Path Integrals on a Compact Manifold with Non-negative Curvature

A typical path integral on a manifold, $M$ is an informal expression of the form \frac{1}{Z}\int_{\sigma \in H(M)} f(\sigma) e^{-E(\sigma)}\mathcal{D}\sigma, \nonumber where $H(M)$ is a Hilbert manifold of paths with energy $E(\sigma) < \infty$, $f$ is a real valued function on $H(M)$, $\mathcal{D}\sigma$ is a \textquotedblleft Lebesgue measure \textquotedblright and $Z$ is a normalization constant. For a compact Riemannian manifold $M$, we wish to interpret $\mathcal{D}\sigma$ as a Riemannian \textquotedblleft volume form \textquotedblright over $H(M)$, equipped with its natural $G^{1}$ metric. Given an equally spaced partition, ${\mathcal{P}}$ of $[0,1],$ let H_{{\mathcal{P}}%}(M) be the finite dimensional Riemannian submanifold of $H(M)$ consisting of piecewise geodesic paths adapted to $\mathcal{P.}$ Under certain curvature restrictions on $M,$ it is shown that $$\frac{1}{Z_{{\mathcal{P}}}}e^{-{1/2}E(\sigma)}dVol_{H_{{\mathcal{P}}}}(\sigma)\to\rho(\sigma)d\nu(\sigma)\text{as}\mathrm{mesh}({\mathcal{P}})\to0,$$ where $Z_{{\mathcal{P}}}$ is a \textquotedblleft normalization\textquotedblright constant, $E:H(M) \to\lbrack0,\infty)$ is the energy functional, Vol_{H_{{\mathcal{P}}%}} is the Riemannian volume measure on $H_{\mathcal{P}}(M) ,$ $\nu$ is Wiener measure on continuous paths in $M,$ and $\rho$ is a certain density determined by the curvature tensor of $M.

Labor Market Segmentation and Efficient Bargaining in a Macroeconomic Model

Claas O. Labor Market Segmentation and Efficient Bargaining in a Macroeconomic Model. Center for Mathematical Economics Working Papers. Vol 600. Bielefeld: Center for Mathematical Economics; 2018.This paper studies the implications of a segmented labor market with efficient wage– employment bargaining on the internal labor market and a competitive external labor market on the temporary equilibrium of a closed monetary macroeconomy of the AS– AD type with government activity, fiat money, and expectations. Workers have identical preferences, those on the internal labor market are represented by a labor union. There is no mobility between the labor markets. Union power measured by the share of the production surplus allotted to the union and union density measured by the fraction of workers who are union members impact the functional income distribution, but neither affect the individual employment levels nor the aggregate employment level and the aggregate supply function. The wage on the internal labor market is above the wage on the external labor market if and only if the profit share of total revenue is smaller than under a fully competitive labor market. Unique temporary equilibria exist for all combinations of union power and union density. The paper provides a complete comparative-statics analysis showing in particular a negative price effect of union power and a positive price effect of union density. In general, the effects of union power and union density on any equilibrium value are usually of opposite signs. Single-labor-market models with a fully competitive or a fully unionized labor market are special or limiting cases of the segmented-labor-market model

Search for additional heavy neutral Higgs and gauge bosons in the ditau final state produced in 36 fb−1 of pp collisions at √s=13 TeV with the ATLAS detector

A search for heavy neutral Higgs bosons and Z′ bosons is performed using a data sample corresponding to an integrated luminosity of 36.1 fb−1 from proton-proton collisions at √s=13 TeV recorded by the ATLAS detector at the LHC during 2015 and 2016. The heavy resonance is assumed to decay to τ+τ− with at least one tau lepton decaying to final states with hadrons and a neutrino. The search is performed in the mass range of 0.2-2.25 TeV for Higgs bosons and 0.2-4.0 TeV for Z′ bosons. The data are in good agreement with the background predicted by the Standard Model. The results are interpreted in benchmark scenarios. In the context of the hMSSM scenario, the data exclude tan β > 1.0 for mA= 0.25 TeV and tan β > 42 for mA=1.5 TeV at the 95% confidence level. For the Sequential Standard Model, ZSSM′ with mZ′< 2.42 TeV is excluded at 95% confidence level, while Z NU′ with mZ ′ < 2.25 TeV is excluded for the non-universal G(221) model that exhibits enhanced couplings to third-generation fermions

