The congruence kernel of an arithmetic lattice in a rank one algebraic group over a local field

Let k be a global field and let k_v be the completion of k with respect to v, a non-archimedean place of k. Let \mathbf{G} be a connected, simply-connected algebraic group over k, which is absolutely almost simple of k_v-rank 1. Let G=\mathbf{G}(k_v). Let \Gamma be an arithmetic lattice in G and let C=C(\Gamma) be its congruence kernel. Lubotzky has shown that C is infinite, confirming an earlier conjecture of Serre. Here we provide complete solution of the congruence subgroup problem for \Gamm$ by determining the structure of C. It is shown that C is a free profinite product, one of whose factors is \hat{F}_{\omega}, the free profinite group on countably many generators. The most surprising conclusion from our results is that the structure of C depends only on the characteristic of k. The structure of C is already known for a number of special cases. Perhaps the most important of these is the (non-uniform) example \Gamma=SL_2(\mathcal{O}(S)), where \mathcal{O}(S) is the ring of S-integers in k, with S=\{v\}, which plays a central role in the theory of Drinfeld modules. The proof makes use of a decomposition theorem of Lubotzky, arising from the action of \Gamma on the Bruhat-Tits tree associated with G.Comment: 27 pages, 5 figures, to appear in J. Reine Angew. Mat

Hardness of Exact Distance Queries in Sparse Graphs Through Hub Labeling

A distance labeling scheme is an assignment of bit-labels to the vertices of an undirected, unweighted graph such that the distance between any pair of vertices can be decoded solely from their labels. An important class of distance labeling schemes is that of hub labelings, where a node $v \in G$ stores its distance to the so-called hubs $S_v \subseteq V$, chosen so that for any $u,v \in V$ there is $w \in S_u \cap S_v$ belonging to some shortest $uv$ path. Notice that for most existing graph classes, the best distance labelling constructions existing use at some point a hub labeling scheme at least as a key building block. Our interest lies in hub labelings of sparse graphs, i.e., those with $|E(G)| = O(n)$, for which we show a lowerbound of $\frac{n}{2^{O(\sqrt{\log n})}}$ for the average size of the hubsets. Additionally, we show a hub-labeling construction for sparse graphs of average size $O(\frac{n}{RS(n)^{c}})$ for some $0 < c < 1$, where $RS(n)$ is the so-called Ruzsa-Szemer{\'e}di function, linked to structure of induced matchings in dense graphs. This implies that further improving the lower bound on hub labeling size to $\frac{n}{2^{(\log n)^{o(1)}}}$ would require a breakthrough in the study of lower bounds on $RS(n)$, which have resisted substantial improvement in the last 70 years. For general distance labeling of sparse graphs, we show a lowerbound of $\frac{1}{2^{O(\sqrt{\log n})}} SumIndex(n)$, where $SumIndex(n)$ is the communication complexity of the Sum-Index problem over $Z_n$. Our results suggest that the best achievable hub-label size and distance-label size in sparse graphs may be $\Theta(\frac{n}{2^{(\log n)^c}})$ for some $0<c < 1$

Study of CP violation in Dalitz-plot analyses of B0 --> K+K-KS, B+ --> K+K-K+, and B+ --> KSKSK+

We perform amplitude analyses of the decays $B^0 \to K^+K^-K^0_S$, $B^+ \rightarrow K^+K^-K^+$, and $B^+ \to K^0_S K^0_S K^+$, and measure CP-violating parameters and partial branching fractions. The results are based on a data sample of approximately $470\times 10^6$ $B\bar{B}$ decays, collected with the BABAR detector at the PEP-II asymmetric-energy $B$ factory at the SLAC National Accelerator Laboratory. For $B^+ \to K^+K^-K^+$, we find a direct CP asymmetry in $B^+ \to \phi(1020)K^+$ of $A_{CP}= (12.8\pm 4.4 \pm 1.3)$, which differs from zero by $2.8 \sigma$. For $B^0 \to K^+K^-K^0_S$, we measure the CP-violating phase $\beta_{\rm eff} (\phi(1020)K^0_S) = (21\pm 6 \pm 2)^\circ$. For $B^+ \to K^0_S K^0_S K^+$, we measure an overall direct CP asymmetry of $A_{CP} = (4 ^{+4}_{-5} \pm 2)$. We also perform an angular-moment analysis of the three channels, and determine that the $f_X(1500)$ state can be described well by the sum of the resonances $f_0(1500)$, $f_2^{\prime}(1525)$, and $f_0(1710)$.Comment: 35 pages, 68 postscript figures. v3 - minor modifications to agree with published versio

The assembly of massive galaxies from NIR observations of the Hubble Deep Field South

We use a deep K(AB)<25 galaxy sample in the Hubble Deep Field South to trace the evolution of the cosmological stellar mass density from z~ 0.5 to z~3. We find clear evidence for a decrease of the average stellar mass density at high redshift, 2<z<3.2, that is 15^{+25}_{-5}% of the local value, two times higher than what observed in the Hubble Deep Field North. To take into account for the selection effects, we define a homogeneous subsample of galaxies with 10^{10}M_\odot \leq M_* \leq 10^{11}M_\odot: in this sample, the mass density at z>2 is 20^{+20}_{-5} % of the local value. In the mass--limited subsample at z>2, the fraction of passively fading galaxies is at most 25%, although they can contribute up to about 40% of the stellar mass density. On the other hand, star--forming galaxies at z>2 form stars with an average specific rate at least ~4 x10^{-10} yr$^{-1}$, 3 times higher than the z<~1 value. This implies that UV bright star--forming galaxies are substancial contributors to the rise of the stellar mass density with cosmic time. Although these results are globally consistent with $\Lambda$--CDM scenarios, the present rendition of semi analytic models fails to match the stellar mass density produced by more massive galaxies present at z>2.Comment: Accepted for publication on ApJLetter

