Symplectic Tate homology

For a Liouville domain $W$ satisfying $c_1(W)=0$, we propose in this note two versions of symplectic Tate homology $\underrightarrow{H}\underleftarrow{T}(W)$ and $\underleftarrow{H}\underrightarrow{T}(W)$ which are related by a canonical map $\kappa \colon \underrightarrow{H}\underleftarrow{T}(W) \to \underleftarrow{H}\underrightarrow{T}(W)$. Our geometric approach to Tate homology uses the moduli space of finite energy gradient flow lines of the Rabinowitz action functional for a circle in the complex plane as a classifying space for $S^1$-equivariant Tate homology. For rational coefficients the symplectic Tate homology $\underrightarrow{H}\underleftarrow{T}(W)$ has the fixed point property and is therefore isomorphic to $H(W;\mathbb{Q}) \otimes \mathrm{Q}[u,u^{-1}]$, where $\mathbb{Q}[u,u^{-1}]$ is the ring of Laurent polynomials over the rationals. Using a deep theorem of Goodwillie, we construct examples of Liouville domains where the canonical map $\kappa$ is not surjective and examples where it is not injective.Comment: 40 pages, 4 figures; v2: various improvement

Prospects for measuring |Vts| at the LHC

36th International Conference on High Energy Physics, July 4-11, 2012 Melbourne, AustraliaWe study the prospects of measuring the CKM matrix element |Vts| at the LHC with the top quarks produced in the processes pp → ttX¯ and pp → t/tX¯ , and the subsequent decays t → W+s and t¯ → W−s¯. To reduce the jet activity in top quark decays, we insist on tagging the W± leptonically, W± → ` ±ν` (` = e,µ, τ), and analyse the anticipated jet profiles in the signal process t → W s and the dominant background from the decay t → W b. To that end, we analyse the V0 (K 0 and Λ) distributions in the s- and b-quark jets concentrating on the energy and transverse momentum distributions of these particles. Noting that the V0s emanating from the t → W b branch have displaced decay vertexes from the interaction point due to the weak decays b → c → s, and that the b-quark jets are rich in charged leptons, the information from the secondary vertex distributions and the absence of energetic charged leptons in the jet provide additional (b-jet vs. s-jet) discrimination in top quark decays. These distributions are used to train a boosted decision tree (BDT), a technique used successfully in measuring the CKM matrix element |Vtb| in single top production at the Tevatron. We show that the BDT-response functions corresponding to the signal (t →W s) and background (t →W b) are very different. Detailed simulations undertaken by us with the Monte Carlo generator PYTHIA are used to estimate the background rejection versus signal efficiency for two representative LHC energies √ s = 7 TeV and 14 TeV. We argue that a benchmark with 5% signal (t → W s) efficiency and a background (t → bW ) rejection by a factor 103 (required due to the anticipated value of the ratio |Vts| 2/|Vtb| 2 ' 1.6×10−3 ) can be achieved at the LHC, given the promised luminosit

Low-T/∣W∣T/|W| instabilities in differentially rotating proto-neutron stars with magnetic fields

Recent hydrodynamical simulations have shown that differentially rotating neutron stars formed in core-collapse supernovae may develop global non-axisymmetric instabilities even when $T/|W|$ (the ratio of the rotational kinetic energy $T$ to the gravitational potential energy $|W|$) is relatively small (less than 0.1). Such low-$T/|W|$ instability can give rise to efficient gravitational wave emission from the proto-neutron star. We investigate how this instability is affected by magnetic fields using a cylindrical stellar model. Wave absorption at the corotation resonance plays an important role in facilitating the hydrodynamic low-$T/|W|$ instability. In the presence of a toroidal magnetic field, the corotation resonance is split into two magnetic resonances where wave absorptions take place. We show that the toroidal magnetic field suppresses the low-$T/|W|$ instability when the total magnetic energy $W_{\rm B}$ is of order $0.2\,T$ or larger, corresponding to toroidal fields of a few $\times 10^{16}$ G or stronger. Although poloidal magnetic fields do not influence the instability directly, they can affect the instability by generating toroidal fields through linear winding of the initial poloidal field and magneto-rotational instability. We show that an initial poloidal field with strength as small as $10^{14}$ G may suppress the low-$T/|W|$ instability.Comment: 12 pages, 6 figures; submitted to MNRA

The t W- Mode of Single Top Production

The t W- mode of single top production is proposed as an important means to study the weak interactions of the top quark. While the rate of this mode is most likely too small to be observed at Run II of the Fermilab Tevatron, it is expected to be considerably larger at the CERN LHC. In this article the inclusive t W- rate is computed, including O(1 / log (m_t^2 / m_b^2)) corrections, and when combined with detailed Monte Carlo simulations including the top and W decay products, indicate that the t W- single top process may be extracted from the considerable t tbar and W+ W- j backgrounds at low luminosity runs of the LHC.Comment: 16 pages, 4 figure

Quantitative Robust Uncertainty Principles and Optimally Sparse Decompositions

We develop a robust uncertainty principle for finite signals in C^N which states that for almost all subsets T,W of {0,...,N-1} such that |T|+|W| ~ (log N)^(-1/2) N, there is no sigal f supported on T whose discrete Fourier transform is supported on W. In fact, we can make the above uncertainty principle quantitative in the sense that if f is supported on T, then only a small percentage of the energy (less than half, say) of its Fourier transform is concentrated on W. As an application of this robust uncertainty principle (QRUP), we consider the problem of decomposing a signal into a sparse superposition of spikes and complex sinusoids. We show that if a generic signal f has a decomposition using spike and frequency locations in T and W respectively, and obeying |T| + |W| <= C (\log N)^{-1/2} N, then this is the unique sparsest possible decomposition (all other decompositions have more non-zero terms). In addition, if |T| + |W| <= C (\log N)^{-1} N, then this sparsest decomposition can be found by solving a convex optimization problem.Comment: 25 pages, 9 figure

t \bar{t} W production and decay at NLO

We present results for the production of a top pair in association with a W-boson at next-to-leading order. We have implemented this process into the parton-level integrator MCFM including the decays of both the top quarks and the W-bosons with full spin correlations. Although the cross section for this process is small, it is a Standard Model source of same-sign lepton events that must be accounted for in many new physics searches. For a particular analysis of same-sign lepton events in which b-quarks are also present, we investigate the effect of the NLO corrections as a function of the signal region cuts.Comment: 10 pages, 7 figure

Supersymmetric effects in top quark decay into polarized W-boson

We investigate the one-loop supersymmetric QCD (SUSY-QCD) and electroweak (SUSY-EW) corrections to the top quark decay into a b-quark and a longitudinal or transverse W-boson. The corrections are presented in terms of the longitudinal ratio \Gamma(t-->W_L b)/\Gamma(t--> W b) and the transverse ratio \Gamma(t-->W_- b)/\Gamma(t--> W b). In most of the parameter space, both SUSY-QCD and SUSY-EW corrections to these ratios are found to be less than 1% in magnitude and they tend to have opposite signs. The corrections to the total width \Gamma(t-->W b) are also presented for comparison with the existing results in the literature. We find that our SUSY-EW corrections to the total width differ significantly from previous studies: the previous studies give a large correction of more than 10% in magnitude for a large part of the parameter space while our results reach only few percent at most.Comment: Version in PRD (explanation and refs added