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

Spectral multipliers on 22-step groups: topological versus homogeneous dimension

Let $G$ be a $2$-step stratified group of topological dimension $d$ and homogeneous dimension $Q$. Let $L$ be a homogeneous sub-Laplacian on $G$. By a theorem due to Christ and to Mauceri and Meda, an operator of the form $F(L)$ is of weak type $(1,1)$ and bounded on $L^p(G)$ for all $p \in (1,\infty)$ whenever the multiplier $F$ satisfies a scale-invariant smoothness condition of order $s > Q/2$. It is known that, for several $2$-step groups and sub-Laplacians, the threshold $Q/2$ in the smoothness condition is not sharp and in many cases it is possible to push it down to $d/2$. Here we show that, for all $2$-step groups and sub-Laplacians, the sharp threshold is strictly less than $Q/2$, but not less than $d/2$.Comment: 17 page

Ricci flow coupled with harmonic map flow

We investigate a new geometric flow which consists of a coupled system of the Ricci flow on a closed manifold M with the harmonic map flow of a map phi from M to some closed target manifold N with a (possibly time-dependent) positive coupling constant alpha. This system can be interpreted as the gradient flow of an energy functional F_alpha which is a modification of Perelman's energy F for the Ricci flow, including the Dirichlet energy for the map phi. Surprisingly, the coupled system may be less singular than the Ricci flow or the harmonic map flow alone. In particular, we can always rule out energy concentration of phi a-priori - without any assumptions on the curvature of the target manifold N - by choosing alpha large enough. Moreover, if alpha is bounded away from zero it suffices to bound the curvature of (M,g(t)) to also obtain control of phi and all its derivatives - a result which is clearly not true for alpha = 0. Besides these new phenomena, the flow shares many good properties with the Ricci flow. In particular, we can derive the monotonicity of an entropy functional W_alpha similar to Perelman's Ricci flow entropy W and of so-called reduced volume functionals. We then apply these monotonicity results to rule out non-trivial breathers and geometric collapsing at finite times.Comment: 41 pages, shortened and references updated, final version, to appear in Ann. Sci. \'Ec. Norm. Sup\'e

Optimal rigidity estimates for maps of a compact Riemannian manifold to itself

Let $M$ be a smooth, compact, connected, oriented Riemannian manifold, and let $\imath: M \to \mathbb R^d$ be an isometric embedding. We show that a Sobolev map $f: M \to M$ which has the property that the differential $df(q)$ is close to the set $SO(T_q M, T_{f(q)} M)$ of orientation preserving isometries (in an $L^p$ sense) is already $W^{1,p}$ close to a global isometry of $M$. More precisely we prove for $p \in (1,\infty)$ the optimal linear estimate $$\inf_{\phi \in \mathrm{Isom}_+(M)} \| \imath \circ f - \imath \circ \phi\|_{W^{1,p}}^p \le C E_p(f)$$ where $$E_p(f) := \int_M {\rm dist}^p(df(q), SO(T_q M, T_{f(q)} M)) \, d{\rm vol}_M$$ and where $\mathrm{Isom}_+(M)$ denotes the group of orientation preserving isometries of $M$. This extends the Euclidean rigidity estimate of Friesecke-James-M\"uller [Comm. Pure Appl. Math. {\bf 55} (2002), 1461--1506] to Riemannian manifolds. It also extends the Riemannian stability result of Kupferman-Maor-Shachar [Arch. Ration. Mech. Anal. {\bf 231} (2019), 367--408] for sequences of maps with $E_p(f_k) \to 0$ to an optimal quantitative estimate. The proof relies on the weak Riemannian Piola identity of Kupferman-Maor-Shachar, a uniform $C^{1,\alpha}$ approximation through the harmonic map heat flow, and a linearization argument which reduces the estimate to the well-known Riemannian version of Korn's inequality

Measurement of the inclusive production cross sections for forward jets and for dijet events with one forward and one central jet in pp collisions at sqrt(s) = 7 TeV

The inclusive production cross sections for forward jets, as well for jets in dijet events with at least one jet emitted at central and the other at forward pseudorapidities, are measured in the range of transverse momenta pt = 35-150 GeV/c in proton-proton collisions at sqrt(s) = 7 TeV by the CMS experiment at the LHC. Forward jets are measured within pseudorapidities 3.2<|eta|<4.7, and central jets within the |eta|<2.8 range. The double differential cross sections with respect to pt and eta are compared to predictions from three approaches in perturbative quantum chromodynamics: (i) next-to-leading-order calculations obtained with and without matching to parton-shower Monte Carlo simulations, (ii) PYTHIA and HERWIG parton-shower event generators with different tunes of parameters, and (iii) CASCADE and HEJ models, including different non-collinear corrections to standard single-parton radiation. The single-jet inclusive forward jet spectrum is well described by all models, but not all predictions are consistent with the spectra observed for the forward-central dijet events.Comment: Submitted to the Journal of High Energy Physic

Study of W boson production in PbPb and pp collisions at sqrt(s[NN]) = 2.76 TeV

A measurement is presented of W-boson production in PbPb collisions carried out at a nucleon-nucleon (NN) centre-of-mass energy sqrt(s[NN]) of 2.76 TeV at the LHC using the CMS detector. In data corresponding to an integrated luminosity of 7.3 inverse microbarns, the number of W to mu mu-neutrino decays is extracted in the region of muon pseudorapidity abs(eta[mu])<2.1 and transverse momentum pt[mu]>25 GeV. Yields of muons found per unit of pseudorapidity correspond to (159 +/- 10 (stat.) +/- 12 (syst.)) 10E-8 W(plus) and (154 +/- 10 (stat.) +/- 12 (syst.)) 10E-8 W(minus) bosons per minimum-bias PbPb collision. The dependence of W production on the centrality of PbPb collisions is consistent with a scaling of the yield by the number of incoherent NN collisions. The yield of W bosons is also studied in a sample of pp interactions at sqrt(s)= 2.76 TeV corresponding to an integrated luminosity of 231 inverse nanobarns. The individual W(plus) and W(minus) yields in PbPb and pp collisions are found to agree, once the neutron and proton content in Pb nuclei is taken into account. Likewise, the difference observed in the dependence of the positive and negative muon production on pseudorapidity is consistent with next-to-leading order perturbative QCD calculations.Comment: Submitted to Physics Letters

The F-pure threshold of quasi-homogeneous polynomials

Inspired by the work of Bhatt and Singh (see: arXiv:1307.1171) we compute the $F$-pure threshold of quasi-homogeneous polynomials. We first consider the case of a curve given by a quasi-homogeneous polynomial $f$ in three variables $x,y,z$ of degree equal to the degree of $xyz$ and then we proceed with the general case of a Calabi-Yau hypersurface, i.e. a hypersurface given by a quasi-homogeneous polynomial $f$ in $n+1$ variables $x_0, \ldots, x_n$ of degree equal to the degree of $x_0 \cdots x_n$