SDSS IV MaNGA - Rotation Velocity Lags in the Extraplanar Ionized Gas from MaNGA Observations of Edge-on Galaxies

We present a study of the kinematics of the extraplanar ionized gas around several dozen galaxies observed by the Mapping of Nearby Galaxies at the Apache Point Observatory (MaNGA) survey. We considered a sample of 67 edge-on galaxies out of more than 1400 extragalactic targets observed by MaNGA, in which we found 25 galaxies (or 37%) with regular lagging of the rotation curve at large distances from the galactic midplane. We model the observed $H\alpha$ emission velocity fields in the galaxies, taking projection effects and a simple model for the dust extinction into the account. We show that the vertical lag of the rotation curve is necessary in the modeling, and estimate the lag amplitude in the galaxies. We find no correlation between the lag and the star formation rate in the galaxies. At the same time, we report a correlation between the lag and the galactic stellar mass, central stellar velocity dispersion, and axial ratio of the light distribution. These correlations suggest a possible higher ratio of infalling-to-local gas in early-type disk galaxies or a connection between lags and the possible presence of hot gaseous halos, which may be more prevalent in more massive galaxies. These results again demonstrate that observations of extraplanar gas can serve as a potential probe for accretion of gas.Comment: 13 pages, 11 figures, accepted for publication in Ap

On First-Order Generalized Maxwell Equations

The generalized Maxwell equations including an additional scalar field are considered in the first-order formalism. The gauge invariance of the Lagrangian and equations is broken resulting the appearance of a scalar field. We find the canonical and symmetrical Belinfante energy-momentum tensors. It is shown that the traces of the energy-momentum tensors are not equal to zero and the dilatation symmetry is broken in the theory considered. The matrix Hamiltonian form of equations is obtained after the exclusion of the nondynamical components. The canonical quantization is performed and the propagator of the fields is found in the first-order formalism.Comment: 14 pages, corrections in Eq.(38),(39),(59

Measurement of the Bottom-Strange Meson Mixing Phase in the Full CDF Data Set

We report a measurement of the bottom-strange meson mixing phase \beta_s using the time evolution of B0_s -> J/\psi (->\mu+\mu-) \phi (-> K+ K-) decays in which the quark-flavor content of the bottom-strange meson is identified at production. This measurement uses the full data set of proton-antiproton collisions at sqrt(s)= 1.96 TeV collected by the Collider Detector experiment at the Fermilab Tevatron, corresponding to 9.6 fb-1 of integrated luminosity. We report confidence regions in the two-dimensional space of \beta_s and the B0_s decay-width difference \Delta\Gamma_s, and measure \beta_s in [-\pi/2, -1.51] U [-0.06, 0.30] U [1.26, \pi/2] at the 68% confidence level, in agreement with the standard model expectation. Assuming the standard model value of \beta_s, we also determine \Delta\Gamma_s = 0.068 +- 0.026 (stat) +- 0.009 (syst) ps-1 and the mean B0_s lifetime, \tau_s = 1.528 +- 0.019 (stat) +- 0.009 (syst) ps, which are consistent and competitive with determinations by other experiments.Comment: 8 pages, 2 figures, Phys. Rev. Lett 109, 171802 (2012

Tau and Charm physics highlights

In tau physics, we are at the frontier between the completion of the LEP program and the start of analyses from b-factories, which are expected to produce results in the coming years. Nice results from CLEO are steadily delivered in the meantime. For charm, impressive progress have been achieved by fixed target experiments in the search for CP violation and D^0 - \bar D^0 oscillations. First results from b-factories demonstrate the power of these facilities in such areas. The novel measurement of the D* width by CLEO happens to be rather different from current expectations. The absence of a charm factory explains the lack or the very slow progress in the absolute scale determinations for charm decays.Comment: "Typos corrected and references added

The evolution of the galaxy luminosity function in the rest frame blue band up to z=3.5

We present an estimate of the cosmological evolution of the field galaxy luminosity function (LF) in the rest frame 4400 Angstrom B -band up to redshift z=3.5. To this purpose, we use a composite sample of 1541 I--selected galaxies selected down to I_(AB)=27.2 and 138 galaxies selected down to K_(AB)=25 from ground-based and HST multicolor surveys, most notably the new deep JHK images in the Hubble Deep Field South (HDF-S) taken with the ISAAC instrument at the ESO-VLT telescope. About 21% of the sample has spectroscopic redshifts, and the remaining fraction well calibrated photometric redshifts. The resulting blue LF shows little density evolution at the faint end with respect to the local values, while at the bright end (M_B(AB)<-20) a brightening increasing with redshift is apparent with respect to the local LF. Hierarchical CDM models overpredict the number of faint galaxies by about a factor 3 at z=1. At the bright end the predicted LFs are in reasonable agreement only at low and intermediate redshifts (z=1), but fail to reproduce the pronounced brightening observed in the high redshift (z=2-3) LF. This brightening could mark the epoch where a major star formation activity is present in the galaxy evolution.Comment: 14 pages, 2 figures, Astrophysical Journal Letters, in pres