Measurements of long-range azimuthal anisotropies and associated Fourier coefficients for pp collisions at √s=5.02 and 13 TeV and p+Pb collisions at √sNN=5.02 TeV with the ATLAS detector

ATLAS measurements of two-particle correlations are presented for √s=5.02 and 13 TeV ppcollisions and for √sNN=5.02 TeV p+Pb collisions at the LHC. The correlation functions are measured as a function of relative azimuthal angle Δϕ, and pseudorapidity separation Δη, using charged particles detected within the pseudorapidity interval |η|2, is studied using a template fitting procedure to remove a “back-to-back” contribution to the correlation function that primarily arises from hard-scattering processes. In addition to the elliptic, cos (2Δϕ), modulation observed in a previous measurement, the pp correlation functions exhibit significant cos (3Δϕ) and cos (4Δϕ) modulation. The Fourier coefficients vn, n associated with the cos (nΔϕ) modulation of the correlation functions for n=2–4 are measured as a function of charged-particle multiplicity and charged-particle transverse momentum. The Fourier coefficients are observed to be compatible with cos (nϕ) modulation of per-event single-particle azimuthal angle distributions. The single-particle Fourier coefficients vn are measured as a function of charged-particle multiplicity, and charged-particle transverse momentum for n=2–4. The integrated luminosities used in this analysis are, 64nb−1 for the √s=13 TeV pp data, 170 nb−1 for the √ s = 5.02 TeV pp data, and 28 nb−1 for the √sNN = 5.02 TeV p+Pb data

Search for Higgs bosons produced via vector-boson fusion and decaying into bottom quark pairs in √s =13 TeV pp collisions with the ATLAS detector

A search for the bb ¯ decay of the Standard Model Higgs boson produced through vector-boson fusion is presented. Three mutually exclusive channels are considered: two all-hadronic channels and a photon-associated channel. Results are reported from the analysis of up to 30.6 fb −1 of pp data at s √ =13 TeV collected with the ATLAS detector at the LHC. The measured signal strength relative to the Standard Model prediction from the combined analysis is 2.5 +1.4 −1.3 for inclusive Higgs boson production and 3.0 +1.7 −1.6 for vector-boson fusion production only

Measurement of differential cross-sections of a top quark produced in association with a W boson at √s=13 TeV with ATLAS

The differential cross-section for the production of a W boson in association with a top quark is measured for several particle-level observables. The measurements are performed using 36.1fb−1 of pp collision data collected with the ATLAS detector at the LHC in 2015 and 2016. Differential cross-sections are measured in a fiducial phase space defined by the presence of two charged leptons and exactly one jet matched to a b-hadron, and are normalised with the fiducial cross-section. Results are found to be in good agreement with predictions from several Monte Carlo event generators

Search for vector-boson resonances decaying to a top quark and bottom quark in the lepton plus jets final state in pp collisions at √s=13TeV with the ATLAS detector

A search for new charged massive gauge bosons, W_, is performed with the ATLAS detector at the LHC. Data were collected in proton–proton collisions at a center-of-mass energy of √s=13TeVand correspond to an integrated luminosity of 36.1fb−1. This analysis searches for W_bosons in the W_→t¯bdecay channel in final states with an electron or muon plus jets. The search covers resonance masses between 0.5 and 5.0TeVand considers right-handed W_bosons. No significant deviation from the Standard Model (SM) expectation is observed and upper limits are set on the W_→t¯bcross section times branching ratio and the W_boson effective couplings as a function of the W_boson mass. For right-handed W_bosons with coupling to the SM particles equal to the SM weak coupling constant, masses below 3.15TeVare excluded at the 95% confidence level. This search is also combined with a previously published ATLAS result for W_→t¯bin the fully hadronic final state. Using the combined searches, right-handed W_bosons with masses below 3.25TeVare excluded at the 95% confidence level

