arises naturally in a limit theorem for the difference of a pair of reactant processes in a catalytic branching system with immigration.Comment: Published at http://dx.doi.org/10.1214/009117905000000747 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Transience and recurrence of random walks on percolation clusters in an ultrametric space

We study existence of percolation in the hierarchical group of order $N$, which is an ultrametric space, and transience and recurrence of random walks on the percolation clusters. The connection probability on the hierarchical group for two points separated by distance $k$ is of the form $c_k/N^{k(1+\delta)}, \delta>-1$, with $c_k=C_0+C_1\log k+C_2k^\alpha$, non-negative constants $C_0, C_1, C_2$, and $\alpha>0$. Percolation was proved in Dawson and Gorostiza (2013) for $\delta0$, with $\alpha>2$. In this paper we improve the result for the critical case by showing percolation for $\alpha>0$. We use a renormalization method of the type in the previous paper in a new way which is more intrinsic to the model. The proof involves ultrametric random graphs (described in the Introduction). The results for simple (nearest neighbour) random walks on the percolation clusters are: in the case $\delta<1$ the walk is transient, and in the critical case $\delta=1, C_2>0,\alpha>0$, there exists a critical $\alpha_c\in(0,\infty)$ such that the walk is recurrent for $\alpha<\alpha_c$ and transient for $\alpha>\alpha_c$. The proofs involve graph diameters, path lengths, and electric circuit theory. Some comparisons are made with behaviours of random walks on long-range percolation clusters in the one-dimensional Euclidean lattice.Comment: 27 page

Shedding Light on the Matter of Abell 781

The galaxy cluster Abell 781 West has been viewed as a challenge to weak gravitational lensing mass calibration, as Cook and dell'Antonio (2012) found that the weak lensing signal-to-noise in three independent sets of observations was consistently lower than expected from mass models based on X-ray and dynamical measurements. We correct some errors in statistical inference in Cook and dell'Antonio (2012) and show that their own results agree well with the dynamical mass and exhibit at most 2.2--2.9$\sigma$ low compared to the X-ray mass, similar to the tension between the dynamical and X-ray masses. Replacing their simple magnitude cut with weights based on source photometric redshifts eliminates the tension between lensing and X-ray masses; in this case the weak lensing mass estimate is actually higher than, but still in agreement with, the dynamical estimate. A comparison of lensing analyses with and without photometric redshifts shows that a 1--2$\sigma$ chance alignment of low-redshift sources lowers the signal-to-noise observed by all previous studies which used magnitude cuts rather than photometric redshifts. The fluctuation is unexceptional, but appeared to be highly significant in Cook and dell'Antonio (2012) due to the errors in statistical interpretation.Comment: 7 pages, submitted to MNRA

GDL: a model infrastructure for a regional digital library

This brief article describes the early days of the Glasgow Digital Library (GDL), when it was a cross-sectoral and city-wide collaborative initiative involving Strathclyde, Glasgow and Caledonian Universities, as well as Glasgow City Libraries and Archives and the Glasgow Colleges Group

Vector form factor in K_l3 semileptonic decay with two flavors of dynamical domain-wall quarks

We calculate the vector form factor in K \to \pi l \nu semileptonic decays at zero momentum transfer f_+(0) from numerical simulations of two-flavor QCD on the lattice. Our simulations are carried out on 16^3 \times 32 at a lattice spacing of a \simeq 0.12 fm using a combination of the DBW2 gauge and the domain-wall quark actions, which possesses excellent chiral symmetry even at finite lattice spacings. The size of fifth dimension is set to L_s=12, which leads to a residual quark mass of a few MeV. Through a set of double ratios of correlation functions, the form factor calculated on the lattice is accurately interpolated to zero momentum transfer, and then is extrapolated to the physical quark mass. We obtain f_+(0)=0.968(9)(6), where the first error is statistical and the second is the systematic error due to the chiral extrapolation. Previous estimates based on a phenomenological model and chiral perturbation theory are consistent with our result. Combining with an average of the decay rate from recent experiments, our estimate of f_+(0) leads to the Cabibbo-Kobayashi-Maskawa (CKM) matrix element |V_{us}|=0.2245(27), which is consistent with CKM unitarity. These estimates of f_+(0) and |V_{us}| are subject to systematic uncertainties due to the finite lattice spacing and quenching of strange quarks, though nice consistency in f_+(0) with previous lattice calculations suggests that these errors are not large.Comment: 23 pages, 11 figures, 7 tables, RevTeX4; v3: one table added, results and conclusions unchanged, final version to appear in Phys.Rev.

Hierarchical equilibria of branching populations

The objective of this paper is the study of the equilibrium behavior of a population on the hierarchical group $\Omega_N$ consisting of families of individuals undergoing critical branching random walk and in addition these families also develop according to a critical branching process. Strong transience of the random walk guarantees existence of an equilibrium for this two-level branching system. In the limit $N\to\infty$ (called the hierarchical mean field limit), the equilibrium aggregated populations in a nested sequence of balls $B^{(N)}_\ell$ of hierarchical radius $\ell$ converge to a backward Markov chain on $\mathbb{R_+}$. This limiting Markov chain can be explicitly represented in terms of a cascade of subordinators which in turn makes possible a description of the genealogy of the population.Comment: 62 page