Search for doubly charged Higgs boson production in multi-lepton final states with the ATLAS detector using proton-proton collisions at √s = 13TeV

A search for doubly charged Higgs bosons with pairs of prompt, isolated, highly energetic leptons with the same electric charge is presented. The search uses a proton–proton collision data sample at a centre-of-mass energy of 13 TeV corresponding to 36.1 fb −1 of integrated luminosity recorded in 2015 and 2016 by the ATLAS detector at the LHC. This analysis focuses on the decays H±±→e±e±, H±±→e±μ± and H±±→μ±μ±, fitting the dilepton mass spectra in several exclusive signal regions. No significant evidence of a signal is observed and corresponding limits on the production cross-section and consequently a lower limit on m(H±±) are derived at 95% confidence level. With ℓ±ℓ±=e±e±/μ±μ±/e±μ±, the observed lower limit on the mass of a doubly charged Higgs boson only coupling to left-handed leptons varies from 770 to 870 GeV (850 GeV expected) for B(H±±→ℓ±ℓ±)=100% and both the expected and observed mass limits are above 450 GeV for B(H±±→ℓ±ℓ±)=10% and any combination of partial branching ratios

Measurement of jet fragmentation in Pb+Pb and pp collisions at √s NN =5.02 TeV with the ATLAS detector

This paper presents a measurement of jet fragmentation functions in 0.49 nb −1 of Pb+Pb collisions and 25 pb −1 of pp collisions at √ sNN =5.02 TeV collected in 2015 with the ATLAS detector at the LHC. These measurements provide insight into the jet quenching process in the quark-gluon plasma created in the aftermath of ultra-relativistic collisions between two nuclei. The modifications to the jet fragmentation functions are quantified by dividing the measurements in Pb+Pb collisions by baseline measurements in pp collisions. This ratio is studied as a function of the transverse momentum of the jet, the jet rapidity, and the centrality of the collision. In both collision systems, the jet fragmentation functions are measured for jets with transverse momentum between 126 GeV and 398 GeV and with an absolute value of jet rapidity less than 2.1. An enhancement of particles carrying a small fraction of the jet momentum is observed, which increases with centrality and with increasing jet transverse momentum. Yields of particles carrying a very large fraction of the jet momentum are also observed to be enhanced. Between these two enhancements of the fragmentation functions a suppression of particles carrying an intermediate fraction of the jet momentum is observed in Pb+Pb collisions. A small dependence of the modifications on jet rapidity is observed

Search for pair production of heavy vector-like quarks decaying into high-pT W bosons and top quarks in the lepton-plus-jets final state in pp collisions at √s = 13 TeV with the ATLAS detector

A search is presented for the pair production of heavy vector-like B quarks, primarily targeting B quark decays into a W boson and a top quark. The search is based on 36.1 fb −1 of pp collisions at √s = 13 TeV recorded in 2015 and 2016 with the ATLAS detector at the CERN Large Hadron Collider. Data are analysed in the lepton-plus-jets final state, characterised by a high-transverse-momentum isolated electron or muon, large missing transverse momentum, and multiple jets, of which at least one is b -tagged. No significant deviation from the Standard Model expectation is observed. The 95% confidence level lower limit on the B mass is 1350 GeV assuming a 100% branching ratio to Wt. In the SU(2) singlet scenario, the lower mass limit is 1170 GeV. This search is also sensitive to a heavy vector-like B quark decaying into other final states (Zb and Hb ) and thus mass limits on B production are set as a function of the decay branching ratios. The 100% branching ratio limits are found to be also applicable to heavy vector-like X production, with charge +5/3, that decay into Wt